Patent Application
20210097739
The invention relates to a method of constructing a model of the motion of one or more mobile devices and related systems. In particular, embodiments may utilise Simultaneous Localisation and Mapping (SLAM). More specifically, the invention relates to the handling of identified loop closures, which may or may not be correctly identified, and preferably outputs a pose graph which provides the model of the motion.
Pose graph Simultaneous Localization and Mapping (SLAM) is one of the most popular and effective techniques for robot localisation in the prior art, and has attracted significant interest over the past decade. A pose graph is usually built by sensor front-ends with edges indicating constraints (e.g. odometry observations, typically subject to long-term drift) and nodes representing robot poses or landmarks. “Pose” is typically held to comprise both position and orientation.
Loop closures occur when revisiting an area e.g. when it is identified by the front-end that a robot (or person) has returned to a location visited previously. A transformation between the pose of the robot on the first visit and the pose of the robot on the subsequent visit can therefore be calculated this transformation links nodes on two different trajectories and is therefore described as a loop closure. Loop closures are represented by inserting additional edges (or constraints) into the graph.
Conveniently, a pose graph SLAM back-end can be used to derive improved robot locations by minimising the errors of the pose graph.
In pose graph SLAM systems, incorrect loop closures can hinder optimisers from converging to correct solutions, significantly degrading both localisation accuracy and map consistency. Therefore, researchers seek to enhance their robustness in the presence of numerous false-positive loop closures. False-positive loop closures refer to loop closures that are identified by the system incorrectly, i.e. which are not true loop closures.
In typical robotic applications, platforms are equipped with highly capable sensors e.g. LIDAR and vision, which can detect loop closures with a high degree of accuracy. However, in some emerging applications using less informative sensors, e.g. the Earth's geomagnetic field for smartphone based localisation, the number of ambiguous loop closures can be disproportionately higher than the true loop closures. Existing approaches tend to fail when working with unreliable front-end systems, where a large proportion, or indeed the majority, of inferred loop closures can be incorrect.
Existing back-end optimisers are tolerant of a small proportion of incorrect loop closures. However, if the number of false-positive loop closures is excessively high (e.g. >50%) then graph optimisation can perform poorly or fail entirely.
In recent years, significant effort has been made to improve the reliability of pose graph SLAM systems by enhancing the robustness of back-ends to false-positive loop closures. Existing algorithms mostly focus on how to detect false-positive loop closures and further mitigate their impacts—see, for example:
In the past few years, several robust back-end algorithms have been proposed to tackle problems produced by false-positive loop closures. They can be roughly divided into two types in terms of the technique used:
Augmented model-based methods focus on how to model pose graph SLAM problems by taking false-positive loop closures into consideration and rejecting outliers during graph optimisation.
Sunderhauf and Protzel [1], [2] indicate that the topology of a factor graph can be partially unfixed and present the idea of Switchable Constraints (SC) where a switchable variable is given to each loop closure constraint. A constraint is turned off during optimisation once it is considered as an outlier.
Based on this work, Agarwal et al. [3] introduce Dynamic Covariance Scaling (DCS) which replaces the quadratic cost with m-estimator and reaches a faster convergence.
Olson and Agarwal [5], [6] create a mixture model by merging two different Gaussian models. Their main insight is to use a max operator between models rather than a sum operator as it can largely simplify the solution of posterior maximum likelihood.
Lee et al. [7] model the robust back-end problem as a Bayesian network and apply the Classification Expectation Maximisation algorithm to solve it. An additional variable is assigned as the weight of each loop closure constraint and finally the weights of outliers are decreased to mitigate the influence of outliers during optimisation.
Although the augmented model-based method can achieve superior performance with a reasonable number of false-positive loop closures, there are some drawbacks. For example, as reported in [3], DCS tends to be less effective to randomly distributed outliers. Furthermore, the approaches rely on parameter tuning.
Graph consistency-based approaches aim at selecting a subset of loop closures for pose optimisation based on consistency check. The Realizing, Reversing, Recovering (RRR) algorithm [4], [8] first divides all the loop closures into several clusters according to timestamps and then applies a number of χ2 tests to check both the intra and inter cluster consistency. The individual loop closures in a cluster or the entire cluster with high χ2 errors are rejected.
More recently [9] and [10] also focus on graph consistency. However, unlike RRR, they search for the largest consistent subset of the constraints.
There are also some other works which do not belong to the above two categories. Segal et al. [11] propose an optimisation approach which applies hybrid inference on the Bayes tree. It combines non-linear least squares with discrete inference and uses discrete states to enable or disable measurements. Fourie et al. [12] propose a non-parametric method and obtain a more general solution to the Bayes Tree.
