Patent Application
20240331535
The present disclosure relates generally to optimization-based control, and more particularly to methods and apparatus of hierarchical optimization-based coordinated control of dynamic traffic rules and mixed traffic in a transportation network of multiple interconnected traffic intersections.
Automated transportation systems, even in the case of partial automation, lead to reduced road accidents and more efficient usage of a road network. Therefore, connected and automated vehicles (CAVs) show large promises for improving safety and traffic flow, and as a consequence for reducing congestion, travel time, emissions and energy consumption. While this has been known for decades, most of the successful developments have been accomplished in recent years due to the technological advances in sensing, computing, control and connectivity. While the on-road scenarios often are highly dynamic, i.e., the vehicle participants and their behavior changes rapidly and significantly, vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communication, also known as vehicle-to-everything (V2X) communication for short, enables efficient planning and decision making by providing access to real-time information on all the vehicles in a certain planning area.
Significant progress has been made in planning and control for automated driving, which typically involves a multi-layer guidance and control architecture implemented on-board. At the highest level, an intelligent navigation system finds a route through the transportation network from the current vehicle position to the requested destination. A decision maker selects the appropriate driving behavior at any point of time, given the route plan, the current environment condition, and the behavior of the other traffic participants, e.g., using automata combined with set reachability or formal languages and optimization. Given the target behavior, including lane following, lane changing or stopping, a motion planning algorithm computes a dynamically feasible and safe trajectory that may be tracked in real-time by a low-level feedback controller. A popular approach uses the combination of a sampling-based motion planner and model predictive control (MPC) for reference tracking. For CAVs, the guidance and control architecture may look similar to that for standard automated driving, but some of the modules may be implemented in the infrastructure, e.g., in mobile edge computers (MECs) and provide decisions to multiple vehicles in the area, while other modules may still be implemented on board of each vehicle individually.
Coordination of cooperative agents allows to reach a socially optimal behavior for the transportation network. One example describes a first come, first serve (FCFS) policy for autonomous traffic management at intersections. More recently, coordination strategies for intersection control have been proposed using nonlinear optimization or using mixed-integer linear programming (MILP). The latter has been extended to a distributed MILP algorithm for scheduling a grid of interconnected intersections. In addition, a MILP-based approach for on-ramp merging of CAVs was proposed. Alternative techniques for coordination of CAVs may be found in the references below, where it may be also noted that the intersection and merging control problems are very similar in nature.
For specific areas, for example, such as parking lots and shipping yards, specific urban networks, automated highways, or industrial complexes, the operation of CAVs may be coordinated from a central infrastructure computer, such as an edge-computer or a cloud computer, to achieve optimization of the overall transportation network, such as minimizing the average or worst-case travel time, the overall idling time, etc. Such central coordination system is hereafter referred to as central traffic coordinator (CTC). In some cases, only autonomous driving vehicles may be present on the road, which means that the CTC has direct control of all the vehicles in the network.
However, in most scenarios, it is reasonable to expect that for many years, possibly even indefinitely, autonomous vehicles will share the road with conventional, i.e., human driven vehicles (HDVs). Hence, guaranteeing a proper interaction of automated vehicles with manual vehicles will be of paramount importance to optimize the traffic behavior of the entire transportation network. In these cases, the CTC may only directly control the CAVs, while assuming a specific behavior for the HDVs. In some approaches, the HDVs are always given priority as nothing could change their behavior, and the CAVs would always adjust their operation to the expected behavior of HDVs. However, that solution is inherently suboptimal because only partial control of the vehicles in the scenario is possible.
In other scenarios with only HDVs, the traffic flow of HDVs is controlled through controllable road infrastructure elements, such as traffic lights. The flow of HDVs is affected by the timing and sequencing of the traffic lights so that the overall operation of the transportation network is positively affected. However, in such models, the vehicles are driven by a human driver so that the control impact on the vehicle is only to make it stop at certain locations at specific times. Thus, the control of only traffic lights yields limited control over the transportation network. To address this problem, a central coordination system and method are used to coordinate the operation of the CAVs and controllable infrastructure elements capable of impacting HDV traffic, such as traffic lights, are used to achieve the overall optimization of the transportation network with mixed CAVs and HDVs along with multiple connected traffic intersections. However, the resulting centralized optimization problem is a large-scale mixed-integer programming (MIP) problem that is computationally difficult to solve in real time.
Thus, there is a need to consider hierarchical optimization-based systems and methods that are computationally tractable and coordinate real-time operation of the CAVs and controllable infrastructure elements capable of impacting HDV traffic, such as traffic lights, by solving one or multiple decoupled optimization problems to achieve the overall optimization of the transportation network with mixed CAVs and HDVs and including multiple connected traffic intersections.
Some embodiments are based on realization that a solution for overall optimization of the transportation network with mixed traffic is required, which is computational tractable and of high computational performance than previous solutions as described above.
It is an object of some embodiments to provide a hierarchical optimization-based system and method for the joint coordination and control of dynamic traffic rules and mixed traffic, including connected and automated vehicles (CAVs) and human driven vehicles (HDVs), in a transportation network of multiple connected traffic intersections. In some embodiments of the disclosure, the hierarchical system computes dynamic traffic rules that affect HDVs over a prediction horizon by means of controllable infrastructure elements referred to herein as traffic signs. Examples of the traffic signs include traffic light signals, electronic lane enabling displays, and variable speed limits. In some embodiments of the disclosure, the hierarchical system computes a sequence of velocity targets over a prediction horizon for each of the CAVs in the traffic transportation network, and these target trajectories may be executed by an on-board planning and control architecture for each of the CAVs.
Some embodiments are based on the recognition that both computational tractability and high control performance is achieved for the hierarchical optimization-based system and method, by dividing the problem into a high-level global central traffic controller (CTC), using a simplified macroscopic traffic model, and into a set of low-level locally decoupled intersection traffic controllers (ITCs) based on a more accurate microscopic traffic model. Some embodiments of the disclosure are based on the realization that the global CTC optimization problem is computationally tractable due to the simplified macroscopic traffic model, and each of the local ITC optimization problems is computationally tractable due to a restriction of the decision variables to vehicles in a local neighborhood around one particular traffic intersection in the transportation network. At each control time step, the global CTC controller computes high-level targets for the traffic flow in the multi-intersection network. Based on the global CTC targets, at each control time step, the local ITCs independently compute safe and optimal control trajectories for one or multiple dynamic traffic rules and for one or multiple CAVs within a neighborhood around each of the traffic intersections in the transportation network.
In an embodiment, the hierarchical system is based on a multi-layer guidance and control architecture, in which some modules are implemented on board of each CAV and other modules operate as centralized or decentralized in the infrastructure of the transportation network, e.g., in a mobile edge computer, in order to exploit V2X connectivity. Specifically, in each CAV, given a target behavior representative of actions such as lane following, lane changing or stopping, a motion planning algorithm computes a dynamically feasible and safe trajectory that may be tracked in real-time by a vehicle controller of a corresponding CAV. Some embodiments are based on a probabilistic sampling-based motion planner, and an MPC algorithm for reference tracking, in each CAV.
Some embodiments are based on the realization that, depending on the infrastructure of the transportation network, obtaining a precise prediction for the HDVs may prove challenging. Accordingly, in some embodiments, a hierarchical vehicle coordination and scheduling module is implemented in a receding horizon fashion based on the most recent information. Some embodiments are based on the realization that the CTC controller may compute high-level targets over a medium- or long prediction horizon at a relatively low frequency, while the ITC controllers may compute control trajectories over a short or medium prediction horizon at a relatively higher frequency, for example, using an update period of 0.5-1 second for each of the ITC controllers versus an update period of 1-2 seconds for the global CTC controller. Any discrepancies in the predictions may be adjusted by the intrinsic feedback mechanism of the receding horizon strategy for the coordination system.
Some embodiments are based on the realization that the presence of other traffic participants, e.g., including bicycles and pedestrians, may be managed as obstacles by on-board modules in the multi-layer guidance and control architecture for each CAV, e.g., the motion planning and/or the vehicle control algorithm. Due to their relatively smaller computational cost, compared to that for the hierarchical vehicle coordination system, the motion planning and vehicle control algorithms may be run at a relatively fast sampling rate in order to have a fast reaction time to unexpected changes in the behavior of the other traffic participants, e.g., including bicycles, pedestrians and other vehicles in the transportation network. For example, vehicle control algorithms are often executed with an update period of 50-100 milliseconds.
In some embodiments, the global CTC controller solves a medium or long horizon optimization problem that computes high-level targets for the traffic flow in the multi-intersection network, based on a simplified macroscopic traffic model for the network of connected intersections. In some embodiments, the high-level targets for each of the traffic intersections correspond to a percentage of the traffic intersection's capacity that should be assigned to each of the traffic directions in which vehicles may pass through the traffic intersection. In this case, the high-level targets may be either a time-varying sequence of percentage values or a constant set of average percentage values over the prediction horizon. These high-level targets may be used to prioritize traffic flow in particular directions through the one or multiple connected traffic intersections, in order to reduce the overall congestion, travel time, emissions and energy consumption for vehicles in the transportation network.
In some embodiments, the simplified macroscopic traffic model may be based on a representation of the transportation network as a directed graph, for example, in which each road segment is represented as a node and each traffic direction is represented as an edge in the directed graph. The state for the macroscopic traffic model may include the number of vehicles that are planning to drive straight, turn left or turn right in each of the road segments represented as nodes in the directed graph. The inputs for the macroscopic traffic model may include the number of vehicles that are transitioning from one road segment to a next, given the directed graph, given the maximum capacity of each traffic intersection, and given time delay constraints that enforce the expected travel time of vehicles in each of the road segments. In other embodiments, the simplified macroscopic traffic model may be based on a cell transmission model (CTM).
In some embodiments, the optimization problem of the global CTC controller is a convex optimization problem for which a globally optimal solution may be computed at each time step of the global CTC controller. For example, the CTC controller may use a linear traffic flow model, linear inequality constraints and a linear objective function, resulting in a convex linear programming (LP) problem that may be solved using an LP optimization algorithm, e.g., a simplex method, active-set method or interior point method. In some embodiments, the optimization problem of the global CTC controller is a non-convex smooth nonlinear programming (NLP) or a mixed-integer programming (MIP) optimization problem for which a locally optimal or suboptimal solution may be computed at each time step of the global CTC controller.
In some embodiments, each of the ITC controllers solves a short or medium horizon optimization problem that computes a sequence of velocity targets and lane change commands for each of the CAVs, and a sequence of commands for one or multiple dynamic traffic rules, e.g., traffic light signals, within a neighborhood of the traffic intersection. The resulting optimization problem is an MIP, e.g., a mixed-integer linear programming (MILP) or mixed-integer quadratic programming (MIQP) problem. Some embodiments of the disclosure are based on the realization that each of the ITC controller solves an MIP based on a microscopic traffic model that includes the prediction and control for each of the vehicles and dynamic traffic rules within the transportation network.
In an example, the microscopic traffic model includes a prediction for the motion of each of the CAVs based on a controlled discrete-time system subject to constraints. The constraints include the physical limitation of the CAVs in terms of acceleration, velocity, lane changing and steering, obstacle avoidance constraints and traffic rules that the CAVs need to satisfy. The traffic rules may be represented as mixed-logical inequality constraints in the MIP. For example, these traffic rules may enforce that a CAV may enter a traffic intersection in a particular direction only if the corresponding traffic light signal is green at that time step. The MIP objective involves the maximization of traffic throughput, while minimizing a combination of waiting time and fuel consumption.
In some embodiments, the microscopic traffic model includes a prediction for the behavior of HDVs using a switched dynamical system to represent reactions of HDVs to the, possibly changing, traffic rules. In an example, state-dependent switched dynamics may include: (1) HDV stops at a traffic light of a particular intersection, if the traffic light for the HDV's desired traffic direction is red and the HDV is within a predetermined distance from a stopping zone of the intersection. (2) Otherwise, HDV follows a leading vehicle and maintains a safe following distance, if the leading vehicle is within a particular predetermined distance in front of the HDV in the transportation network. (3) Otherwise, HDV travels at a desired target speed in the network.
In some embodiments, HDV modeling may be used to model both HDVs and CAVs that are controlled by a different ITC. To that end, each CAV may be assigned to a particular ITC for either control or for prediction only. This technique is used to increase safety of the traffic controller, especially when vehicles transition from one ITC to the next. In some embodiments, assignment of vehicles to each of the ITC controllers may be performed, but not limited to, the given steps: (1) Each HDV is assigned to their next traffic intersection's ITC for prediction, if it is within a predetermined distance.
In some embodiments of the disclosure, each ITC computes CAV velocities and lane change trajectories as well as the traffic light phase switching trajectories for its particular traffic intersection, and the computations for each ITC may be executed in parallel on separate computing units.
Some embodiments are based on the realization that the optimization problems for the CTC controller and the ITC controllers may be solved exactly or inexactly. Exact solutions are feasible and locally or globally optimal, while inexact solutions may be approximately feasible or suboptimal. Examples of exact optimization algorithms may include, but are not limited to, interior point methods, active-set methods, gradient methods, operator splitting methods, sequential quadratic programming, sequential convex programming, branch-and-bound, branch-and-cut, and branch-and-price methods. Examples of inexact optimization algorithms may include, but are not limited to, heuristic rules, early termination of exact optimization algorithms, rounding methods, machine learning-based approximations of optimal solutions, or approximate dynamic programming.
In some embodiments, one or both of CTC and ITC control policies may be approximated by a deep neural network architecture. In an example, but not limited to, reinforcement learning may be used to directly maximize a reward function for reducing congestion, travel time, emissions and energy consumption in the transportation network. In other embodiments, one or both of the CTC and the ITC control policies may be implemented using the deep neural network architecture, based on imitation learning that aims to approximate expert solutions of the corresponding optimization problems using exact optimization algorithms.
Accordingly, some embodiments disclose a traffic control system for jointly controlling one or multiple connected and automated vehicles (CAVs) and one or multiple human-driven vehicles (HDVs) moving across multiple intersections of roads subject to integer constraints for crossing each of the multiple intersections. The traffic control system comprises least one processor and a memory having instructions stored thereon that, when executed by the at least one processor, cause the traffic control system to collect digital representation of states of each of the CAVs, each of the HDVs, and each of traffic signs regulating traffic on the roads. The at least one processor further causes the traffic control system to solve an optimization problem jointly optimizing traffic flows based on a macroscopic traffic flow model in a centralized traffic controller (CTC) for the multiple intersections using convex optimization subject to convex relaxation of the integer constraints for crossing each of the multiple intersections. The at least one processor further causes the traffic control system to solve, individually for each of the multiple intersections, a multi-variable mixed-integer programming (MIP) problem in each of multiple intersection traffic controllers (ITCs) optimizing a cost function, and minimizing tracking errors in traffic flow values of a microscopic traffic flow model with respect to relaxed traffic flow values from the CTC, subject to the integer constraints to produce values of control commands changing states of each of the CAVs associated with an intersection of the multiple intersections and values of control commands changing states of each of the traffic signs associated with the intersection, wherein the cost function is optimized subject to a motion model of a CAV associated with the intersection described by a differential equation relating a control command to the CAV with a change of a state of the CAV, and subject to a motion model of an HDV described by a switch function relating a dynamic traffic rule for the HDV with a state of the HDV and a state of a corresponding traffic sign. The at least one processor further causes the traffic control system to transmit the optimized values of the control commands to the corresponding CAVs and corresponding traffic signs.