Although these approaches have contributed towards accurate localisation, it is still challenging for the approaches to operate in the presence of numerous false-positive loop closures.
Embodiments described herein therefore aim to ameliorate at least some of the problems described above and/or provide a method/system that more accurately localises within an environment.
According to a first aspect of the invention, there is provided a computer-implemented method of constructing a model of the motion of a mobile device. The method may comprise using a sensor of the device to obtain data providing an estimated pose of the mobile device; the data may be referred to as positional data. An initial graph is then generated which may be based upon the positional data from the sensor, nodes of which graph provide a series of possible poses of the device, and edges of which graph represent odometry and/or loop closure constraints. The method may then process the graph to estimate confidence scores for each loop closure. Typically, the confidence score is generated by performing pairwise consistency tests between each loop closure and a set of other loop closures. Conveniently, the method then generates an augmented graph from the initial graph.
Generating the augmented graph may comprise retaining and/or deleting each loop closure based upon the confidence scores.
Generation of the augmented graph may further include the step of inserting artificial loop closure edges into the graph between pairs of retained loop closures. In such embodiments, the artificial loop closures may be created by selecting one or more pairs of nodes of the graph and calculating an edge to link the pair of nodes, each new edge representing a new loop closure. The artificial edges may be calculated by determining a transformation that transforms the pose of a first node of the pair to a pose of second node of the pair.
The consistency checks performed between pairs of nodes may be spatial consistency checks.
The estimated pose of the mobile device may be determined relative to one or more of:
A loop closure may be deleted from the graph if its confidence score is below a first level. The first level may be fixed or learned. In such embodiments, a loop closure may be retained if the confidence score is above the first level.
The loop closures may be clustered into two groups using k-means clustering or other clustering. The loop closures in the group, generated by the clustering, with the lower centre value of the two groups may be deleted from the graph. The group with the lower centre value may be described as the outlier group. A loop closure may be retained if it is in the group with the higher centre value. The group with the higher centre value may be described as the inlier group.
A pair of loop closures may be used to seed the generation of artificial loop closures if the relevant confidence scores are above a second level. The second level may be fixed or learnt from the data.
In embodiments using k-means clustering, the second level may be the centre value of the retained group (the inlier group).
The method may further comprise using the augmented graph to generate a model of the internals of a building. The model may be thought of as a map or the like.
The method may further comprise using the augmented graph to allow a first device of the one or more mobile devices to localise itself with respect to the trajectories of the other mobile devices.
The device may be a mobile telephone, smart watch, inertial measurement unit (IMU), or smart camera.
The device may be arranged to be carried by a person, robot, or vehicle.
The device may be, or may be a part of, a vehicle or robot able to move itself.
According to a second aspect of the invention, there is provided a machine-readable medium containing instructions which, when read by a processor, cause that processor to implement the method of the first aspect of the invention.
According to a third aspect of the invention, there is provided system comprising a processor arranged to perform at least one of the following steps:
The processor may be arranged to insert artificial loop closures into the graph between pairs of retained loop closures. The processor may be further arranged to identify a subset of the retained loop closures based on the confidence scores, and to use only loop closures in the subset of the retained loop closures to seed artificial loop closures.
The system may further comprise the mobile device. The mobile device may comprise, or have mounted thereon, the sensor which is arranged to provide the positional data.
The system may be provided by the mobile device. The mobile device may comprise, or have mounted thereon:
The steps may be split between a plurality of processors; any reference above to “a processor” may therefore equivalently mean two or more processors sharing the processing.
Since no algorithm can easily remove all false-positive loop closures, pose graph SLAM systems can be made more robust by enlarging the proportion of inliers, namely correct loop closures, to outliers (false-positive loop closures) within pose graphs. To this end, techniques disclosed herein may not only reject false-positive loop closures, but also inject additional true-positive loop closures by reinforcing loop closures that are highly consistent with one another. The results discussed herein demonstrate how this novel combination of approaches can yield benefits in the face of high proportions of erroneous loop closures.
Aspects and/or embodiments may provide at least one of the following contributions:
The skilled person would understand that features described with respect to one aspect of the invention may be applied, mutatis mutandis, to the other aspects of the invention.
The machine readable medium referred to in any of the above aspects of the invention may be any of the following: a CDROM; a DVD ROM/RAM (including −R/−RW or +R/+RW); a hard drive; a memory (including a USB drive; an SD card; a compact flash card or the like); a transmitted signal (including an Internet download, ftp file transfer of the like); a wire; etc.
There now follows by way of example only a detailed description of embodiments of the present invention with reference to the accompanying drawings in which:
The embodiment being described implements a middle layer, embedded between front- and back-ends, to boost the robustness of a SLAM (Simultaneous Localisation And Mapping) system. In many embodiments, the embedding is such that identical front- and back-ends can be used as in the prior art. The skilled person will appreciate that embodiments need not be implemented in a so-called middle layer and could be provided as part of other elements, or indeed in other topologies.
Embodiments are described in relation to the localisation of one or more devices moving in an environment. Here, a device may be any device capable of providing data giving an estimate of the device position; i.e. positional data. Such a device may be carried by a person (e.g. smartphone/smartwatch), a robot (e.g. ground/aerial) or an object (e.g. wheelchair). The skilled person will appreciate that there is a level of uncertainty in the data provided by any sensor, and whilst some sensor modalities are more accurate than others, the positional data will only give an estimate of the device position. The positional data may be generated from any suitable sensor but in particular the sensor may be any of the following examples: magnetometers; accelerometers, gyroscopes, WIFI, GSM (Global System for Mobile communication), UMTS (Universal Mobile Telecommunication System), LTE (Long Term Evolution), cameras, GPS (Global Positioning System—including GLONASS, Galileo, BeiDou-2, etc.), LiDAR (Light Detection and Ranging), cameras, and the like.
Conveniently, the device is arranged to process positional data locally using processing circuitry that is part of that device. However, it is conceivable that the positional data is processed remote from the device, or indeed partially processed on the device and partially processed remote from the device. The skilled person will appreciate how to modify embodiments to split the processing between devices and in view of this the following description is agnostic as to where the processing is performed. The skilled person will appreciate that a mobile device may simply gather and transmit sensor data for remote processing, and may not perform any significant data processing locally.
Embodiments which process positional data remotely will typically have a network connection thereto. Such a network connection will likely be provided by technologies including GSM; UMTS; LTE; WIFI; Bluetooth; or the like.
In summary, embodiments are arranged to alter a pose graph (conveniently referred to as a graph herein). Conveniently, the pose graph is generated by a front-end. Further conveniently, the altered graph can then be optimised by a back-end system.
Extensive experiments have been conducted to demonstrate the significantly improved accuracy and robustness compared with state-of-the-art methods and various back-ends, verifying the effectiveness of the proposed approach (see
For the avoidance of doubt,
The embodiment being described therefore does not model the environment 102 per se, but rather the motion of one or more devices 101 in the environment. The skilled person will appreciate that, indirectly, this can allow estimation of an approximate map of the environment 102, especially when a large number of devices 101 or of trajectories of the same device 101 pass through the environment. For example, this could be used for the generation of approximate floorplans based on crowdsourced data, or other collection mechanisms of data.
Three loop closures, L1, L2 and L3, are marked, where a loop closure, as the skilled person will appreciate, can be thought of as a determination that the device has previously visited that location, within a degree of confidence.
In
Although the longest loop closure (L3) in
The same applies to newly inserted (artificial) loop closures; in embodiments being described, a transformation for an artificial loop closure is calculated with a probability propagation method, for example an RTS smoother.
The skilled person will appreciate that a distance between two end-points of a loop closure is not necessarily short the nodes do not necessarily have to be physically “close”. Where the transformation indicated by the loop closure is similar to ground truth, the loop closure is correct. In
Many false positives result from two places which are far from each other but which have certain features in common; similar observations of the two different places can be obtained due to insufficient features in the observation, leading the approach used to think that the two places are close or the same.
Further, the definition of “close” can vary between embodiments, and it is not necessary for the two poses to be physically close (there may be no specific requirement on distance, such as 1 or 2 meters). Whether or not there is a loop closure may, in some embodiments, be determined by the confidence in the positional data, or other similar constraints. The loop closure expresses the transformation (position and orientation) constraint between two poses (from single or multiple devices). Once the transformation can be calculated accurately, the physical distance is not important.
In the embodiment being described, this is normally assessed in two steps:
The same applies for the artificial loop closures discussed below and their transformations are calculated with a probability propagation method in this case an Rauch-Tung-Striebel (RTS) smoother.
In
In
It can be seen that the system architecture 300 of the embodiment being described (one implementation of the embodiments provided here is provided by the Graph-Tinker (GTk) algorithm provided by the inventors) has an extra portion 310 as compared to the prior art system architecture 30. That is, the embodiment being described is implemented as a middle layer 310 between a SLAM front-end 24 and back-end 38.
The prior art architecture 30 takes raw data 32 and passes this to a SLAM front-end 34. An initial graph 37 (a pose graph) is then formed by a graph module 36 of the front-end 34, the initial graph 37 including pose nodes, odometry edges and loop-closure edges. The pose nodes may conveniently be referred to as nodes and provide what may be thought of as a possible position and orientation of the device at a given instance.