According to another embodiment, a method is disclosed for jointly controlling one or multiple connected and automated vehicles (CAVs) and one or multiple human-driven vehicles (HDVs) moving across multiple intersections of roads subject to integer constraints for crossing each of the multiple intersections. The method comprises collecting digital representation of states of each of the CAVs, each of the HDVs, and each of traffic signs regulating traffic on the roads. The method further comprises solving an optimization problem jointly optimizing traffic flows based on a macroscopic traffic flow model in a centralized traffic controller (CTC) for the multiple intersections using convex optimization subject to convex relaxation of the integer constraints for crossing each of the multiple intersections. The method further comprises solving, individually for each of the multiple intersections, a multi-variable mixed-integer programming (MIP) problem in each of multiple intersection traffic controllers (ITCs) optimizing a cost function, and minimizing tracking errors in traffic flow values of a microscopic traffic flow model with respect to relaxed traffic flow values from the CTC, subject to the integer constraints to produce values of control commands changing states of each of the CAVs associated with an intersection of the multiple intersections and values of control commands changing states of each of the traffic signs associated with the intersection, wherein the cost function is optimized subject to a motion model of a CAV associated with the intersection described by a differential equation relating a control command to the CAV with a change of a state of the CAV, and subject to a motion model of an HDV described by a switch function relating a dynamic traffic rule for the HDV with a state of the HDV and a state of a corresponding traffic sign. The method further comprises transmitting the optimized values of the control commands to the corresponding CAVs and corresponding traffic signs.
Accordingly, yet another embodiment discloses a non-transitory computer-readable storage medium embodied thereon a program executable by a processor for performing a method for jointly controlling one or multiple connected and automated vehicles (CAVs) and one or multiple human-driven vehicles (HDVs) moving across multiple intersections of roads subject to integer constraints for crossing each of the multiple intersections. The method comprises collecting digital representation of states of each of the CAVs, each of the HDVs, and each of traffic signs regulating traffic on the roads. The method further comprises solving an optimization problem jointly optimizing traffic flows based on a macroscopic traffic flow model in a centralized traffic controller (CTC) for the multiple intersections using convex optimization subject to convex relaxation of the integer constraints for crossing each of the multiple intersections. The method further comprises solving, individually for each of the multiple intersections, a multi-variable mixed-integer programming (MIP) problem in each of multiple intersection traffic controllers (ITCs) optimizing a cost function, and minimizing tracking errors in traffic flow values of a microscopic traffic flow model with respect to relaxed traffic flow values from the CTC, subject to the integer constraints to produce values of control commands changing states of each of the CAVs associated with an intersection of the multiple intersections and values of control commands changing states of each of the traffic signs associated with the intersection, wherein the cost function is optimized subject to a motion model of a CAV associated with the intersection described by a differential equation relating a control command to the CAV with a change of a state of the CAV, and subject to a motion model of an HDV described by a switch function relating a dynamic traffic rule for the HDV with a state of the HDV and a state of a corresponding traffic sign. The method further comprises transmitting the optimized values of the control commands to the corresponding CAVs and corresponding traffic signs.
The presently disclosed embodiments will be further explained with reference to the attached drawings. The drawings shown are not necessarily to scale, with emphasis instead generally being placed upon illustrating the principles of the presently disclosed embodiments.
Some embodiments of the present disclosure provide a system and a method for controlling one or multiple connected and automated vehicles (CAVs) within a transportation network that consists of one or multiple interconnected traffic intersections and that includes a dynamic environment. The dynamic environment includes, but not limited to, one or multiple human-driven vehicles, traffic participants or dynamic obstacles.
As used in this specification and claims, the terms “for example,” “for instance,” and “such as,” and the verbs “comprising,” “having,” “including,” and their other verb forms, when used in conjunction with a listing of one or more components or other items, are each to be construed as open ended, meaning that that the listing is not to be considered as excluding other, additional components or items. The term “based on” means at least partially based on. Further, it is to be understood that the phraseology and terminology employed herein are for the purpose of the description and should not be regarded as limiting. Any heading utilized within this description is for convenience only and has no legal or limiting effect.
The hierarchical traffic control system 102 may include suitable logic, circuitry, code, and/or interfaces that may be configured to generate control commands changing states of controlled vehicles and control commands changing states of traffic signs or traffic lights associated with multiple intersections in the transportation network 104. The hierarchical traffic control system 102 transmits the generated control commands to the controlled vehicles and the traffic signs or traffic lights. Examples of the hierarchical traffic control system 102 may include, but are not limited to, a server, a computer work-station, a mainframe machine, and/or a laptop.
The transportation network 104 may include controlled vehicles 110, human driven vehicles 112, traffic controllers 114, and sensors 116. In
The communication network 106 may include a communication medium through which the hierarchical traffic control system 102 may communicate with the transportation network 104 and other devices which are omitted from disclosure for the sake of brevity. The communication network 106 may be one of a wired connection or a wireless connection. Examples of the communication network 106 may include, but are not limited to, the Internet, a cloud network, a Wireless Fidelity (Wi-Fi) network, a Personal Area Network (PAN), a Local Area Network (LAN), or a Metropolitan Area Network (MAN). Various devices in the network environment 100 may be configured to connect to the communication network 106 in accordance with various wired and wireless communication protocols. Examples of such wired and wireless communication protocols may include, but are not limited to, at least one of a Transmission Control Protocol and Internet Protocol (TCP/IP), User Datagram Protocol (UDP), Hypertext Transfer Protocol (HTTP), File Transfer Protocol (FTP), Zig Bee, EDGE, IEEE 802.11, light fidelity (Li-Fi), 802.16, IEEE 802.11s, IEEE 802.11g, multi-hop communication, wireless access point (AP), device to device communication, cellular communication protocols, and Bluetooth (BT) communication protocols.
The database 108 may include suitable logic, circuitry, and/or interfaces that may be configured to store a traffic model for the transportation network 104. In another embodiment, the database 108 may store program instructions to be executed by the hierarchical traffic control system 102. The traffic model may include a microscopic traffic model or a macroscopic traffic model. Example implementations of the database 108 may include, but are not limited to, Random Access Memory (RAM), Read Only Memory (ROM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Hard Disk Drive (HDD), a Solid-State Drive (SSD), a CPU cache, and/or a Secure Digital (SD) card.
At 200-1, digital representation of states of each of the CAVs, each of the HDVs, and each of traffic signs or traffic lights regulating traffic on the roads is collected. Details of the collection of the states of each of the CAVs, each of the HDVs, and each of traffic signs are describes, for example, with reference to
At 200-2, an optimization problem for jointly optimizing traffic flows is solved based on a macroscopic traffic flow model in a centralized traffic controller (CTC) for the multiple intersections using convex optimization subject to convex relaxation of the integer constraints for crossing each of the multiple intersections. In an embodiment, optimizing traffic flows include optimizing traffic flow values by convex relaxation of the integer constraints for crossing each of the multiple intersections. The optimization of the traffic flow values results in relaxed traffic flow values. Integer constraints are carefully designed and incorporated into the optimization problem, for example, to avoid collisions while crossings an intersection. Integer constraints restrict some or all the variables in the optimization problem to take on only integer values. This enables accurate modeling of the optimization problem involving discrete quantities such as the discrete representation of the states of each of the CAVs, each of the HDVs, and each of traffic signs or traffic lights regulating traffic on the roads. The convex optimization of the integer constraints is a problem where all of the constraints are convex functions, and the objective is a convex function if minimizing, or a concave function if maximizing. In general, relaxation denotes a technique of simply dropping certain constraints from the optimization problem. Specifically, convex relaxation means that upon relaxation or upon dropping certain constraints, the problem becomes convex. In an embodiment, the convex relaxation of the integer constraints that enforce multiple traffic rules includes the convex relaxation of the integer constraints for vehicles crossing each of the intersections and for the switching behavior of the traffic lights. To this end, the traffic flow values are relaxed using the convex relaxation, which includes dropping certain constraints, to result in relaxed traffic flow values that make the optimization problem convex.
At 200-3, a multi-variable mixed-integer programming (MIP) problem is solved in each of multiple intersection traffic controllers (ITCs) to produce values of control commands changing states of each of the CAVs associated with an intersection of the multiple intersections and values of control commands changing states of each of the traffic signs associated with the intersection. The multi-variable MIP problem optimizes a cost function and minimizes tracking errors in traffic flow values of a microscopic traffic flow model with respect to the relaxed traffic flow values from the CTC, subject to the integer constraints to produce the values of the control commands changing the states of each of the CAVs associated with the intersection and the values of the control commands changing the states of each of the traffic signs associated with the intersection. In an embodiment, the cost function is optimized subject to a motion model of a CAV associated with the intersection described by a differential equation relating a control command to the CAV with a change of a state of the CAV, and subject to a motion model of an HDV described by a switch function relating a dynamic traffic rule for the HDV with a state of the HDV and a state of a corresponding traffic sign.
At 200-4, the optimized values of the control commands are transmitted to the corresponding CAVs and corresponding traffic signs or traffic lights.
Although the flowchart 200 is illustrated as discrete operations, such as 200-1, 200-2, 200-3, and 200-4, the disclosure is not so limited. Accordingly, in certain embodiments, such discrete operations may be further divided into additional operations, combined into fewer operations, or eliminated, depending on the particular implementation without detracting from the essence of the disclosed embodiments.
The example of the traffic scenario
The transportation network may include one or more conflict zones and one or more conflict-free zones. The multiple interconnected traffic intersections 101 and 103 are examples of the one or multiple conflict zones or merging points in the transportation network. The multiple interconnected traffic intersections 101 and 103 may connect multiple lanes or the road segments 105, 107, 109, 111, 113, 114, 116. Examples of the one or more conflict-free zones are the road segments 105, 107, 109, 111, 113, 114, 116, consisting of one or multiple lanes that allow either a single direction or multiple directions of traffic.
In an embodiment, each of the vehicles 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146 in the transportation network may be either an autonomous, semi-autonomous or manually operated vehicle. In an example, the autonomous and semi-autonomous vehicles are connected and automated vehicles (CAVs). Alternatively, the autonomous and semi-autonomous vehicles may be referred as controlled vehicles. In an example, the manually operated vehicles or other traffic participants may be an examples of human-driven vehicles (HDVs). In another example, the vehicles 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146 include two-wheeler vehicles, such as motor bikes, four-wheeler vehicles, such as cars, or more than four-wheel vehicles, such as trucks.
In an embodiment, the vehicles 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146 follow general traffic rules. In an example, the general traffic rules include, but are not limited to, rules of crossing intersections, avoiding collision with neighbor vehicles, occupying an open lane, or satisfying lane speed limits. In an embodiment, the general traffic rules may include dynamic traffic rules that dynamically change upon receiving corresponding control commands. In an example, the general traffic rules include constraints for crossing through an intersection of the multiple intersections based on a collision-free state of a corresponding traffic sign, capacity limit constraints for each of the multiple intersections or each of road segments in the transportation network, collision avoidance constraints between pairs of vehicles, lane change constraints for overtaking of vehicles, speed limit constraints, and traffic sign timing constraints. Examples of the dynamic traffic rules include traffic signs such as traffic lights, which can receive control commands to change their timing to let more or fewer vehicle pass through in a certain crossing direction, variable speed limits, that can receive control commands to change the maximum speed of vehicles in certain lanes, and dynamically enabled lanes, which can receive control commands to open or block access to the lane, and the like. The dynamic traffic rules may be displayed on digital displays on the road segments 105, 107, 109, 111, 113, 114, 116 to inform the vehicles 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146 of state of the dynamic traffic rules. For example, the traffic light display 150 may be configured to display a state of the traffic light for the multiple interconnected traffic intersection 101, a lane speed display configured to display a lane speed limit. In an example, the lane access status display 151 may be configured to display a status indicating whether access to a lane 153 of the transportation network is enabled or disabled.
The one or more RSUs 122, 124 may be used for infrastructure-based real-time sensing of the state of the vehicles 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146 and other traffic participants in a local area around each of the RSUs 122, 124. In an embodiment, the traffic scenario
In an embodiment, a multi-hop communication is established among different vehicles, for example, the vehicles 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146 in the transportation network. A communication between the cloud network 118 and a vehicle, such as the vehicle 126 on the road segment 105, needs to propagate through the RSU 122 or the RSU 124 and the core network 120. In some embodiments, safe mobility of the vehicles 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146 is controlled by a hierarchical optimization-based traffic control system using a cloud-based or edge-based network. In an example, the cloud network 118 and core network 120 may be used to implement the hierarchical optimization-based traffic control system. In another embodiment, the hierarchical optimization-based traffic control system is implemented using one or multiple mobile edge computers (MECs). As an example of implementation, but not limited to, the MECs may be embedded as part of the one or more RSUs 122, 124 or they may be separate devices that are connected to one or more network elements such as the RSUs 122, 124, the cloud network 118 and core network 120. Embodiments of the present disclosure include the solution of one or multiple constrained optimization problems at each sampling time step for coordinated control of the dynamic rules, the traffic lights, and the vehicles in the transportation network, for which the computations can be executed either in the cloud network 118 or in the one or multiple MECs.
In some embodiments, the traffic scenario 300 in
In other embodiments, the traffic scenario 300 in
In the transportation network of the traffic scenario 300 in
Some embodiments are based on the realization that different communication technologies may be utilized to support vehicular communications. For example, IEEE Dedicated Short-Range Communications/Wireless Access in Vehicular Environments (DSRC/WAVE) standard family for vehicular networks, 3GPP Cellular-Vehicle-to-Anything (C-V2X), and the like. However, due to high cost reasons, it is impractical for vehicles, for example the vehicles 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, to support more than one short-range communication technologies which leads to compatibility issues among the vehicles to communicate with each other. Therefore, the vehicles equipped with the IEEE DSRC/WAVE cannot communicate with other vehicles equipped with the 3GPP C-V2X, and vice versa. Consequently, the accuracy of real-time control decisions by the on-board, multi-layer guidance and control architecture in each individual vehicle would be severely affected because the real-time decisions would be based on incomplete information of the traffic scenario
Some embodiments of the present disclosure are based on the realization that edge infrastructure devices, for example the RSU 122 and the RSU 124, have advantages for controlling multi-vehicle traffic over usage of only the cloud network or only the on-board device including the multi-layer guidance and control architecture. For example, the edge infrastructure devices may be installed at intersections or merging points, such as the multiple interconnected traffic intersections 101, 103, and they could directly communicate with the vehicles approaching the intersection or merging point. In addition, the edge infrastructure devices may be equipped with multiple communication technologies to be able to communicate with all the connected vehicles. In an embodiment, the edge infrastructure devices may be stationary, which enable them in providing reliable communication with vehicles as well as in collecting relatively high-quality environmental data.