Typically, a node has an associated probability function that gives the probability of a device being at that position. In the pose graph of the embodiment being described, all the nodes are modelled as a Gaussian distribution which uses a mean and covariance matrix to represent the probability of the position or pose of this node.
This graph 37 is then passed to a SLAM back-end 38. The SLAM back-end 38 performs further processing and outputs a final graph 39.
In the embodiment being described, the same raw data 32 is passed to a SLAM front-end 34, in the same manner as in the prior art. Indeed the front-end 34 may be the same front end as that used in the prior-art. Should the same front end be used, the same graph 37 as for the prior art system 30 is then formed by the graph module 36 of the front-end 34, the graph 37 including pose nodes, odometry edges and loop-closure edges.
However, in the embodiment being described, this initial graph 37 is not passed directly to the back-end 38, but rather to a middle layer 310.
As described in more detail below, the middle layer 310 performs outlier rejection at an outlier rejection module 302. The outlier rejection module 302 detects and eliminates inconsistent loop closures (i.e. outliers—for example line 303 which may be thought of as being equivalent to the loop closure L3 of
Inlier injection is then performed on the consistent subgraph 305 by an inlier injection module 306. A set of artificial loop closures are reconstructed and inserted through the inlier injection module 306, generating 308 an augmented graph 307.
The augmented graph 307 includes pose nodes, odometry edges, consistent loop closures (the original loop closures deemed to be correct) and injected loop closures (loop-closures generated based on the original loop closures deemed to be correct). The injected loop closures within the augmented graph 307 facilitate a more robust output from the back-end 38 in view of more positive loop closures (see for example region 311 of graph 307).
In the embodiment being described, the augmented graph 307 is then passed to the back-end 38 as used in the prior art architecture 30. As the augmented graph 307 is more accurate than the first (initial) graph 37, the final graph 309 output by the back-end 38 in the embodiment being described is different from that output by the prior art system 30, even if an identical back-end 38 is used to the prior art system 30. Here, the final graph 309 provides what may be thought of as a model of the motion of the device 101 through its environment.
The skilled person will appreciate that embodiments may use trajectories of a plurality of devices a loop closure may indicate that one device, A, is in the same place as another device, B, was previously (or at least in a place sufficiently close and well-identified for a transformation between the two to be calculated with confidence); the trajectories used to form loops may not have been travelled by the same device.
The three pose graphs 37, 305, 307 give an example using the MIT-Killian-Court dataset. Dashed 303 and dash-dotted 311 lines represent false-positive and injected loop closures, respectively.
Conveniently, embodiments structure themselves as a middle layer 310 which is a complement to prior art back-ends 38, and which can operate in tandem with them. However, the skilled person will appreciate that the concepts described herein need not be so structured.
The middle layer 310 of the embodiment being described takes, as its input, an initial pose graph 36, 37 from a front end 34 (i.e., in at least this embodiment, a process that generates a pose graph 36, 37) and outputs an augmented pose graph 307 for use by the back-end 38.
From the description of
The generation of artificial loop closures can be thought of as the identification of correct but previously undetected loop-closures. The inlier injection module 306 uses the known loop closures in which there is confidence along with odometry data to establish which other pose nodes are actually nearby, and the transformations between them, and injects these as additional loop closures.
The division of loop closures into subsets (outliers, and then separating the consistent loop closures (inliers) into a subset to be used to generate artificial loop closures and the remainder) is performed as described below in the embodiment being described:
After calculating the pass rate of each loop closure, k-means clustering is used to classify all loop-closure into two groups according to the pass rate. Based on k-means, each group has a centre value. The group with a higher centre value of pass rate is regarded as the group containing correct loop-closures and is called the inlier group while the other group is call outlier group, and is rejected.
More specifically, the following steps are followed in this embodiment:
Thus, in the embodiment being described, the middle layer 310 generates what may be thought of as an augmented pose graph 307, 308, which augmented pose graph 308 is then passed to a SLAM back-end 38 for the back-end 38 to calculate appropriate device poses through optimisation. The embodiment being described used g2o in the back-end 38 (as described in R. Kummerle, G. Grisetti, H. Strasdat, K. Konolige, and W. Burgard, “g 2 o: A general framework for graph optimization,” in Robotics and Automation (ICRA), 2011 IEEE International Conference on. IEEE, 2011, pp. 3607-3613).
Further information on graph SLAM and its back end can be found in each of:
In the next subsection, methods of applying spatial consistency checks to estimate whether a loop closure is correct or not are discussed.
A spatial consistency test is applied to each pair of loop closures in the constructed graph.
Consider as a first example, and referring to
For example, starting at the initial point of trajectory T1, in any of the four sub-figures of
The top two graphs 402, 452 in
In particular, on the left hand side 400 of
L3 fails the spatial consistency test when jointly tested with any other loop closure, so is a false positive and inconsistent with the true displacement of two places.
The skilled person will appreciate that the top graph 402 is equivalent to the bottom graph 404 with a rotation and translation to set the initial position as the origin the trajectories and loop closures match the ground truth.
By contrast, on the right hand side 450 of
The intuition is that the relative poses encapsulated in the loop closure pair should be consistent with the odometry information of the outbound and inbound trajectory segments (i.e. the portions of the trajectory between pose nodes of the loop closures). Here a segment, as will be understood by the person skilled in the art, is a section (i.e. segment) of a trajectory, such as for example each T1 and T2. Two loop closures and the trajectories between them form a closed chain, or circle in the graph, as shown in
More specifically, inspiration is drawn from the statistics method in M. Mazuran, G. D. Tipaldi, L. Spinello, W. Burgard, and C. Stachniss, “A statistical measure for map consistency in slam,” in Robotics and Automation (ICRA), IEEE, 2014, pp. 3650-3655 to measure the consistency between two loop closures. For simplicity, the initial point of trajectory T1 is taken as a starting point with an initial pose vector and a zero covariance matrix. With the relative pose information provided by both odometry edges and loop closure edges, the probability distribution of final pose after traversing the circle can be calculated through dead reckoning. The relative pose and covariance matrix of the odometry edges in the inbound trajectory T2 and loop closure L1 are calculated in a reverse direction to form a unidirectional circle. Then, it can be assumed that the mean of the distribution of final pose should be close to the initial pose if these two loop closures are consistent with each other. This is because the error provided by odometry drift should be small when the distance travelled is short. Thus, a null hypothesis of a distribution where the mean is a zero vector (the same as initial pose) and the covariance is equal to the one of calculated final pose is provided. Eventually, a χ2 test is applied to check whether the final pose is accepted as the null hypothesis.
As shown in
Based on the pose nodes, odometry edges and loop closure edges, it is possible to calculate the probability distribution of a final pose matching with its initial pose.
Let p0T(u1T
(un
(l1, s1l) and
(l2, s2l) respectively. Note that the above data are all available directly in the constructed pose graph. The relative poses and covariance matrices in the inbound trajectory segment T2 and loop closure L1 are reversed to form the unidirectional circle. Define the probability distribution p0 of the initial pose as:
p
0
(m0,S0), m0=(x0,y0,θ0)T, S0=0 (1)
where 0 is a 3×3 zero matrix. Therefore, the distribution of the final pose pfin˜(mfin,Sfin) can be derived with the following chain equations:
where mk and Sk are the mean and covariance of the dead reckoning at time k, Ik and Vk are mean and covariance of the control variable at time k, and f(⋅) is device's motion model. pfin=pn
In the embodiment being described, this distribution itself is not used to provide a level of confidence as to whether two loop closures are spatially consistent, but is used as part of a test. A χ2 test is applied to decide whether the calculated distribution should be accepted as the null hypothesis where the final pose is a zero mean distribution. If mfinTSfinmfin<χ2(α) the null hypothesis is accepted and it is considered that this pair of loop closures is consistent with a confidence of 1−α. χ2(α) is the inverse function of chi-square cumulative distribution function and a is set to be 0.1 as default. The skilled person will appreciate that, in the chi-squared test, there are several commonly used value including 0.01, 0.05, 0.1. The value of 0.1 was chosen to be less strict (as compared to the other two standard values listed), but more strict, or still less strict, values could be used in other embodiments.
This confidence is given by the parameter alpha of the chi-squared test. If a small alpha is set and the pair of loop closures still passes the chi-squared test, there is a high confidence that these two loop closures are spatially consistent with each other. A confidence score may be assigned to the pair of loop closures indicating that they are consistent; this may be termed a high confidence score within the method being used.
A confidence scores for a single loop closure is calculated by performing multiple pairwise spatial consistency tests between that loop closure and other loop closures, as is discussed in more detail below.
Measuring the spatial consistency on each pair of loop closures is undesirable since long trajectory segments suffer from large accumulative drifts on odometry, leading to an inaccurate result from a spatial consistency test. Another reason is that computational overhead grows quadratically with respect to the number of loop closures. Thus, in the embodiment being described a limitation is set on the maximum distance of two trajectory segments between loop closures.