The edge infrastructure devices are capable of continuously monitoring multi-vehicle traffic and the environment for accurate decision making. In an example, the edge infrastructure devices use sensors, but not limited to, distance range finders, radars, lidars, or cameras to accurately detect the state of the vehicles and the dynamic environment, including both connected and non-connected vehicles, autonomous, semi-autonomous and manually operated vehicles and other traffic participants such as bicycles and pedestrians. In another example, the edge infrastructure devices may use sensor fusion technologies in order to accurately detect the state of the vehicles and the dynamic environment. Accordingly, the edge infrastructure devices are appropriate to use for coordinated control of dynamic traffic rules and mixed traffic, within the transportation network of the multiple interconnected traffic intersections.
In an embodiment, the CAVs may be controlled continuously at any point in time and space from the edge infrastructure devices, to achieve optimization of the transportation network, such as minimizing an average or worst-case travel time, an overall idling time, and the like. In contrast, the HDVs are non-controlled vehicles. In other words, it is impossible or at least impractical to control motion of the HDVs at each point in time and space. In different traffic scenarios with only HDVs, the motion of the HDVs is controlled through the traffic signs. For example, a flow of the HDVs is affected by timing and sequencing of the traffic lights so that an overall operation of the transportation network is positively affected. As such, the motion of the HDVs is controlled indirectly by controlling the traffic signs. However, since the HDVs are driven by human drivers and are controlled indirectly based on the traffic signs, the control of the HDVs is possible only at specific locations, which yields limited control over the transportation network.
Some embodiments are based on the recognition that it can be beneficial to jointly control the CAVs and the HDVs to optimize overall benefits for the CAVs and the HDVs such as minimizing the average or worst-case travel time, the overall idling time, and the like. To that end, it is an object of some embodiments to provide a traffic control system for jointly controlling the CAVs and HDVs. In some embodiments, the traffic control system is implemented using the one or multiple MECs, which may be either embedded as part of the one or more RSUs 122, 124 or they can be separate devices that are connected to the one or more RSUs 122, 124, the cloud network 118 or core network 120.
In an illustrative example traffic scenario 400A in
Additionally, the traffic control system also controls the CTRs lights or signs. For instance, it may reduce green light duration of CTR traffic lights 211, 213, 215 in the east-west direction, and hence increase the green light duration in the north south direction, so that the more congested north-south direction is allowed to flow more so that the traffic congestion should reduce. However, the traffic control system may enable the green light to be turned on in 211, 213, 215, exactly when specific vehicles such as the vehicle 219 is able to pass through, as opposed to in a way related to average traffic. This allows to enable green lights when needed according to the specific vehicle objectives. For instance, the CTR light or sign 211 may be green in East-west direction, but it may be turned red when both HDV 221 the vehicle 219 are approaching the intersection 201, so that HDV 221 stops to let the vehicle 219 pass.
However, it may be noted that each of the sequence of roads and turns 275a, 275b, 275c, 275d, 275e, 276f, 275g, 275h by itself does not yet specify a motion plan or a path for the vehicle 223. There are a number of discrete decisions to take such as in what lane the vehicle is to drive, if the vehicle should change lane or stay in a current lane, if the vehicle should start decelerating to stop at the stop line or not, if the vehicle is allowed to cross the intersection, and likewise. Furthermore, there are a number of continuous decisions to make, such as timed sequence of positions and orientations that the vehicle should achieve during the predicted travel from its initial position to its destination. Furthermore, it is also necessary to decide behavior of the CTRs which affect operation of both CAVs and HDVs. According to some embodiments, a motion plan, which includes a sequence of one or multiple of the aforementioned discrete and/or continuous decisions along the route from the current position to the desired destination, may be computed by the traffic control system for one or multiple CAVs, for example, the vehicles 223, 225, 227 and 229 and for one or multiple CTRs, e.g., 263, 265, 267, and 269.
In some embodiments, the mapping and navigation system 304 computes real-time routing information for each of the CAVs 306 from a current position to a desired destination or a desired sequence of destinations for each of the CAVs 306. In an example, the mapping and navigation system 304 may be implemented as a centralized system. In another example, the mapping and navigation system 304 may be decentralized by being embedded as part of the CAVs 306. The routing information for each of the CAVs is communicated from the mapping and navigation system 304 to the hierarchical traffic control system 302 and to each of the CAVs 306. Similarly, the mapping and navigation system 304 may receive information either from the hierarchical traffic control system 302 or from each of the CAVs 306.
In some embodiments, the hierarchical traffic control system 302 computes a sequence of future traffic light commands for each of the TLCs 312 and a coarse motion plan for each of the CAVs 306 in the transportation network along its route from the current position of the CAV to the desired destination or sequence of desired destinations of the CAV. This motion plan is then communicated from the hierarchical traffic control system 302 to each of the CAVs 306. In another example, the motion plan may be communicated from the hierarchical traffic control system 302 to each of the CAVs 306 indirectly via communication with the one or multiple MECs 301 that provide up to date information from the hierarchical traffic control system to the CAVs 306. Similarly, the sequence of traffic light commands is communicated from the hierarchical traffic control system to each of the TLCs directly 312, or instead indirectly via communication with one or multiple MECs 314 that provide up to date information from the hierarchical traffic control system 302 to the TLCs 312.
In an embodiment, the real time information may be communicated directly to the hierarchical traffic control system 302 from the CAVs 306, HDVs 308, RSUs 310, and TLCs 312. In another embodiment, the real time information may be communicated indirectly via communication interface 301 from the MECs 314. In some embodiments, the MECs 314 may collect real-time information about the state of traffic participants and of the dynamic environment in a local area of the transportation network, by communicating with CAVs 306, HDVs 308, RSUs 310, and TLCs 312 that are currently present in a local area of the transportation network. In some embodiments, the RSUs 310 use additional sensors, for example, distance range finders, radars, lidars, or cameras to accurately detect the state of the vehicles and the dynamic environment, including the CAVs 306, HDVs 308, and other traffic participants such as bicycles or pedestrians. In another embodiment, sensor fusion technology may also be used to accurately detect the state of the vehicles and the dynamic environment.
Some embodiments are based on the realization that the number of MECs 314, CAVs 306, HDVs 308, RSUs 310, and TLCs 312 may vary at each sampling time step for the hierarchical traffic control system 302. Most importantly, the number of vehicles may vary significantly as traffic participants enter and exit the transportation network in which the hierarchical traffic control system 302 operates.
In an embodiment, the CTC 404 performs one more computation. The computations in the CTC 404 include the solution of a convex optimization problem subject to a macroscopic traffic flow model for the entire transportation network of multiple interconnected intersections and subject to a convex relaxation of mixed-integer constraints that enforce each of the multiple traffic rules. In an example, the convex relaxation of the mixed-integer constraints that enforce each of the multiple traffic rules may include, but are not limited to, a convex relaxation of mixed-integer constraints for vehicles crossing each of the intersections or for the switching behavior of the traffic lights. In an embodiment, the macroscopic traffic flow model defines a high-level approximate representation of the traffic flow in the transportation network, where modeling of the behavior for individual vehicles is omitted and instead the general behavior of vehicles at the level of the transportation network is modeled using traffic flow values, density values and mean speed values of traffic streams. Some embodiments are based on the realization that the use of the macroscopic traffic flow model in combination with the convex relaxation of multiple mixed-integer traffic constraints allows the efficient computation of a high-level traffic flow plan for the entire transportation network of multiple interconnected intersections by the CTC 404. The operations performed for the efficient computation of a high-level traffic flow plan for the entire transportation network are explained in detail with reference to
In some embodiments of the disclosure, computations in each of the ITCs 408, 410 include the solution of a mixed-integer programming (MIP) problem subject to a microscopic traffic flow model for a local area around one or multiple intersections within the transportation network and subject to mixed-integer constraints that enforce each of the multiple traffic rules within the network. In an example, the mixed-integer constraints that enforce each of the multiple traffic rules within the network includes mixed-integer constraints for vehicles crossing each of the intersections, collision avoidance constraints, mixed-integer constraints for the switching behavior of the traffic lights. In an embodiment, the microscopic traffic flow model is a detailed representation of the traffic flow in the transportation network that includes modeling the behavior of each individual vehicle, using a motion model to control and predict the behavior of CAVs and a switched dynamical model to predict the behavior of HDVs and to predict their reactions to the CAVs and to the changing traffic lights. Some embodiments of the disclosure are based on the realization that the use of a microscopic traffic flow model in a restricted local area around one or multiple intersections within the transportation network, for each of the ITCs 408, 410, allows the efficient computation of a low-level motion plan and a sequence of future control commands for each CAV in the groups of CAVs 412, 416 and each TLC in the groups of TLCs 414, 418, by minimizing the average travel time, wait time, and fuel consumption for all vehicles in the local area of the transportation network that is assigned to the ITC 408, 410.
In an embodiment, one particular ITC may be assigned to a set of CAVs and a set of TLCs which are inside a local area around one particular traffic intersection and having that particular ITC within the transportation network of multiple interconnected intersections. In an example, the group of CAVs 412 and the group of TLCs 414 are assigned to the ITC 408 if the group of CAVs 412 and the group of TLCs 414 are inside the local area around the traffic intersection belonging to the ITC 408. Similarly, the group of CAVs 416 and the group of TLCs 418 are assigned to the ITC 410 if the group of CAVs 416 and the group of TLCs 418 are inside the local area around the traffic intersection belonging to the ITC 410. This results in a total number of ITCs that is equal to the number of traffic intersections in the network. In other embodiments, each ITC may be assigned to a local area around a group of multiple traffic intersections within the transportation network. For example, in some embodiments of the disclosure, traffic intersections within the transportation network may be divided into disjoint subsets of traffic intersections, and the CAVs and TLCs in each of these subsets can be controlled by one ITC. This results in a total number of ITCs that is less than the number of traffic intersections.
In some embodiments, both the computations in the CTC 404 and the computations in each of the ITCs 408, 410 are performed in real time in order to account for the dynamically changing traffic situation in the transportation network. In an example, the sampling period for the CTC 404 may be the same or different from the sampling period for each of the ITCs 408, 410. For example, in some embodiments, the sampling period for both the CTC 404 and for each of the ITCs 408, 410 may be set equal to 1 second, which means that the CTC 404 computes a new traffic flow plan every second and each of the ITCs 408, 410 individually computes new control commands for their respective CAVs and TLCs every second. In some embodiments of the disclosure, the sampling period for the CTC 404 can be longer than the sampling period for each of the ITCs 408, 410. For example, in some embodiments, the sampling period for the CTC 404 may be in a range of 1-2 seconds and the sampling period for each of the ITCs 408, 410 may be in a range of 0.5-1 seconds.
In an embodiment, the CTC 404 predicts, in the macroscopic traffic model, a number of external vehicles entering the transportation network from each of in-flow directions at each time step in a prediction time window, based on historical data that is collected for a similar transportation network during a time period in the past similar to the prediction time window. In another embodiment, the CTC 404 computes at least one of values for each pair of the road segment and a traffic flow maneuver in the transportation network for the prediction time window based on historical data that is collected for a similar transportation network during a time period in the past similar to the prediction time window.
In some embodiments, the convex optimization problem in the CTC 404 is a convex linear programming (LP), including a linear objective, linear equality constraints and linear inequality constraints, or a convex quadratic programming (QP) problem, including a linear-quadratic objective, linear equality constraints and linear inequality constraints. Examples of optimization algorithms to efficiently solve the convex LPs or convex QPs may include, but are not limited to, active-set methods, interior point methods, projected gradient methods, operator splitting methods, or the alternating direction method of multipliers (ADMM).
In some embodiments, the MIP problem in each of the ITCs is a mixed-integer linear programming (MILP) or a mixed-integer quadratic programming (MIQP) problem. Some embodiments of the disclosure are based on the realization that the MILPs or MIQPs may be solved efficiently if they are formulated as mixed-integer convex programming (MICP) problems. In other words, the MILPs or MIQPs may be solved efficiently if the optimization problem becomes convex when relaxing each of the integer feasibility constraints. For example, the MILP becomes a convex LP or the MIQP becomes a convex QP when relaxing the integer feasibility constraints. Examples of efficient optimization algorithms for the solution of the MICPs include, but are not limited to, branch-and-bound, branch-and-cut and branch-and-price methods.
A set of values is convex if for any two points in the set, points on a line segment joining the two points lies entirely within the set. Particularly, a set C∈Rn is deemed as a convex set if for any two points x1 and x2 in C and any scalar λ,
wherein, λ∈[0,1].
A function f: C→R is said to be convex if for any x1, x2∈C and λ∈[0,1] relation (2) is satisfied:
The relation (2) implies that any point, on the line segment joining two points on a convex function, lies above the value of the function at that point.
If C⊆Rn is a nonempty convex set and f: C→R be a convex function then a convex programming problem is defined as min f(x) such that x∈C. Property of the convex function may include that every local minimum of the convex function is a global minimum and set of all optimal solutions to a convex programming problem form a convex set.
The convex programming problem may be modified such that inequality or equality are added to it. If C⊆Rn is a nonempty convex set and f: C→R be a convex function then a constrained convex programming problem is defined as min f(x) such that hi(x)≤0, wherein h is a convex function and i=1 to m. ej(x)=0, wherein e(x)=aT+b and therefore convex and j=1 to n. Solutions to h(x) and e(x) i.e. the constraints to the convex function f(x), are also convex sets.
In some embodiments, heuristic search techniques may be used in the CTC 404 and in each of the ITCs 408, 410 to compute a feasible but possibly suboptimal solution to the MICP, for example, including rounding schemes, a feasibility pumping method, approximate optimization algorithms, or the use of deep learning or supervised learning. For example, in some embodiments, a deep neural network may be used to predict the optimal values for each of the binary or integer optimization variables in the CTC 404 or in each of the ITCs 408, 410, resulting in the solution of one or multiple convex programming (CP) problems after fixing each of the binary or integer optimization variables.
At each control time step, given the current sensing information from the infrastructure sensing module 406 and the current CTC traffic flow plan 420, the ITC 408 computes a sequence of future control commands at microscopic scale and these control commands are sent to each of the TLCs 452, 454, 456 and to each of the CAVs 422, 424, 426. In some embodiments, each of the TLCs 452, 454, 456 control one or multiple traffic light signals for one traffic intersection in the transportation network. For example, in some embodiments, the TLC 452 controls the timing of one traffic light signal for a particular crossing direction of one traffic intersection. In other embodiments of the disclosure, the TLC 454 controls the timing of multiple traffic light signals for the multiple crossing directions of one traffic intersection in the transportation network.
Some embodiments are based on the realization that planning and control for (semi-)automated driving may be implemented effectively using a multi-layer guidance and control architecture, typically implemented on board of each individual vehicle, including one or multiple layers of algorithms and technologies for decision making, motion planning, vehicle control or estimation. In some embodiments, a multi-layer guidance and control architecture is used in each of the CAVs 422, 424, 426 to execute the sequence of future control commands that is computed by the ITC 408, given real-time information from the infrastructure sensing 406, given the CTC traffic flow plan 420 and given real-time information from one or multiple on-board sensors 434, 442, 450 of each individual CAVs 422, 424, 426.
In an example, the CAVs 422, 424, 426 includes decision making layers 428, 436, 444, motion planners or motion planning algorithms 430, 438, 446, vehicle controllers 432, 442, 450, and one or multiple on-board sensors 434, 442, 450 respectively. The decision-making layer 428 for the CAV 422 selects the appropriate driving behavior at any point of time, given the motion plan 460 from the ITC, the current environment condition, the behavior of other traffic participants, for example, using automata combined with set reachability or formal languages and optimization for vehicle decision making. Given the target behavior from the decision making layer 428, including either lane following, lane changing or stopping, the motion planning algorithm 430 computes a dynamically feasible and safe motion trajectory that can be tracked in real-time by a low-level vehicle controller 432. Real-time sensor fusion and estimation using on-board and infrastructure sensing information may be performed in each vehicle, for example the CAVs 422, 424, 426, in order to provide feedback to the higher-level algorithms for decision making, motion planning and control. A similar, but potentially different, multi-layer guidance and control architecture may be used for (semi-)automated driving in one or multiple CAVs in the transportation network.
In an example, an approach for (semi-)automated driving uses the combination of a finite-state machine (FSM) for decision making in the decision making layers 428, 436, 444, a sampling-based motion planning algorithm in the motion planners 430, 438, 446, and a model predictive control (MPC) algorithm for reference trajectory tracking in the vehicle controllers 432, 440, 448. One example of an algorithm for sampling-based motion planning uses probabilistic particle filtering to sample the input space and adds an additional correction term based on one or multiple driving requirements. One example of a predictive algorithm for vehicle control uses one or multiple iterations of a sequential quadratic programming (SQP) method to solve a linear time-varying or nonlinear MPC problem in real time. Some embodiments are based on the realization that the use of predictive algorithms for motion planning and reference tracking control for (semi-)automated driving can more effectively benefit from the predictive information in the motion plan that is computed by the hierarchical traffic control system 600A. Examples of algorithms for sensor fusion and estimation are based on, but not limited to, moving horizon estimation (MHE), extended or linear-regression Kalman filtering, or particle filtering.
In some embodiments, the different components of the multi-layer guidance and control architecture 428, 430, 432, 434 may be implemented on board of each controlled vehicle such as the CAV 422, while other modules such as the hierarchical traffic control system 600A, the mapping and navigation system 304, and some or all of the sensor fusion technologies for the infrastructure sensing 406 may be implemented in the infrastructure such as the cloud network 118 or the one or multiple MECs 314, in order to provide decisions or feedback information to multiple connected vehicles in the transportation network.
In some embodiments of the disclosure, the infrastructure sensing 406 corresponds to the one or more RSUs, such as the RSUs 122, 124 that include one or multiple sensors, for example, distance range finders, radars, lidars, or cameras, as well as sensor fusion technologies in order to accurately detect the state of the vehicles and the dynamic environment in the transportation network, including both connected and non-connected vehicles, autonomous, semi-autonomous and manually operated vehicles and other traffic participants such as bicycles and pedestrians.
Some embodiments are based on the realization that safety constraints with respect to other dynamic traffic participants such as vehicles, bicycles, or pedestrians, may be handled by obstacle avoidance techniques in on-board modules of the multi-layer guidance and control architecture for each CAV. The obstacle avoidance techniques may be implemented by, for example, the motion planning or the vehicle control algorithm. Due to their relatively smaller computational cost, compared to that for the hierarchical traffic control system 600A, the motion planning and vehicle control algorithms may be run at a relatively fast sampling rate in order to have a fast reaction time to unexpected changes in the dynamic behavior of other vehicles or the other traffic participants. For example, real-time vehicle control algorithms are typically executed with an update period of 50-100 milliseconds but, in some embodiments of the disclosure, the sampling period for the CTC 404 can be equal to 1-2 seconds and the sampling period for each of the ITCs 408, 410 may be equal to 0.5-1 seconds.
Some embodiments are based on the realization that a different vehicle motion model, with a different modeling accuracy or a different computational complexity, may be used by one or multiple of the components in the architecture as illustrated by
Alternatively, one or multiple of the lower levels of the multi-layer guidance and control architecture could use a higher-dimensional or nonlinear dynamic model to describe the motion of the vehicle based on force-torque balances, for example, in a nonlinear MPC-based vehicle controller. In an example, a single-track nonlinear vehicle model may be used in an MPC-based vehicle controller for which the state is described by the two-dimensional position, the longitudinal and lateral velocities, the yaw angle and yaw rate of the vehicle. The single-track vehicle model lumps together the left and right wheel on each axle. In some embodiments, a vehicle model with an even higher modeling accuracy and computational complexity may be used. For example, the vehicle model with higher modeling accuracy may be based on a double-track vehicle model such that the longitudinal and lateral load transfer between the four wheels of the vehicle could be accurately modeled. In some embodiments, the nonlinear relation between the longitudinal and lateral tire-friction forces and the slip ratios and slip angles may be modeled using Pacejka's magic formula, which exhibits the typical saturation behavior in the tire forces. Under combined slip conditions, the coupling between longitudinal and lateral tire forces can be modeled using a friction ellipse or using weighting functions.
For example, ITC 408 computes the future control commands 464 for the group of CAVs 412 and for the group of TLCs 414 that are assigned to the ITC 408, given real-time information from the infrastructure sensing 406 and given the CTC traffic flow values 460 for each of the crossing directions of one or multiple intersections that are assigned to the ITC 408 within the transportation network. Similarly, a different such as the ITC 410 computes the future control commands 466 for the group of CAVs 416 and the group of TLCs 418 that are assigned to the ITC 410, given real-time information from the infrastructure sensing 406 and given the CTC traffic flow values 462 for each of the crossing directions of one or multiple intersections that are assigned to the ITC 410 within the transportation network.
The hierarchical traffic control system 600A divides the method of controlling the CAVs and the HDVs broadly in two steps 702 and 704. However, in certain embodiments, such discrete operations may be further divided into additional operations, combined into fewer operations, or eliminated, depending on the particular implementation without detracting from the essence of the disclosed embodiments.
At 702, the traffic flows are jointly optimized for all intersections using the convex optimization subject to the convex relaxation of the integer constraints on the multiple interconnected intersections. In an embodiment, the CTC 404 of the hierarchical traffic control system 600A computes the high-level traffic flow plan based on the macroscopic traffic flow model for the mixed traffic of the CAVs and the HDVs. In an embodiment, the optimization of the traffic flows includes optimization of traffic flow values, for example, the CTC traffic flow values 460 or 462 associated with ITCs 408 or 410 as illustrated in
At 704, a cost function of the MIP problem in each of the ITCs is optimized with respect to the relaxed traffic flow values from the CTC 404 and subject to the integer constraints to produce values of the control commands changing the states of each of the CAVs associated with an intersection and values of the control commands changing the states of each of the traffic signs associated with the intersection.
A vehicle arriving from the North 815 may make a right turn resulting in crossing direction d1 801, the vehicle may drive straight resulting in crossing direction d2 802 or it can make a left turn resulting in crossing direction d3 803. A vehicle arriving from the East 816 may make a right turn resulting in crossing direction d4 804, the vehicle may drive straight resulting in crossing direction d5 805 or it can make a left turn resulting in crossing direction d6 806. A vehicle arriving from the South 817 may make a right turn resulting in crossing direction d7 807, the vehicle can drive straight resulting in crossing direction d8 808 or it can make a left turn resulting in crossing direction d9 809. A vehicle arriving from the West 818 can make a right turn resulting in crossing direction d10 810, the vehicle can drive straight resulting in crossing direction d11 811 or it can make a left turn resulting in crossing direction d12 812.
In some embodiments, the TLC 820 decides if and when to switch one or multiple traffic light signal values, for example, switching from green to red or from red to green in order to avoid collisions and to reduce traffic congestion and fuel consumption. Traffic participants are allowed to cross an intersection in a particular crossing direction if the traffic light signal is green for the crossing direction, but they need to stop and wait if the traffic light signal is red for the desired crossing direction. Some embodiments are based on the realization that multiple collision-free states exist for the traffic light signals of an intersection, i.e., the current state of the traffic light signals is equal to one of multiple collision-free states at each time step, in order to allow for the traffic light signals of an intersection to be either red or green for one or multiple crossing directions at each time step while avoiding collisions between vehicles arriving at the traffic intersection from different directions.
Some embodiments of the disclosure are based on the realization that the traffic light state 822 is collision-free because no collisions can happen between vehicles traveling from East 816, via crossing directions d4 804 or d5 805, and vehicles traveling from West 818 via crossing directions d10 810 or d11 811. For example, a traffic light state 828 is collision-free because no collisions can happen between vehicles traveling from South 817, via crossing directions d7 807, d8 808 or d9 809, and vehicles traveling from West 818 via crossing direction d10 810. Similarly, a traffic light state 824 is collision-free because no collisions can happen between vehicles traveling from North 815, via crossing directions d1 801 or d2 802, and vehicles traveling from South 817 via crossing direction d7 807 or dg 808.
In some embodiments, the traffic flow values 840 are real-valued relaxed approximations of pure integer values. The pure integer values are relaxed based on a convex relaxation of the mixed-integer constraints that enforce the hybrid dynamical behavior of vehicles crossing one or multiple of the traffic intersections. For example, in
In some embodiments of the disclosure, the CTC traffic flow values 840 satisfy a macroscopic traffic flow model and they satisfy a convex relaxation of one or multiple mixed-integer constraints that enforce each of the multiple traffic rules for the entire transportation network of one or multiple interconnected traffic intersections. In some embodiments, the summation of CTC traffic flow values 840 is not allowed to exceed a maximum capacity limit at each time step and for each traffic intersection in the transportation network. Similarly, the CTC traffic flow values 840 are not allowed to exceed the number of vehicles arriving at the traffic intersection that are predicted to cross the traffic intersection in that particular crossing direction. For example, given the future CTC traffic flow values 840 in
At 901, a microscopic traffic model of an ITC, such as the ITC 408 as illustrated in
At 902, the microscopic traffic model of the ITC 408 may be used to compute a prediction of future traffic flow values over a prediction time horizon.
At 903, future CTC traffic values may be calculated by the CTC 404 of the hierarchical traffic control system such as the hierarchical traffic control system 600A as illustrated in
At 904, a tracking error is calculated between the future traffic flow prediction values calculated at step 902 and the future CTC traffic flow values calculated at step 903. In an embodiment, the optimal traffic flow probability values of the CTC 404 are used in the ITC 408 to minimize the tracking error between the future traffic flow prediction values calculated at step 902 and the future CTC traffic flow values calculated at step 903 over a prediction time horizon of the ITCs for each crossing direction of the multiple intersections
At 905, the tracking error 603 calculated at step 904 is minimized over the prediction time horizon in the cost function of the ITC 408. Some embodiments of the disclosure are based on the realization that the minimization of the difference in traffic flow predictions may be computed using a least squares tracking error, between the predicted traffic flow values calculated at 902 and the reference CTC traffic flow values calculated at 903, in the cost function adaptation method 900 of the hierarchical traffic control system 600A. In some embodiments, the cost function of the constrained optimization problem that is solved in each of the ITCs 408, 410 includes one or multiple additional terms, for example, minimization of fuel consumption 906-1, minimization of traffic congestion 906-2, maximization of traveled distance for one or multiple vehicles 906-3, and maximization of safety for one or multiple vehicles 906-4 in a local neighborhood of the transportation network over the prediction time horizon.
At 906, adaptation of the cost function of the constrained optimization problem that is solved by the ITC 408 is performed. The cost function adaptation method 900 is based on a direct policy mapping from the CTC traffic flow values calculated at step 905 and from the real-time information of the infrastructure sensing 406 to one or multiple parameter values in the cost function of the ITC 408. In an example, the one or multiple parameter values may include one or multiple weight values that quantify the penalization of higher traffic flow values in one or multiple crossing directions for each of the traffic intersections of the transportation network. In some embodiments, the direct policy mapping can be implemented using a deep neural network architecture, for example, using reinforcement learning (RL) to directly maximize a reward function for reducing congestion, travel time, emissions and energy consumption in the transportation network. For example, in some embodiments of the disclosure, the CTC 404 is implemented by training an RL policy based on model-free or model-based RL techniques. In other embodiments, the policy mapping may be implemented using a deep neural network architecture, based on imitation learning that aims to approximate expert or heuristic solutions.
A deep neural network architecture may be based on one or multiple layers that include one or multiple feedforward neural networks, recurrent neural networks (RNNs), convolutional neural networks (CNNs), long short-term memory (LSTM) networks, or gated recurrent units (GRUs).
In some embodiments, the vehicle density values 1000B over the prediction time horizon 1015-1018 satisfy the macroscopic traffic flow model and they satisfy a convex relaxation of one or multiple mixed-integer constraints that enforce each of the multiple traffic rules for the entire transportation network of the one or multiple interconnected traffic intersections. For example, the flow of vehicles out of the road segment 1005 is enforced to be equal to the flow of vehicles into the traffic intersection 1006, and the flow of vehicles through the traffic intersection is upper bounded by a maximum capacity limit at each time step and for each traffic intersection in the transportation network.
For example, the traffic flow value for crossing direction d1 of 2.3 at the first time step 1055 represents the number of vehicles that is predicted to flow in direction d1, i.e., from road segment s1 to road segment s11 or s12. The dynamic behavior of the traffic flow value 1041, and the vehicle density values for s1 1021, s11 1031 and s12 1032, may be predicted for the subsequent time steps 1055-1057 and 1035-1038, respectively, based on the macroscopic traffic flow model for the transportation network. For example, the traffic flow value for crossing direction d1 of 2.3 at the first time step 1055 is equal to the vehicle density value for s1 of 8 at the first time step 1035 minus 5.7 at the second time step 1036. In addition, the flow of vehicles into road segments s11 and s12 from the first to the second time step, (5.15−4)+(3.15−2)=2.3 is equal to the traffic flow value for crossing direction d1 of 2.3 plus the traffic flow value for crossing direction d4 of 0 744 at the first time step 1055. A similar dynamic traffic behavior can be observed in
For example, the traffic flow value for crossing direction d2 of 1.7 at the first time step 1055 represents the number of vehicles that is predicted to flow in direction d2 1062, i.e., from road segment s2 to road segment s7 or s8. The dynamic behavior of the traffic flow value 1042, and the vehicle density values for s2 1022, s7 1027 and s8 1028, may be predicted for the subsequent time steps 1055-1057 and 1035-1038, respectively, based on the macroscopic traffic flow model for the transportation network. For example, the traffic flow value for crossing direction d2 of 1.7 at the first time step 1055 is equal to the vehicle density value for s2 of 4 at the first time step 1035 minus 2.3 at the second time step 1036. In addition, the flow of vehicles into road segments s7 and s8 from the first to the second time step, (2.85−2)+(3.85−3)=1.7 is equal to the traffic flow value for crossing direction d2 of 1.7 plus the traffic flow value for crossing direction d5 of 0 745 at the first time step 1055 in the prediction horizon of the CTC 404.