When all spatial consistency tests are finished, each loop closure L may pass np tests and fail in nf tests. It can be assumed that the ratio between np and np+nf which is named as pass rate should be similar to the true-positive rate (ratio between the number of true-positives and all the loop closures) in the graph. The intuition behind this assumption is that true-positives are more likely to be consistent with each other while a false-positive struggles to be consistent with any other loop closure. Since random outliers are the main focus in the initial graph 37, being the most common type of outliers generated by front-end systems 34, all loop closures, including true-positives and false-positives, tend to be evenly distributed in the graph 37 in some degree, especially when the number of loop closures is quite large. Therefore, the local ratio true-positive rate should be similar to the global true-positive rate. To filter out false positives, a threshold Theta based on the pass rate of each loop-closure is used; filtering out false positives may be thought of as rejecting loop closures that fall below a certain pass rate. This threshold may be fixed or it may be determined based on the pass rate values of existing loop closures by statistical methods, such as clustering (e.g. mixture of Gaussians or k-means). In the embodiment being described, k-means clustering is used.
Thus, it can be seen that the pass rate of a loop closure may be thought of as determining a confidence (or validity) score for that loop closure. This may be thought of as a level of confidence in that loop closure. The skilled person will appreciate that other functions of np and nf could be used to derive alternative metrics of confidence.
Therefore, after the above loop closure detection and selection, a consistent subgraph 305 where, at least, the majority of the loop closures are true-positive is produced. It is worth noting that it is not necessary to eliminate all false-positives at this stage because in the subsequent reconstruction steps, artificial loop closures will be constructed and injected to further reinforce true-positive loop closures of this subgraph.
This section explains how artificial loop closures are reconstructed and then introduced into a subgraph 305 previously generated with selected consistent loop closures. These artificial loop closures may be thought of as the generation of additional loop closures seeded from loop closures that have high confidence (or validity) scores (i.e. a good degree of confidence).
Each consistent loop closure is first assigned with a consistent neighbour loop closure, which is discovered by a shortest path algorithm among loop closures. More specifically, in the embodiment being described, by starting at one node of the selected loop closure, a Dijkstra's shortest path algorithm is employed to find another loop closure that is on the shortest path between the two nodes of the selected loop closure and is spatially consistent with it. The search result is accepted if and only if a unique loop closure exists on this shortest path and the length of the shortest path is under a maximum distance threshold. Thus, a pair of loop closures in the graph is selected as a candidate to seed further loop closures between them.
The reason for constructing artificial loop closures between a loop closure and its consistent neighbour rather than all consistent loop closures is that a spatial consistency test is generally more reliable when the distance traversed on the circle is shorter due to odometry drifts. As such, an advantage of constructing loop closures in this manner is that more robust artificial loop closures e.g. 311 are generated. A way of ensuring that artificial loop closures are inserted between two correct loop closures is to demand that both loop closures have high confidence (validity) scores, i.e. the confidence metric (e.g. pass rates) of both loop closures may exceed a more stringent threshold (Theta′) than the one used (Theta) to decide whether to keep or reject loop closures. This more stringent threshold can be set to a fixed value or determined based on the data via statistical methods, such as clustering (as the original threshold Theta). Theta and Theta′ may be thought of as first and second levels of confidence.
For each loop closure that has a consistent neighbour, artificial loop closures 311 are constructed on the two trajectory segments between them. To this end, two kinds of information are used. One is connectivity indicating which two pose nodes should be connected by an artificial edge, which can be calculated to link the nodes. The other is a relative transformation between the two pose nodes and its covariance matrix. To calculate them correctly, it is useful to know the relative transformation between two trajectory segments.
Since the relative transformation between the two trajectory segments can be defined by either the selected loop closure or its consistent neighbour loop closure, the one having passed more spatial consistency tests, which indicates a stronger consistency, is used. In the embodiment being described, if the two loop closures coincidentally have equal consistencies, one is randomly chosen. Then, one of the trajectory segments can be transformed to have a roughly correct relative pose with respect to another trajectory segment according to the relative transformation of the two poses of the chosen loop closure.
Once the relative transformation between two trajectory segments are known and one trajectory segment is rotated to have correct relative pose with respect to the other, the next step is to construct connectivity of artificial loop closures. Dynamic Time Warping (DTW) (see for example M. Müller, “Dynamic time warping,” Information retrieval for music and motion, pp. 69-84, 2007) is utilised to match poses of the two trajectories. Since DTW only allows associating trajectories traversed in the same direction, one trajectory segment would be reversed if the directions of two trajectory segments are different. All matches of poses between the two trajectory segments are the potential artificial loop closures, which, however, only contain connectivity without transformation and covariance information needed for a loop closure. The subsequent subsections focus on how to compute this information.