In some embodiments, the state information vector in the macroscopic traffic flow model includes both the vehicle density values 1020, the traffic flow values 1040 through one or multiple intersections, and the position of vehicles in each road segment of the transportation network. In some embodiments, each road segment is divided in one or multiple smaller sub-segments and current vehicle density values are estimated and future vehicle density values are predicted for each of the sub-segments in order to improve the accuracy of the macroscopic traffic flow model in the hierarchical traffic control system 600A. In some embodiments, vehicles are expected to travel from one sub-segment to the next sub-segment in one sampling time period and vehicles can only enter a traffic intersection from a road sub-segment that is sufficiently close to the traffic intersection in the transportation network. This results in a more accurate modeling of the travel time for each of the vehicles to drive from the beginning of a road segment to the end of the road segment, given a desired or estimated average speed for each of the vehicles.
In some embodiments, historical data is collected from the database 108 and used to estimate predict vehicle density values 1020 and traffic flow values 1040 to improve the performance of the hierarchical traffic control system 600A in the transportation network. For example, given a crossing direction d3 1063 from road segment s5 to road segment s3 or s4, the percentage of vehicles in the traffic flow of crossing direction d3 1063 entering either road segment s3 or s4 can be predicted based on vehicle density values 1020 and traffic flow values 1040 in the same or a similar transportation network during a similar time period in the past. Similarly, the number of external vehicles entering the transportation network from each of the in-flow directions at each time step in the prediction horizon can be predicted based on historical data that is collected for the same or a similar transportation network during a similar time period in the past. For example, historical data may be used to predict typical traffic in-flow values or to predict the typical routing of vehicles entering a particular transportation network on a Monday morning at 8 am versus a Saturday afternoon at 2 pm, which can be used to improve predictions of a macroscopic traffic flow model in the hierarchical traffic control system 600A.
At 1101, the CTC 404 receives mapping information, for example, location data (e.g., GPS data) for road segments, lanes, traffic intersections and stopping zones in the transportation network.
At 1105, the CTC 404 receives additional inputs, for example, feedback signals on state and planned routing information from the CAVs. In an example, the feedback signal also includes information from the infrastructure sensing module 406.
At 1106, the CTC 404 receives additional inputs, for example, feedback signals on state and predicted routing information from HDVs. In some embodiments, the feedback signals are obtained directly or indirectly from the sensing infrastructure module 406 (e.g., RSUs) or from connected vehicles, which can be either autonomous, semi-autonomous and/or human-driven vehicles. The feedback signals on state and planned routing information for CAVs may be referred to as type 1 feedback signals. The feedback signals on state and predicted routing information for HDVs may be referred to as type 2 feedback signals.
At 1110, the CTC 404 constructs a constrained optimization problem based on a macroscopic traffic flow model for the CTC 404.
At 1115, the CTC 404 solves the constrained optimization problem to compute a macroscopic traffic flow motion plan for the one or multiple traffic lights and connected and (semi-) automated vehicles in the transportation network that includes the multiple interconnected traffic intersections. In an embodiment, the CTC 404 solves the constrained optimization problem with a cost function that includes at least one of a maximization of a sum of traffic flow variables or a minimization of a sum of traffic congestion variables in the transportation network.
At 1120, the CTC 404 computes an optimal sequence of high-level control target values for the traffic flow over a prediction time window of the CTC 404 in the transportation network, based on the solution to the constrained optimization problem. The CTC 404 controls the mixed traffic within the transportation network.
At 1121, the CTC 404 sends the computed optimal sequence of high-level control target values for the traffic flow to each of the one or multiple ITCs 821 in the hierarchical traffic control system 600A that controls mixed traffic in the transportation network.
At 1122, the CTC 404 receives map segment and lane information for the multiple interconnected traffic intersections in the transportation network.
At 1125, the CTC 404 receives feedback signals related to sensing and routing from controlled, non-controlled and/or semi-controlled vehicles.
At 1135, the CTC 404 constructs matrices and vectors in CP data of the CTC 404 for objective, equality, and inequality constraints. In an embodiment, the matrices and vectors are constructed using the received feedback signals related to the sensing and routing, and the map segment and lane information.
At 1140, the CTC 404 solves a CP problem based on a convex relaxation of non-convex traffic rules. In some embodiments, the CP includes the convex relaxation of one or multiple mixed-integer equality and/or mixed-integer inequality constraints that enforce each of the multiple traffic rules for the entire transportation network of one or multiple interconnected traffic intersections. In some embodiments, the CP problem includes a convex optimization problem in the CTC 404. The convex optimization problem may be a convex linear programming (LP) problem, including a linear objective, and one or multiple linear equality and/or inequality constraints. In some embodiments, the convex optimization problem in the CTC 404 is a convex quadratic programming (QP) problem, including a linear-quadratic objective, and one or multiple linear equality and/or inequality constraints. In some embodiments, the convex optimization problem in the CTC 404 is a convex quadratically constrained quadratic programming (QCQP) problem, including a linear-quadratic objective, one or multiple linear equality and/or inequality constraints, and one or multiple quadratic inequality constraints. In some embodiments, the convex optimization problem in the CTC 404 is a convex conic programming problem, including a linear objective, one or multiple linear equality and/or inequality constraints, and one or multiple convex cone inequality constraints. Some embodiments of the disclosure are based on the realization that numerical optimization algorithms exist for the computationally efficient solution of the convex optimization problem in the CTC 404. Examples of the optimization algorithms to efficiently solve the CP at step 1140 include active-set methods, interior point methods, projected gradient methods, operator splitting methods, or the alternating direction method of multipliers (ADMM).
At 1145, the CTC 404 computes an optimal sequence of high-level target values for the traffic flow in the multi-intersection transportation network over a prediction time window.
At 1150, the CTC 404 sends the computed optimal sequence of high-level target values for the traffic flow to each of the ITCs in the hierarchical traffic control system 600A of the transportation network.
At 1152, the CTC 404 receives map segment and lane information for the multiple interconnected traffic intersections in the transportation network.
At 1154, the CTC 404 receives feedback signals related to sensing and routing from controlled, non-controlled and/or semi-controlled vehicles.
At 1156, the CTC 404 constructs matrices and vectors in convex QP data of the CTC 404 for objective, equality, and inequality constraints. In an embodiment, the matrices and vectors are constructed using the received feedback signals related to the sensing and routing, and the map segment and lane information.
At 1158, the CTC 404 solves the convex QP based on a convex relaxation of non-convex traffic rules. According to some embodiments, the convex QP includes a linear-quadratic objective function 1158-1, one or multiple linear equality constraints 1158-2, and one or multiple linear inequality constraints 1158-3.
At 1160, the CTC 404 computes and sends optimal traffic flow values to each of the ITCs in the hierarchical traffic control system 600A of the transportation network.
In some embodiments, the construction of the CP in the CTC 404 includes a macro-level traffic network structure using multiple network parameters, for example, including road segment length, number of lanes, road segment connections and traffic intersection connectivity. For each road segment r, the macro-level traffic network structure defines possible future traffic flow maneuvers w∈{straight, left, right}, i.e., a vehicle can drive straight, turn left or turn right in road segment r when arriving at a traffic intersection. In some embodiments of the disclosure, the CTC 404 computes vehicle density probability values Prw for each road segment-maneuver pair (r, w), e.g., using historical data that is collected for the same or a similar transportation network during a similar time period in the past. Computing probability values Prw for each road segment-maneuver pair (r, w) using historical data involves collecting the usage of each road and maneuver over a large enough time window in order to make accurate predictions for a future time period.
In some embodiments, a sampling time period for a receding horizon implementation of the CTC 404 is equal to or longer than a sampling time period for a receding horizon implementation for each of the ITCs 408, 410 in the hierarchical traffic control system 600A. In some embodiments, a length of the prediction time window of the CTC 404 is equal to or longer than a length of the prediction time window for each of the ITCs 408, 410 in the hierarchical traffic control system 600A.
In some embodiments of the disclosure, the macroscopic traffic flow model in the CTC 404 may be described as a directed graph, where each node corresponds to a road segment and each edge corresponds to a connection between road segments, i.e., a direction to cross through a traffic intersection in the transportation network that is controlled by the hierarchical traffic control system.
In some embodiments, the CP of the CTC 404 may include one or multiple of the following optimization variables:
Some embodiments are based on the realization that the CP of the CTC 404 is an optimal control block-sparsity structured convex optimization problem that includes state variables zr,w(t), for each road segment-maneuver (r, w) pair at each time step t∈[0, N] in a prediction time window, and control variables fr,win(t), fr,wout(t), for each road segment-maneuver (r, w) pair at each time step t∈[0, N−1] in a prediction time window, and control variables er,s(t) for each pair of connected road segments r and s and for each time step t E [0, N−1] in a prediction time window of the CTC 404.
In some embodiments, vehicle positions and velocities at the current time step are used to compute initial state values of the macroscopic traffic flow model in the CTC 404 of the hierarchical traffic control system 600A. For example, vehicle positions may be used to compute a vehicle density value zr,w, i.e., a number of vehicles in each road segment-maneuver pair (r, w). In some embodiments, each road segment r is divided in one or multiple smaller sub-segments r1, r2, . . . , rn, and current vehicle density values are estimated and future vehicle density values are predicted for each of the sub-segments zr
In some embodiments, a set of discrete-time differential equations is used to define a dynamical system that describes the macroscopic traffic flow model in the CTC 404, for example,
given the initial state values zr,w(0)={circumflex over (z)}r,w, which are obtained from feedback signals on sensing and routing controlled, non-controlled and/or semi-controlled vehicles 1154, and given the in-flow and out-flow variables fr,win(t), fr,wout(t), for each road segment-maneuver (r, w) pair at each time step t∈[0, N−1] in a prediction time window of the CTC 404.
In some embodiments, the inequality constraints 1158-3 of the convex optimization problem in the CTC 404 includes one or multiple inequality constraints on the maximum flow along an edge in the directed graph that represents the transportation network of the interconnected intersections, for example, including the inequality constraints
where fmax is the maximum flow limit and A represents an adjacency matrix for the directed graph, i.e., A(r, s)=1 if road segments r and s are connected, otherwise A(r, s)=0 if road segments r and s are not connected.
In some embodiments of the disclosure, a flow buffer can be used to store (approximately) a time step at which each subset of vehicles entered each road segment-maneuver pair (r, w) in order to make a prediction of the time step at which each subset of vehicles exit the road segment and crosses the next traffic intersection in the transportation network. For example, if it takes approximately 3 sampling time periods for one or multiple vehicles to cross road segment r, then the CP of the CTC 404 may include one or multiple inequality constraints to ensure that vehicles can only exit road segment r at least 3 sampling time periods after they entered the road segment.
In some embodiments of the disclosure, flow output for each road segment at each time step is upper bounded by the number of vehicles in the road segment at that time step, and this for each possible maneuver w∈{straight, left, right}, minus the number of vehicles that entered the road segment within a particular time window, according to the macroscopic traffic flow model in the CTC 404 of the hierarchical traffic control system 600A. The latter ensures time delay constraints for each road segment corresponding to an expected duration for each vehicle to travel through the road segment, given the physical length of the road segment, given the expected congestion of the road segment and the expected velocity for the vehicles in the road segment. For example, in some embodiments of the disclosure, the inequality constraints 1158-3 of the convex optimization problem in the CTC 404 includes one or multiple time delay constraints as
where τ(r) denotes an expected time delay value for vehicles traveling through road segment r and the in-flow values fr,win(t) are given for −τ(r)≤t≤−1, i.e., the in-flow value fr,win(t) defines the number of vehicles entering road segment r at time step t with a (estimated or predicted) plan to perform maneuver w.
In some embodiments of the disclosure, the inequality constraints 1158-3 of the convex optimization problem in the CTC 404 includes one or multiple traffic intersection capacity limit constraints, for example,
where ϵ(j) denotes one or multiple edges in a directed graph that correspond to one or multiple crossing directions of a traffic intersection j∈ in the transportation network, and zjmax denotes a maximum number of vehicles that is able to cross through the traffic intersection at a time step t∈[0, N] in a prediction time window of the CTC 404.
In some embodiments, the equality constraints 1158-2 of the convex optimization problem in the CTC 404 includes one or multiple equality constraints as
which define the values of edge variables based on the out-flow variables, and where a transition from road segment r to road segment s corresponds to a road segment-maneuver pair (r, w). Some embodiments of the disclosure are based on the realization that the latter equality constraints can be used to numerically eliminate the edge variables from the convex optimization problem, resulting in a reduced CP of smaller dimensions that is computationally cheaper to solve at each time step of the CTC 404 in the hierarchical traffic control system 600A.
In some embodiments, the equality constraints 1158-2 of the convex optimization problem in the CTC 404 includes one or multiple equality constraints as
which define the values of in-flow variables based on the incoming edge variables, where frext(t) denotes the predicted external in-flow values, and the Prw values denote the estimated probability for vehicles in road segment r to perform a possible maneuver w∈{straight, left, right}.
In some embodiments of the disclosure, the optimal solution of the convex optimization problem includes optimal traffic flow probability values Pjd,* for each pair of traffic intersection j∈ and a corresponding crossing direction d∈
j in the transportation network. The optimal traffic flow probability values pjd,* for each intersection-direction pair are sent to each of the ITCs in the transportation network, and each ITC aims to minimize a least squares tracking error between the predicted traffic flow values 902 and the reference CTC traffic flow values 903 in a cost function adaptation method 900 of the hierarchical traffic control system 600A, according to some embodiments.
In some embodiments, at each sampling time period of the hierarchical traffic control system 600A, the CTC 404 computes an optimal solution to a convex LP or a convex QP that reads as
where dist(r) is the physical distance of road segment r∈ in the transportation network that is controlled by the hierarchical traffic control system 600A.
At 1201, the ITC 408 or 410 receives mapping information, for example, location data (e.g., GPS data) for road segments, lanes, traffic intersections and stopping zones in the transportation network.
At 1205, the ITC 408 or 410 receives additional inputs, for example, feedback signals on state and planned routing information from the CAVs. In an example, the feedback signal also includes information from the infrastructure sensing module 406.
At 1206, the ITC 408 or 410 receives additional inputs, for example, feedback signals on state and predicted routing information from HDVs. In some embodiments, the feedback signals are obtained directly or indirectly from the sensing infrastructure module 406 (e.g., RSUs) or from connected vehicles, which can be either autonomous, semi-autonomous and/or human-driven vehicles. The feedback signals on state and planned routing information for CAVs may be referred to as type 1 feedback signals. The feedback signals on state and predicted routing information for HDVs may be referred to as type 2 feedback signals.
At 1210, the ITC 408 or 410 constructs a constrained optimization problem based on a microscopic traffic model for the transportation network of the ITC. In some embodiments, the constrained optimization problem is a mixed-integer programming (MIP) problem constructed based on the microscopic traffic model.
At 1215, the ITC 408 or 410 solves the MIP problem to compute a microscopic traffic flow motion plan of the ITC 408 or 410 for traffic lights and for one or multiple traffic lights and/or for connected and (semi-) automated vehicles in the transportation network. The ITC 408 or 410 computes a solution to the MIP at each sampling time step.
At 1220, the ITC 408 or 410 computes an optimal sequence of target control commands for each CAV in a local area around one or multiple traffic intersections within the transportation network and an optimal sequence of traffic light commands over a prediction time window of the ITC 408 or 410.
At 1225, the ITC 408 or 410 sends commands to a multi-layer guidance and control architecture for each CAV and the ITC sends control commands to each traffic light in a local area around one or multiple traffic intersections within the transportation network that is controlled by the hierarchical traffic control system 600A.
Some embodiments are based on the realization that the hierarchical traffic control system 600A can be implemented by solving the constrained optimization problem 1210 to compute the motion plan for each of the CAVs and to compute optimal control commands for each of the TLCs, given the input information from V2X communication. In some embodiments, the constrained optimization problem may be the MIP problem, for example, a mixed-integer linear programming (MILP) or mixed-integer quadratic programming (MIQP) problem. In some embodiments, one or multiple MIP problems at each sampling instant of the hierarchical traffic control system 600A may be solved by a global optimization algorithm, for example, including branch-and-bound, branch-and-cut and branch-and-price methods. In other embodiments of the disclosure, heuristic techniques can be used to compute a feasible but suboptimal solution to the one or multiple MIP problems, for example, including rounding schemes, a feasibility pumping method, approximate optimization algorithms, or (deep) machine learning, e.g., using supervised learning.
In some embodiments, a long-term future route plan is used for each of the CAVs in the local area that is controlled by the ITC around the one or multiple traffic intersections within the transportation network. Some embodiments are based on the realization that, depending on the infrastructure system, obtaining a precise future prediction 1212 for the route of each HDV may prove challenging. Because of this, in some embodiments, the hierarchical traffic control system 600A is implemented in a receding horizon fashion based on the most recent information from the sensing infrastructure (e.g., RSUs) and from connected vehicles. Some embodiments are based on the realization that an approximate short-term future route prediction 1212 for HDVs is sufficient and can typically be obtained relatively easily, e.g., from the current position of each HDV until the next traffic intersection, a current lane of each HDV, and a detection of turn signals of the one or multiple HDVs. Some embodiments of the disclosure are based on the realization that discrepancies in the predictions can be adjusted by the intrinsic feedback mechanism of the receding horizon strategy. For example, an update period of 1 second allows for real-time computation of the hierarchical traffic control system 600A, while providing sufficiently fast updates to the multi-layer guidance and control architecture for each CAV and providing sufficiently fast updates 1223 to each of the TLCs, to account for erroneous prediction of HDV behaviors.
In some embodiments, the future driving behavior of an HDV is modeled using a switched dynamical system that is able to predict reactions of the HDV to an estimated or predicted driving behavior of one or multiple CAVs or HDVs in a local neighborhood around the HDV, and to predict reactions of the HDV to traffic rules or traffic lights in the transportation network. In particular, the HDV predictive motion model predicts a new state for the HDV, given the current state of the HDV using real-time information from the infrastructure sensing module 406.
The steps identified in
At 1231, a current state of an HDV is received and fed to the HDV predictive motion model.
At 1235, the HDV predictive motion model determines if a traffic light is red for a crossing direction and the HDV is within a safety distance from a stopping zone. In some embodiments, a value of the safety distance may be predetermined based on experimental observations or may be set by a local authority.
At 1236, the HDV predictive motion model predicts that the HDV performs a stopping maneuver in the stopping zone at a traffic intersection if the traffic light is red for the crossing direction and the HDV is within the safety distance from the stopping zone.
At 1240, the HDV predictive motion model determines whether a vehicle leading the HDV is within safety distance in front of the HDV when either of the condition mentioned at step 1235 is not satisfied, i.e, either the traffic light is not red for the crossing direction or the HDV is not within the safety distance from the stopping zone.
At 1241, the HDV predictive motion model predicts that the HDV performs a safe leader following behavior if the HDV is not within the safety distance from the stopping zone and/or the traffic light is not red, but if a leading vehicle is within a safety distance in front of the HDV and it is in the same lane as the HDV.
At 1242, the HDV predictive motion model predicts that the HDV continues traveling at a desired average speed if there is no leading vehicle within the safety distance in front of the HDV and/or the leading vehicle is not in the same lane as the HDV.
Selection of a function to be active for the HDV depends on states 1256 of the traffic signs, a state 1254 of the HDV, and other vehicles' states 1258. The state 1254 of the HDV includes at least one of a position, a velocity, an acceleration, and a lane of the HDV. Hence, while the functions 1246-1252 themselves may not be dependent on the states 1256 of the traffic signs, however, the selection of the function to be active at a particular control step depends on the states 1256 of the traffic signs. Collectively, the functions 1246-1252 are referred to herein as a switch (discontinuous) function that selects a function representing the motion model for the HDV, based one or a combination of the states 1256 of the traffic signs, the state 1258 of the HDV, and the other vehicles' states 1258. The functions 1246-1252 individually describe dynamic traffic rules that the HDVs should follow.
According to an embodiment, the selected function can be used as the motion model of the HDV for the joint optimization of a CAV and the HDV. In particular, the traffic control system solves a MIP optimizing a cost function for values of the control commands changing states of each of the CAVs and values of the control commands changing states of each of the traffic signs. The cost function is optimized subject to the motion model of each of the CAVs and the motion model of each of the HDVs.
According to an embodiment, the motion model of the CAV may represented as a dynamical system
where t is an index of a time instant in a discrete-time sequence of sampling instants, equispaced with sampling period Ts, xi is CAV state vector, ui is a control vector (also referred to as control command)determined by the traffic control system, f is a state update function, which is normally a continuous function determining an evolution of system state xi over time, hp and h□ are output functions that provide a current position of the CAV along its route (route-relative position) and a current lane of the CAV.
The CAV is also subject to constraints which represents limitations on the velocity, acceleration, and possibly control commands,
where i,
i are admissible state and input regions, respectively.
In some embodiments, constraints that model the general traffic rules are formulated. For example, an exemplary model is described for the traffic lights. Other traffic rules can be modelled similarly with modifications due according to their functions. A traffic light in conflict zone j∈ where
is a set of all conflict zones, is represented by a number of variables ψjd with logic values where true (or 1) indicates passing the conflict zone j in direction d is allowed, while false (or 0) indicates that passing the conflict zone j in direction d is not allowed where d∈
(j)indexes directions
(j) in the conflict zone j. Thus, the fact that only one direction is allowed to cross the intersection at the same time is represented by a logic constraint
where V is an exclusive or (xor) operator, and hence 1 and only 1 direction is allowed to pass through the intersection at any time. In certain embodiments of the constraint (13) is modified to allow group of directions to cross the intersection at the same time as long as that does not cause the vehicles to possibly collide, i.e., directions in the intersection do not cross.
Further, in an embodiment, the optimization of the cost function is subject to timing constraints. The timing constraints include at least one of a timer enabling or disabling a change of the traffic signs and a timer enabling or disabling a change of CAV driving lane. For example, timers ψ
The traffic control system may update a timer v monitoring a change of variable
by evaluating
models the constraints on when value of can change, based on timer value
v.
The traffic control system ensures that the CAVs are assigned to available lanes by computing control commands that satisfy constraint
where jd(i)
jd(i) is a set of positions of the i-th vehicle (CAV or HDV) along its route for which it is in j-th zone, either conflict or conflict-free, in d-th direction, and
λd(j) is a set of lanes available in the j-th zone in the d-th direction. Additionally, constraints on minimum time between two lane changes may be imposed using a time for lane change of i-th CAV,
where λ
which ensure that if i-th vehicle is in the intersection in the d-th direction, then a different vehicle cannot be in the same intersection with a different direction, and that if the traffic light does not allow a direction to pass, no vehicle is in the intersection going through that direction. The traffic control system may also group directions into compatible directions that are allowed to pass through the intersection at the same time, as long as they do not cause collisions.
When value of ψjd can be changed by control commands for jointly controlling the CAVs and HDVs, the intersection rule (18) is a dynamic traffic rule in the sense that since for fixed vehicle positions, the satisfaction or violation of the traffic rule will not always be the same, since it depends on an actual value of ψjd, decided by the traffic control system.
Additionally, the traffic control system generates control commands for the CAVs, which avoid rear end collisions, by imposing the constraints
which ensure that if i-th vehicle is behind another vehicle in the same j-th zone going in the same d-th direction at a certain time instant t, then it will be behind the same vehicle at the next time instant t+1, or they will be in a different lane, where function zji(pi) provides a position of i-th vehicle in the j-th zone in global coordinates for route-relative vehicle position pi.
The collision avoidance rule (19) on the position of the vehicle, is independent from other variables controlled from the traffic control system, other than the position of the vehicles themselves, and hence it is not a dynamic traffic rule, since for fixed vehicle positions, the satisfaction of violation of the traffic rule will always be the same.
In an embodiment, the motion model for the HDV may be described as a switched dynamical system of form
X={xi}i∈ is a set of all vehicle states, ψ={ψjd}j∈
, d∈
(j) is a set of all controlled direction traffic lights, g0 is a function describing the rule-free motion model, and gξ, ξ∈Ξ are functions representing the motion models in presence of the traffic rules. The traffic rule activates the motion model gξ, ξ∈Ξ, when the function
ξ, ξ∈Ξ is non-positive and
i.e., non-positivity of the functions ξ, ξ∈Ξ is mutually exclusive.
As a specific example of (20) in the case when stopping at red traffic light is considered, the motion model for the HDV may be given as
where in case a position of the i-th HDV is not yet in the d-th direction of the j-th conflict zone but it is not more than away from it, and the traffic light does not enable crossing in the d-th direction of the j-th conflict zone, the i-th HDV stops, otherwise, it proceeds with its current speed. In case of the motion model (20) there is only one traffic rule and hence two models: one for when the HDV is affected by such traffic rule, which occurs near the intersection, when the light is red, and another one is the rule-free model that is used otherwise.
Further, to jointly control the CAVs and the HDVs, the traffic control system determines the values of the control commands changing the states of each of the CAVs and the values of the control commands changing the states of each of the traffic signs according to a cost function, to be minimized, which represents the individual objectives and the common objective that the CAVs and HDVs must achieve. In an embodiment, the cost function be formulated as
where PN=(P(0|t) . . . P(N|t)) is a sequence of predicted positions at time t over the future horizon of N steps of all the vehicles, e.g., the vehicles 126-146, ΛN=(Λ((0|t) . . . Λ((N|t)) is a sequence of predicted lane occupation at time t over future horizon of N steps by all the vehicles, UN=(U(0|t) . . . U((N|t)) is a sequence of predicted control commands at time t over the future horizon of N steps for all the CAVs and ψN=(ψ(0|t) . . . ψ((N|t)) are the control commands for the traffic signs, F is a terminal cost, L is a stage cost, and notation α(k|t) describes value of a predicted k steps ahead of time t.
The stage and terminal costs may be composed of multiple terms. For instance, a term
sums a normalized distance of the vehicles 126-146 to an end of their travel piend, where l=1,2 determines whether that distance is square or not, andip≥0 are weights encoding priorities of the vehicles 126-146 and a priority of this term with respect to other terms. (24a) enables controlling of the vehicles 126-146 such that they reach their destination at the earliest, and as such enables optimizing the individual time of completion of the objective of each specific individual vehicle.
Further, a term
gives the maximum normalized distance among all the vehicles 126-146 from their destination and m≥0 is a weight encoding the priority of this term with respect to other terms. (24b) enables controlling of the vehicles 126-146 such that the last vehicle to reach its destination, reaches its destination as soon as possible, and as such enables optimizing the time of completion of the common objective for the specific group of individual vehicles considered in the optimization.
In some implementations, in both (24a) and (24b) the normalization may be removed.
Further, in some embodiments, when the CAV control signal u is a commanded velocity tracked by a CAV on-board velocity controller, a term
sums differences between the commanded velocities and a desired velocity vref in an area, where iu≥0 are weights encoding the priorities of the vehicles 126-146 and a priority of this term with respect to other terms. (24c) is indicative of a difference between a commanded/current velocity and the desired velocity of each of the CAVs and the HDVs. (24c) enables controlling of the vehicles 126-146 such the vehicles 126-146 maintain a velocity close to the target velocity, and hence at avoiding slowdowns/speed-ups from such target velocity, with an effect to reducing accelerations/decelerations and idling, with consequences of reducing fuel consumption and emissions.
Further, a term
where iλ≥0 are weights encoding the priorities of vehicles 126-146 and a priority of this term with respect to other terms. (24d) is indicative of a difference between a current lane and a desired lane of each of the CAVs and the HDVs. (24d) enables controlling of the vehicles 126-146 such that the vehicles 126-146 keep a lane as close as possible to the desired lane, e.g., the rightmost one. Furthermore, a term
where ψ≥0wψ≥0 is a weight encoding a priority of this term with respect to other terms. (24e) indicates a difference between a combination, specifically the sum, of the current state of all traffic signs and a desired value for such combination. (24e) enables controlling of the traffic signs such that their operation is as close as possible to a desired target, for instance a desired total number of green traffic lights.
Additionally, a term
where Δψ≥0 is a weight encoding a priority of this term with respect to other terms, penalizes a change of the traffic light status, e.g., from red to green and vice versa, and (24f) avoids excessively frequent changes to the traffic signs, which aims at ensuring traffic lights do not cycle too quickly as this can create undesired effects on HDV traffic such as excessive stop and go, which increases pollution due to idling engines.
Similarly to (24f), a term
where iΔλ are
iΔλ≥0 are weights encoding a priority of this term with respect to other terms, penalizes a change of lanes of each vehicle, and (24f) prevents CAVs to change the lane, e.g., from left lane to right lane, which in turn avoids creating undesired effects on the HDV traffic, like excessive speed variations due to vehicles changing lanes in front. In some embodiments, reference values vref, λref, ζref, vary depending on the zone, direction, vehicle, and time instant.
At 1260, the ITC 408 or 410 receives map segment and lane information for the multiple interconnected traffic intersections in the transportation network.
At 1262, the ITC 408 or 410 receives feedback signals related to sensing and routing from controlled, non-controlled and/or semi-controlled vehicles.
At 1264, the ITC 408 or 410 constructs matrices and vectors in MIP data of the ITC for objective, equality and inequality constraints.
At 1266, the ITC 408 or 410 solves the MIP problem based on mixed-integer equality and inequality constraints for predictive motion models of one or multiple CAVs, HDVs and TLCs in the transportation network and mixed-integer equality and inequality constraints for non-convex traffic rules.
At 1268, the ITC 408 or 410 computes and sends the optimal control commands to one or multiple CAVs and TLCs in the transportation network that is controlled by the hierarchical traffic control system 600A.
According to some embodiments of the disclosure, the MIP problem includes a linear-quadratic objective function 1266-1, one or multiple linear inequality constraints 1266-2, one or multiple linear equality constraints 1266-3, and one or multiple integer feasibility constraints 1266-4. Some embodiments are based on the realization that the MIP problem is a mixed-integer convex programming (MICP) problem, i.e., the MIP problem becomes a convex programming (CP) problem for fixed values of the integer optimization variables, and the MICP may be solved computationally efficiently, e.g., using a branch-and-bound optimization method.