To calculate relative transformation, including translation and rotation, and corresponding covariance of each potential artificial loop closure, a graphical model is formulated as shown in
{circumflex over (L)}0, {circumflex over (L)}1, . . . , {circumflex over (L)}n are potential loop closures from the two trajectory segments T1 and T2. L0 is directly regarded as the initial artificial loop closure {circumflex over (L)}0 and Ln is modelled as the observation of the last artificial loop closure {circumflex over (L)}n.
(solid black arrows). The selected loop closure and its consistent neighbour are L0 and Ln respectively (dashed vertical arrows). Since the connectivity of all the potential artificial loop closures are established in the last step, they are represented by {circumflex over (L)}0, {circumflex over (L)}1, . . . , {circumflex over (L)}n (dash-dotted arrows) in the figure. Once the odometry information of the trajectory segments between any two loop closures is available, the distribution of one loop closure can be deduced from the distribution of the other one through probability propagation by dead reckoning. Therefore, by considering the selected loop closure L0 as the initial loop closure and its consistent neighbour Ln as the observation of the last loop closure {circumflex over (L)}n, a loop closure chain 520 as shown in the bottom part of the figure can be obtained. Thus, in the embodiment being described, all loop closures, including artificial ones and two real ones, are modelled into nodes (black and white filled circles) in the model whose relative pose and covariance will be calculated next.
The distribution of all the artificial loop closures can be calculated by dead reckoning where each loop closure rather than a pose is taken as the state variable. The probability is propagated from the initial loop closure through an Extended Rauch-Tung-Striebel (ERTS) smoother and the propagated mean and variance are constrained by the observation of the last artificial loop closures to avoid divergence. Note that all the artificial loop closure mentioned above are still potential ones.
Assume {circumflex over (L)}k˜({circumflex over (x)}k, Ŝkt), (k=0, 1, 2, . . . , n) are potential artificial loop closures where {circumflex over (x)}k and Ŝkl are the state variable and covariance to be calculated, except for the initial one which is the same as the selected loop closure, i.e. {circumflex over (L)}0=L0˜
(l0,S0l), while Ln˜
(ln,Snl), which actually is the consistent neighbour, is regarded as an observation of the last potential artificial loop closure {circumflex over (L)}n in the model. Note that all {circumflex over (x)}k, x0 and xn are vectors indicating relative poses in the loop closures while Ŝkl, S0l and Snl are covariance matrices. Furthermore, the odometry edges of trajectory segments T1 and T2 between two potential artificial loop closures are represented by oiT
(uiT
(ujT
Since a standard ERTS smoother as mentioned in S. Särkkä, “Bayesian filtering and smoothing”. Cambridge University Press, 2013, vol. 3 is applied in this embodiment, only the transition model and the observation model used in the smoother are addressed herein. The former solves the propagation from a potential artificial loop closure {circumflex over (L)}k-1 to the successor {circumflex over (L)}k with odometry edges oiT
where equation 3a is the transition from {circumflex over (L)}k-1 to {circumflex over (L)}k. Its nonlinearity is the reason why ERTS is chosen rather than RTS smoother. Matrix M is a rotation matrix and ΔθiT
The above equations propagate distributions in the forward process when there is no observation of the potential artificial loop closure. For the last loop closure {circumflex over (L)}n which has an observation Ln, the following observation model is used to execute an update step.
ŷ
n
=H{circumflex over (X)}
n
+r
n
, r
n˜(0,Snl) (4)
where matrix H is a 3×3 identity matrix, it sums up the mean value of the last potential artificial loop closure {circumflex over (L)}n with a zero-mean Gaussian noise whose covariance function is the same as the one of its neighbour, the consistent neighbour loop closure Ln. Due to the linearity, the calculation of partial derivation is avoided for the observation model.
Among all potential artificial loop closures, only a fixed percentage of them (e.g. 10%) that have the smallest uncertainties are injected into the graph 305 in the embodiment being described, producing an augmented pose graph 307 for back-ends 38. In other embodiments an amount other than 10% may be injected. For example roughly any of the following may be injected: 5%; 15% 20%, 25%.
The embodiment being described was implemented in Matlab and tested on eight public datasets.
In terms of competing approaches, RRR [8] is considered as another middle layer, and back-ends (DCS [3], SC [1] and Cauchy robust kernel—[19] P. Agarwal, “Robust graph-based localization and mapping,” PhD thesis, University of Freiburg, Germany, 2015), and open-source implementations are used. It is worth noting that further extensive experimental results can be found in a supplementary file at: https://github.com/xie9187/IROS2017-Supplementary-results.
To fairly assess the approach disclosed herein and compare it with other approaches, eight different public datasets were used for experiments. Bicocca, Bovisa04 and Bovisa06 datasets are from reference [8]. Manhattan3500Olson (M3500Olson), ringCity, city10000 and intel datasets are available in the open source package of vertigo [2] (https://openslam.org/vertigo). MIT-Killian-Court (MIT) dataset is also open source (http://www.lucacarlone.com/index.php/resources/datasets).