In some embodiments of the disclosure, the MIP problem may be a mixed-integer linear programming (MILP) or mixed-integer quadratic programming (MIQP) problem. For example, the MIP that is illustrated in 0 and a gradient vector h. The MIP can additionally include one or multiple linear inequality constraints 1266-2, defined by the constraint matrix C and constraint vector c, and one or multiple linear equality constraints 1266-3, defined by the constraint matrix F and constraint vector f. Finally, the MIQP 1266 for the hierarchical traffic control system 600A may include one or multiple integrality constraints 1266-4, which restrict one or multiple optimization variables z; to lie in the set of integer values, i.e., zj∈
. In some embodiments of the disclosure, the objective function 1266-1 is a linear function, i.e., H=0, such that the resulting MIP 1266 is an MILP optimization problem.
In some embodiments of the disclosure, the microscopic traffic model in one ITC 408 or 410 of the hierarchical traffic control system 600A defines the dynamics of one or multiple CAVs and HDVs as the evolution of a positional state p along the direction of motion in the transportation network and according to a target velocity v, for example, the MIP equality constraints 1266-3 may include one or multiple linear equality constraints as follows
where Δt is the discretization time of the vehicle dynamics. In some embodiments of the disclosure, to ensure realistic target velocities, the velocity assigned by the ITC 408 or 410 to one or multiple CAVs needs to be within a speed limit, v(t)≤
In some embodiments of the disclosure, the MIP 1266 defines one or multiple binary optimization variables to represent a prediction model for lateral dynamics of CAVs and/or HDVs, for example, using binary variables of σih=1 if vehicle i∈ is in lane h∈
1m
1m
In some embodiments of the disclosure, a prediction motion model for lateral dynamics of CAVs and/or HDVs is defined using discrete switching between lanes in a road segment of the transportation network that is controlled by a hierarchical traffic control system. For example, some embodiments of the disclosure introduce two binary optimization variables li,uc(t), li,dc(t)∈{0,1} in the MIP problem 1266 of an ITC to represent a lane change up and down respectively as follows
The latter implications can be enforced, for example, by adding the following mixed-integer inequality constraints for each vehicle i∈ and for each time step t∈
0N-1 to the MIP inequality constraints 1266-2
Similarly, in some embodiments of the disclosure, one or multiple mixed-integer inequality constraints for each vehicle i∈ and for each time step t∈
0N-1 are added to the MIP inequality constraints 1266-2 to impose the following implication that each vehicle remains in the same lane of a road segment at two subsequent time steps if no lane change maneuver is performed, i.e.,
In addition, in some embodiments of the disclosure, the following MIP inequality constraints 1266-2 prevent lane changes both up and down at the same time step, they prevent a lane change down from the lowest lane, and they prevent a lane change up from the highest lane in a road segment of the transportation network, i.e.,
In some embodiments of the disclosure, the MIP 1266 of each ITC includes one or multiple obstacle avoidance constraints for each pair of vehicles that are sufficiently close to each other within the transportation network and whose trajectories may lead to potential collisions. For example, in some embodiments of the disclosure, vehicles within one road segment or vehicles in adjoining road segments of the transportation network are paired up to impose one or multiple collision avoidance constraints in the MIP problem 1266. For such vehicle pairs, we enforce that the lead vehicle should remain ahead of the following vehicle, while both vehicles are in the same lane, for example, using following implications
for each lane h∈1m
, i2∈
, and for each time step t∈
0N-1 in a prediction time window of an ITC. Some embodiments of the disclosure are based on the realization that the latter implications can be enforced by adding one or multiple auxiliary variables and one or multiple mixed-integer inequality constraints to the MIP inequality constraints 1266-2.
In some embodiments of the disclosure, the MIP problem 1266 of each ITC includes one or multiple obstacle avoidance constraints by adding the following mixed-integer inequality constraints to the MIP inequality constraints 1266-2
where Li defines the physical length of each vehicle i∈ and the latter set of obstacle avoidance constraints use a time-varying value for the safety distance, which is defined as a base value Ds plus a velocity-dependent component with coefficient kv, and Ri
, i2∈
, and sic≥0 represents a continuous slack variable that is added to the optimization variables of the MIP problem 1266 to ensure feasibility of the constrained optimization problem for each ITC in the presence of model mismatch and disturbances. In some embodiments of the disclosure, additional binary optimization variables are added to the MIP problem 1266 for each ITC to define the obstacle avoidance constraints, for example, including the binary variable γi
and i2∈
are in the same lane at each time step t∈
0N-1, and the binary variable γi
and i2∈
to enforce collision avoidance at each time step t∈
0N-1.
In some embodiments of the disclosure, the MIP inequality constraints 1266-2 include one or multiple linear inequality constraints to enforce the relationship between traffic light states and individual traffic light signal values, for example,
where the matrix Fsd∈{0,1} defines a mapping between multiple collision-free traffic light states and individual traffic light signal values for all states s∈ and all directions d∈
in each traffic intersection j∈
, for example, see the mapping 830 in
ΦjS=1 for each traffic intersection j∈
at each time step t∈
0N in a prediction time window of an ITC in the hierarchical traffic control system.
In some embodiments of the disclosure, additional binary variables δi,jd(t)∈{0,1} are added to the optimization variables of the MIP problem 1266 to represent the presence of a vehicle i∈ inside of a traffic intersection j∈
at a time step t∈
0N. As part of the predicted or planned routing inputs to each ITC in the hierarchical traffic control system, according to some embodiments of the disclosure, fixed binary values ai,jd∈{0,1} are given to indicate whether a vehicle i∈
intends to cross a traffic intersection j∈
in a particular crossing direction d∈
. For each vehicle i∈
, each ITC knows the position in relative coordinates at which the vehicle enters Pi,jin and exits Pi,jout each of the traffic intersections. Therefore, in some embodiments of the disclosure, the MIP 1266 includes the following bi-conditional constraints to define the binary variables δi,jd(t)∈{0,1}, i.e.,
The latter bi-conditional constraints can be implemented, for example, using a big-M formulation in multiple mixed-integer inequality constraints 1266-2 as
where M>0 is a large constant value, δi,jl(t), δi,ju(t)∈{0,1} are auxiliary binary variables that are added to the optimization variables of the MIP 1266, and siδ(t)≥0 denotes a continuous slack variable that is added to the optimization variables of the MIP problem 1266 for each vehicle i∈ and each time step t∈
0N to ensure feasibility of the MIP problem 1266 in the presence of model mismatch and disturbances.
In some embodiments of the disclosure, we can impose an upper bound on the maximum number of vehicles that can be inside each traffic intersection of the transportation network at each time step t∈0N in the prediction time window of the ITC, for example, using a mixed-integer inequality constraint 1266-2 as
where Cjd defines a maximum traffic intersection capacity limit (upper bound based on physical intersection dimensions) for a specific direction d∈ and ψjd(t) defines the traffic light signal value for that crossing direction, i.e., ψjd=0 (red) or ψjd=1 (green). The latter mixed-integer inequality constraint 962 additionally ensures that vehicles can only enter the intersection if the corresponding traffic light signal value is green, i.e., if ψjd=1.
In some embodiments of the disclosure, a safe reference velocity vis(t) is computed for each HDV i∈h, which is used to predict HDV motion trajectories depending on a mode in the switched dynamical prediction model for the HDV. Therefore, in some embodiments of the disclosure, additional binary variables bif(t), bix(t)∈{0,1} are added to the optimization variables of the MIP 1266 to model switching between different modes in the switched dynamical prediction model for HDVs, i.e., indicating whether an HDV i∈
h is in the lead vehicle following mode or stopping for red traffic light mode. For example, for each HDV i∈
h, we introduce the index il∈
to denote its leading vehicle, if a vehicle exists ahead of the HDV i∈
h within a predetermined safety distance, and the leading vehicle could be either a CAV or an HDV in the transportation network. In some embodiments of the disclosure, a safe following distance is defined as a base value Df plus a velocity-dependent component with coefficient kf. In some embodiments of the disclosure, the MIP problem 1266 includes the following bi-conditional constraints to define the binary variables bif(t)∈{0,1}, i.e.,
where Rih and its leading vehicle il∈
, and where Li
In some embodiments of the disclosure, the binary indicator variables bix(t)∈{0,1} are defined for an HDV stopping at a red traffic light, using a state of the associated traffic light signal and a set membership of the HDV in the braking region prior to the traffic intersection in the transportation network. Therefore, some embodiments of the disclosure include two additional binary variables bil(t)∈{0,1} and biu(t)∈{0,1} such that the HDV i∈h is inside of the braking region when both these binary variables are equal to 1 for the next traffic intersection in the transportation network along the predicted route of the HDV. For each HDV i∈
h, we denote an initial distance to the next traffic intersection as Pitl, and a safe stopping distance is defined using a base value DI plus a velocity-dependent component with coefficient kI. In some embodiments of the disclosure, the MIP 1266 includes the following implication constraints to define the binary variables bil(t), biu(t), bix(t)∈{0,1}, i.e.,
where j∈ denotes the next traffic intersection such that the HDV stops if and only if the HDV is inside the braking region and the traffic light is red for the corresponding crossing direction of the HDV i∈
h. The latter implication constraints can be implemented, for example, using a big-M formulation in multiple mixed-integer inequality constraints 1266-2 as
where we omit the time index t for a compact notation.
In some embodiments of the disclosure, the safe reference velocity vis(t) for HDV i∈h is defined based on the indicator variables bif(t), bix(t)∈{0,1}, using the following implication constraints in the MIP 1266, i.e.,
where vi for HDV i∈
h, and the value {right arrow over (v)} denotes a desired target speed for the HDV. The latter implication constraints can be implemented, for example, using a big-M formulation in multiple mixed-integer inequality constraints 1266-2 as
where we omit the time index t for a compact notation.
Some embodiments of the disclosure include two additional binary variables bimax(t), bimin(t)∈{0,1} in order to impose maximum acceleration and maximum deceleration constraints for the HDV i∈h, i.e., the HDV velocity prediction model can be implemented using following implication constraints in the MIP problem 1266
Some embodiments of the disclosure include additional binary variables lj,stl(t)∈{0,1} in the optimization variables of the MIP 1266 for each collision-free traffic light state s∈ of each traffic intersection j∈
, for example, lj,stl(t)=1 if and only if the traffic light state changes, and this can be implemented using multiple mixed-integer inequality constraints 1266-2 as
In addition, in some embodiments of the disclosure, an additional binary variable {circumflex over (l)}jtl(t)∈{0,1} is added to the optimization variables of the MIP problem 1266 to denote if the overall state of the traffic intersection j∈ has changed at each time step t∈
0N, for example, this can be implemented using multiple mixed-integer inequality constraints 1266-2 as
In some embodiments of the disclosure, using the binary variable {circumflex over (l)}jtl(t)∈{0,1}, an additional timer state variable tjtl(t) can be defined in the optimization variables of the MIP problem 1266 using update and/or reset constraints that can be implemented using multiple mixed-integer inequality constraints 1266-2 as
In some embodiments of the disclosure, the constraints of the MIP problem 1266 include one or multiple traffic light timing constraints to impose a minimum time between two consecutive traffic light change commands as well as an upper bound for the timer state variable as follows
In some embodiments of the disclosure, the objective function 1266-1 of the MIP problem 1266 is defined as a maximization of the following reward function
with user-defined weight values wi≥0 for i=1, . . . , 5. According to some embodiments of the disclosure, the first term in the latter reward function aims to maximize the traveled distance pi(t) for all vehicles i∈ in the transportation network that is controlled by the hierarchical traffic control system. The second term aims to penalize vehicles for not being in their preferred lane by minimizing |σi(t)−σiref(t)|, in which the absolute value can be implemented by defining auxiliary optimization variables in the MIP formulation 1266. The third and fourth terms aim to penalize unnecessary lane changes by minimizing the sum of the binary variables li,uc(t), li,dc(t) over the prediction time window of an ITC 408 or 410. Finally, the fifth and sixth terms aim to penalize a similar sum of continuous slack variables siδ(t), sic(t)≥0 that ensure feasibility of the MIP 1266 in the presence of model mismatch and disturbances. In some embodiments of the disclosure, large penalty weight values w4, w5»0 are used to ensure that a solution with zero slack variables, i.e., with siδ(t)=0 and sic(t)=0 is computed, whenever feasible.
Some embodiments of the disclosure are based on the realization that the prediction time window for the CTC 404 may be longer than the prediction time window for each of the ITCs 408 or 410 in the hierarchical traffic control system 600A that controls the mixed traffic in a transportation network of multiple interconnected traffic intersections, due to the use of the macroscopic traffic flow model and the use of convex relaxations of the non-convex traffic rules in the CTC 404 that results in a convex optimization problem 1158 that is computationally much easier to solve compared to the MIP formulation 1266 that is solved in each ITC 408 or 410.
In some embodiments, the mixed-integer optimization (minimization) problem 1266 can be solved using a branch-and-bound (B&B) optimization method that searches for a global optimal solution within a search space to produce an optimal control signal, where the B&B optimization iteratively partitions the search space into a nested tree of regions to find a solution with a globally optimal (minimal) objective value. The B&B method iteratively solves convex relaxations to compute lower bounds for the objective value within a region from the nested tree of regions. One or multiple regions can be pruned when the corresponding lower bounds are greater than the currently known upper bound to the globally optimal objective value. The upper bound to the globally optimal objective value can be updated when an integer feasible solution is found with an objective value that is smaller than the currently known upper bound to the globally optimal objective value.
Some embodiments of the disclosure are based on the realization that redundant optimization variables may be removed automatically by a pre-solve routine in the numerical optimization algorithm that is used to solve the MIP problem 1266 in the hierarchical traffic control system 600A. In some embodiments, one or multiple redundant optimization variables may be fixed explicitly to a particular value by adjusting the corresponding simple bounds for each redundant optimization variable in the MIP problem 1266. Some embodiments of the disclosure are based on the realization that, after fixing one or multiple binary optimization variables, one or multiple of the corresponding inequality constraints may become redundant and they may be removed by setting the corresponding lower bound values to −∞ and/or by setting the corresponding upper bound values to ∞.
Some embodiments of the disclosure are based on the realization that a switched dynamical prediction model may be used in each ITC for both HDVs and for CAVs that are controlled by a different ITC in the hierarchical traffic control system. For example, each CAV could be assigned to one ITC “for control”, and the same CAV could be assigned to one or multiple other ITCs “for prediction” in order to increase control performance and safety for all vehicles, especially when vehicles transition from one ITC to the next ITC in the transportation network.
In some embodiments, each of the vehicles i∈ is assigned to one or multiple subsets of vehicles, i.e.,
j for each traffic intersection that is controlled by an ITC j∈
in the transportation network. For example, this assignment can be computed based on the following set of rules
In some embodiments of the disclosure, a CAV 1331 and/or an HDV 1332 that is currently not within a predetermined distance from any of the traffic intersections in the transportation network is currently not assigned to any of the ITCs in the hierarchical traffic control system, and it is therefore not included in the MIP formulation 1266 of any of the ITCs. However, the CAV 1331 and/or HDV 1332 can be assigned to an ITC at a future time step, when it is within a predetermined distance from any of the traffic intersections in the transportation network.
Some embodiments are based on the realization that the latter set of rules for assignment of vehicles to ITCs can ensure that the velocity commands and lane change commands for each CAV are computed by at most one ITC in the hierarchical traffic control system. And if a CAV is not assigned to any ITC, given the predetermined threshold distance, then control is returned to the on-board control architecture of the CAV, according to some embodiments of the disclosure. In some embodiments of the disclosure, considering the region immediately after a traffic intersection, both HDVs and CAVs are treated equally in the MIP formulation 1266 of an ITC and their behavior is predicted to prevent possible collisions with any vehicles further upstream. In some embodiments of the disclosure, each ITC provides control commands to CAVs only prior to the traffic intersection and while the vehicle is physically within the traffic intersection. Control is handed back to the vehicle or it is handed to the ITC corresponding to the next traffic intersection after the CAVs exit the intersection.
For example, the partition P1 1401 represents a discrete search region that can be split or branched into two smaller partitions or regions P2 1402 and P3 1403, i.e., a first and a second region that are nested in a common region. The first and the second region are disjoint, i.e., the intersection of these regions is empty P2∩P3=ϕ 1407, but they form the original partition or region P1 together, i.e., the union P2∪P3=P1 1406 holds after branching. The branch-and-bound method then solves an integer-relaxed optimization problem for both the first and the second partition or region of the search space, resulting in two solutions (local optimal solutions) that can be compared against each other as well as against the currently known upper bound value to the optimal objective value. The first and/or the second partition or region can be pruned if their performance metric is less optimal than the currently known upper bound to the optimal objective value of the MIP problem. The upper bound value can be updated if the first region, the second region or both regions result in a discrete feasible solution to the MIP problem. The branch-and-bound method then continues by selecting a remaining region in the current nested tree of regions for further partitioning.
While solving each partition may still be challenging, it is fairly efficient to obtain local lower bounds on the optimal objective value, by solving local relaxations of the mixed-integer program (MIP) or by using duality. If the MIP solver happens to obtain an integer-feasible solution while solving a local relaxation, the MIP solver can then use it to obtain a global upper bound for the mixed-integer solution of the original MIP problem in the hierarchical traffic control system. This may help to avoid solving or branching certain partitions that were already created, i.e., these partitions or nodes can be pruned. This general algorithmic idea of partitioning can be represented as the binary search tree 1400A, including the root node, e.g., P1 1401 at the top of the tree, and the leaf nodes, e.g., P4 1404 and P5 1405 at the bottom of the tree. In addition, the nodes P2 1402 and P3 1403 are typically referred to as the direct children of node P1 1401, while node P1 1401 is referred to as the parent of nodes P2 1402 and P3 1403. Similarly, nodes P4 1404 and P5 1405 are children of their parent node P2 1402. In some embodiments of the disclosure, the MIP problem can be a mixed-integer linear programming (MILP) or mixed-integer quadratic programming (MIQP) problem.
As long as the gap between the lower and upper bound value is larger than a particular tolerance value at step 1411, and a maximum execution time is not yet reached by the optimization algorithm, then the branch-and-bound method continues to search iteratively for the mixed-integer optimal solution 1455. Each iteration of the branch-and-bound method starts by selecting the next node in the tree, corresponding to the next region or partition of the integer variable search space, with possible variable fixings based on pre-solve branching techniques 1415. After the node selection, the corresponding integer-relaxed problem is solved, with possible variable fixings based on post-solve branching techniques 1420.
If the integer-relaxed problem has a feasible solution, then the resulting relaxed solution provides a lower bound on the objective value for that particular region or partition of the integer variable search space. At step 1421, if the objective is determined to be larger than the currently known upper bound for the objective value of the optimal mixed-integer solution, then the selected node is pruned or removed from the branching tree 1440. However, at step 1421, if the objective is determined to be lower than the currently known upper bound, and the relaxed solution is integer feasible 1425, then the currently known upper bound and corresponding mixed-integer solution estimate is updated at step 1430.
If the integer-relaxed problem has a feasible solution and the objective is lower than the currently known upper bound 1421, but the relaxed solution is not yet integer feasible, then the global lower bound for the objective can be updated 1435 to be the minimum of the objective values for the remaining leaf nodes in the branching tree and the selected node is pruned from the tree 1440. In addition, starting from the current node, a discrete variable with a fractional value is selected for branching according to a particular branching strategy 1445, in order to create and append the resulting subproblems, corresponding to regions or partitions of the discrete search space, as children of that node in the branching tree 1450.
An important step in the branch-and-bound method is how to create the partitions, i.e., which node to select 1415 and which discrete variable to select for branching 1445. Some embodiments are based on branching one of the binary optimization variables with fractional values in the integer-relaxed solution. For example, if a particular binary optimization variable d∈{0,1} has a fractional value as part of the integer-relaxed optimal solution, then some embodiments create two partitions of the mixed-integer program by adding, respectively, the equality constraint d=0 to one subproblem and the equality constraint d=1 to the other subproblem. Some embodiments are based on a reliability branching strategy for variable selection 1445, which aims to predict the future branching behavior based on information from previous branching decisions.
Some embodiments are based on a branch-and-bound method that uses a depth-first node selection strategy, which can be implemented using a last-in-first-out (LIFO) buffer. The next node to be solved is selected as one of the children of the current node and this process is repeated until a node is pruned, i.e., the node is either infeasible, optimal or dominated by the currently known upper bound value, which is followed by a backtracking procedure. Instead, some embodiments are based on a branch-and-bound method that uses a best-first strategy that selects the node with the currently lowest local lower bound. Some embodiments employ a combination of the depth-first and best-first node selection approach, in which the depth-first node selection strategy is used until an integer-feasible solution is found, followed by using the best-first node selection strategy in the subsequent iterations of the branch-and-bound based optimization algorithm. The latter implementation is motivated by aiming to find an integer-feasible solution early at the start of the branch-and-bound procedure (depth-first) to allow for early pruning, followed by a more greedy search for better feasible solutions (best-first).
The branch-and-bound method continues iterating until either one or multiple of the following conditions have been satisfied:
The maximum execution time for the processor is reached.
All the nodes in the branching search tree have been pruned, such that no new node can be selected for solving convex relaxations or branching.
The optimality gap between the global lower and upper bound value for the objective of the mixed-integer solution is smaller than the tolerance.
Some embodiments are based on the realization that the optimization problems for the CTC controller and/or for the ITC controllers can be solved exactly or inexactly. Exact solutions are feasible and locally or globally optimal, while inexact solutions can be approximately feasible and/or suboptimal. Examples of exact optimization algorithms are interior point methods, active-set methods, gradient methods, operator splitting methods, sequential quadratic programming, sequential convex programming, branch-and-bound, branch-and-cut and branch-and-price methods. Examples of inexact optimization algorithms are heuristic rules, early termination of exact optimization algorithms, rounding methods, machine learning-based approximations of optimal solutions, approximate dynamic programming, etc.
In some embodiments, the CTC and/or the ITC control policies can be approximated by a deep neural network architecture, for example, using reinforcement learning to directly maximize a reward function for reducing congestion, travel time, emissions and energy consumption in the transportation network. In other embodiments, the CTC and/or the ITC control policies can be implemented using a deep neural network architecture, based on imitation learning that aims to approximate expert solutions of the corresponding optimization problems using exact optimization algorithms.
The hierarchical traffic control system 1500 comprises a number of interfaces connecting the decision making system 1500 with other systems and devices. For example, the decision making system 1500 comprises a network interface controller (NIC) 1502 that is adapted to connect the decision making system 1500 through a bus 1504 to a network 1506 connecting the decision making system 1500 with one or more devices 1508. Examples of such devices include, but are not limited to, vehicles, traffic lights, traffic sensors, road-side units (RSUs), mobile edge computers (MECs), and passengers' mobile devices. Further, the decision making system 1500 includes a transmitter interface 1510, using a transmitter 1512 and/or one or multiple of the devices 1508, configured to transmit an optimal sequence of entering and exiting times and average velocities 1522 and/or a velocity profile, one or multiple lane change commands and a sequence of planned stops 1524, determined by one or multiple processors 1514, to each of the connected and automated vehicles (CAVs) along its future planned route in the transportation network. In each of the CAVs, the commands received from the hierarchical traffic control system can be used by a multi-layer guidance and control architecture to control the motion of the vehicle in order to improve overall safety, time and energy efficiency of the traffic flow in the transportation network.
In some embodiments of the disclosure, the decision making system 1500 includes a transmitter interface 1510, using a transmitter 1512 and/or one or multiple of the devices 1508, which is additionally configured to transmit an optimal sequence of traffic light change commands, determined by one or multiple processors 1514, to each of the traffic light controllers (TLCs) over a prediction time window in the transportation network of interconnected traffic intersections.
Through the network 1506, the hierarchical traffic control system 1500 receives real-time traffic data 1532 using a receiver interface 1528 connected to a receiver 1530. The decision making system 1500 can receive traffic information for one or multiple of the interconnected conflict zones and road segments in the transportation network. The traffic data 1532 can include information of vehicle states (e.g., acceleration, location, heading, velocity) and of planned and/or predicted future routes (e.g., sequence of future road segments, track lanes, desired destinations, waiting times) for each of the vehicles in the transportation network. Additionally, or alternatively, the decision making system 1500 can include a control interface 1534 configured to transmit commands to the one or multiple devices 1508 to change their respective state, such as acceleration, velocity, and the like. The control interface 1534 may use the transmitter 1512 to transmit the commands and/or any other communication means.
In some embodiments of the disclosure, a human machine interface (HMI) 1540 connects the decision making system 1500 to a keyboard 1536 and pointing device 1538, wherein the pointing device 1538 can include a mouse, trackball, touchpad, joy stick, pointing stick, stylus, or touchscreen, among others. The decision making system 1500 can also be linked through the bus 1504 to a display interface adapted to connect the decision making system 1500 to a display device, such as a computer monitor, camera, television, projector, or mobile device, among others. The decision making system 1500 can also be connected to an application interface adapted to connect the decision making system 1500 to one or more equipment for performing various power distribution tasks.
The decision making system 1500 can include one or multiple processors 1514 configured to execute stored instructions, as well as a memory (at least one memory) 1516 that stores instructions that are executable by the processor (at least one processor) 1514. The processor(s) 1514 can be a single core processor, a multi-core processor, a computing cluster, a network of multiple connected processors, or any number of other configurations. The memory 1516 can include random access memory (RAM), read only memory (ROM), flash memory, or any other suitable memory systems. The processor(s) 1514 can be connected through the bus 1504 to one or more input and output devices. These instructions implement a method for hierarchical traffic control, using one centralized traffic controller (CTC) and one or multiple intersection traffic controllers (ITCs), to control mixed traffic of CAVs and HDVs in a transportation network of multiple interconnected traffic intersections. In some embodiments of the disclosure, the decision making system 1500 includes a map configuration 1518. For example, the map configuration 1518 can include location data (e.g., GPS data) for conflict-free road segments, traffic intersections, stopping zones, conflict zones and lanes within each of the road segments of the transportation network.
The decision making system 1500 includes constraints and objectives 1520 of one or multiple MIP problems 1266 and constraints and objectives 1520 of the convex optimization problem 1158 that are solved at each time step of the hierarchical traffic control system. For example, the constraints and objectives 1520 can be configured to enforce physical limitations, vehicle speed limits and/or safety constraints, and to minimize a weighted combination of travel times, waiting times and/or energy consumption for each of the vehicles in the transportation network.
The vehicle can also include an engine 1606, which can be controlled directly by the multi-layer guidance and control architecture 1602 or by other components of the vehicle 1601. The vehicle can also include one or more on-board sensors 1604 to sense the surrounding environment. Examples of the sensors 1604 include distance range finders, radars, lidars, and cameras. The vehicle 1601 can also include one or more on-board sensors 1605 to sense its current motion quantities and internal status. Examples of the sensors 1605 include global positioning system (GPS), accelerometers, inertial measurement units, gyroscopes, shaft rotational sensors, torque sensors, deflection sensors, pressure sensors, and flow sensors. The on-board sensors provide information to the multi-layer guidance and control architecture 1602. The vehicle can be equipped with a transceiver 1608 enabling communication capabilities for the multi-layer guidance and control architecture 1602 through wired or wireless communication channels, e.g., for the vehicle 1601 to communicate with the hierarchical traffic control system, according to some embodiments of the disclosure.
The following description provides exemplary embodiments only, and is not intended to limit the scope, applicability, or configuration of the disclosure. Rather, the following description of the exemplary embodiments will provide those skilled in the art with an enabling description for implementing one or more exemplary embodiments. Contemplated are various changes that may be made in the function and arrangement of elements without departing from the spirit and scope of the subject matter disclosed as set forth in the appended claims.
Specific details are given in the following description to provide a thorough understanding of the embodiments. However, understood by one of ordinary skill in the art can be that the embodiments may be practiced without these specific details. For example, systems, processes, and other elements in the subject matter disclosed may be shown as components in block diagram form in order not to obscure the embodiments in unnecessary detail. In other instances, well-known processes, structures, and techniques may be shown without unnecessary detail in order to avoid obscuring the embodiments. Further, like reference numbers and designations in the various drawings indicate like elements.
Also, individual embodiments may be described as a process which is depicted as a flowchart, a flow diagram, a data flow diagram, a structure diagram, or a block diagram. Although a flowchart may describe the operations as a sequential process, many of the operations can be performed in parallel or concurrently. In addition, the order of the operations may be re-arranged. A process may be terminated when its operations are completed but may have additional steps not discussed or included in a figure. Furthermore, not all operations in any particularly described process may occur in all embodiments. A process may correspond to a method, a function, a procedure, a subroutine, a subprogram, etc. When a process corresponds to a function, the function's termination can correspond to a return of the function to the calling function or the main function.
Furthermore, embodiments of the subject matter disclosed may be implemented, at least in part, either manually or automatically. Manual or automatic implementations may be executed, or at least assisted, through the use of machines, hardware, software, firmware, middleware, microcode, hardware description languages, or any combination thereof. When implemented in software, firmware, middleware or microcode, the program code or code segments to perform the necessary tasks may be stored in a machine readable medium. A processor(s) may perform the necessary tasks.
Various methods or processes outlined herein may be coded as software that is executable on one or more processors that employ any one of a variety of operating systems or platforms. Additionally, such software may be written using any of a number of suitable programming languages and/or programming or scripting tools, and also may be compiled as executable machine language code or intermediate code that is executed on a framework or virtual machine. Typically, the functionality of the program modules may be combined or distributed as desired in various embodiments.
The above-described embodiments of the present disclosure can be implemented in any of numerous ways. For example, the embodiments may be implemented using hardware, software or a combination thereof. When implemented in software, the software code can be executed on any suitable processor or collection of processors, whether provided in a single computer or distributed among multiple computers. Such processors may be implemented as integrated circuits, with one or more processors in an integrated circuit component. Though, a processor may be implemented using circuitry in any suitable format.
Embodiments of the present disclosure may be embodied as a method, of which an example has been provided. The acts performed as part of the method may be ordered in any suitable way. Accordingly, embodiments may be constructed in which acts are performed in an order different than illustrated, which may include performing some acts concurrently, even though shown as sequential acts in illustrative embodiments.
Although the present disclosure has been described with reference to certain preferred embodiments, it is to be understood that various other adaptations and modifications can be made within the spirit and scope of the present disclosure. Therefore, it is the aspect of the appended claims to cover all such variations and modifications as come within the true spirit and scope of the present disclosure.