The databases used are listed in Table I.
In each dataset, varying numbers of additional outliers are randomly generated according to the number of original loop closures in the graph (25%, 50%, 100%, 200%). Thus for each dataset, four extra datasets are created with additional outliers. The relative pose in each outlier is sampled from a uniform distribution in Special Euclidean Group SE(2) while the information matrix is set to the average value of information matrices of original loop closures in a graph.
B. With and without Middle Layer 310
In this section, the enhanced robustness of the whole system 300 when the embodiment being described is employed as a middle layer 310 between the front- 34 and back-ends 38 is validated.
Three robust back-end algorithms, Cauchy robust kernel (Cauchy) [19], DCS [3] and SC [1], implemented in g2o and vertigo are adopted to use in conjunction with the proposed middle layer 310. The performance of these back-ends 38 is compared when they are combined with/without the middle layer 310 on all datasets with a growing number of outliers. Although experiments have been performed on all datasets with several numbers of outliers, only results from M3500Olson, ringCity and MIT datasets with 50%, 100% and 200% outliers are illustrated in Table II and
indicates data missing or illegible when filed
As shown in Table II, which lists root-mean-square errors (RMSE) for optimised pose graphs, the embodiment being described (GTk) is capable of improving, perhaps significantly, the robustness of the three robust back-ends. Although there are few cases in which the RMSE increases slightly when the embodiment being described (GTk) is applied, improvements in the robustness of the whole system 300 are generally seen, enabling back-ends 38 to converge to correct results. Moreover, RRR, applied as another middle layer, is also mentioned in this table and will be discussed more in the next subsection.
Table II-A, below, shows equivalent data for a slightly different embodiment of GTk, compared to no middle-layer and an outlier-removal only middle layer:
indicates data missing or illegible when filed
Table II-A again shoes the root-mean-square error (RMSE) of optimised pose graphs. It can be seen that, when using the proposed outlier rejection (OR) algorithm alone, the system becomes more robust to false positive loop closures than systems without a middle layer. The Table shows that, when this embodiment of GTk is applied, the robustness of the system is further enhanced, generally increasing accuracy. Although there are few cases in which the error increases slightly when this embodiment is applied, improvements in the robustness of the whole system are generally seen, facilitating back-ends converging to correct results.
Further analysis of these experiments indicated that the optimisation result is improved by the outlier rejection (OR) algorithm because it effectively removes most of the false-positive loop closures. However, since a number of true-positives are also rejected, the graph loses some essential constraints, and does not converge globally to the ground-truth. By contrast, when an embodiment including the further step of the GTk embodiment being described of inserting artificial loop closures is applied, these discarded constraints are artificially constructed by the inlier injection algorithm, which enables the back-end to converge to an accurate reconstruction. In general, it can be seen that the combination of outlier rejection and inlier insertion together can make existing SLAM approaches more robust, without extensive parameter tuning.
For the MIT-Killian-Court dataset, the benefit of incorporating the embodiment being described (GTk) only comes when used with Cauchy and SC because DCS fails even when there are no additional outliers where the parameter Φ is tuned from 0.1 to 10. Thus, the embodiment being described (GTk) cannot improve the DCS back-end on this dataset. While for the Intel Research dataset, since its initialisation of pose nodes is already close to ground truth, it is easy for all approaches to reach a satisfactory result after optimisation with any number of outliers.
In ringCity and M3500Olson datasets, dramatic improvements are achieved by the embodiment being described (GTk), RMSE is reduced by several times, except for applying SC on M3500Olson dataset which does not fail with any number of outliers.
The solid line 602a-f shows the ground truth. The dotted line 604a-f shows the calculation using the combination of GTk/no-GTk with a back end.
For more results, please refer to the supplementary file referenced above.
The skilled person will appreciate that, whilst the datasets shown relate to x-y coordinates of a global map, the approach discussed herein can be used in any context in which loop closures exist whether or not there is a global map. For example, it may be used in Experience-Based Navigation type situations, as discussed in WO2013117940, “METHOD OF LOCATING A SENSOR AND RELATED APPARATUS”.
C. Comparison with RRR
For existing robust graph SLAM algorithms and back-ends 38, RRR is the most similar to the embodiment being described with open-source resources. Therefore, it is chosen as a comparison.
The combinations of RRR and the middle layer 310 with DCS and SC back-ends 38 were tested with all datasets.
Some of the results are shown in Table II (above),
Red and blue boxes (first two, i.e. leftmost two, in each cluster) represent results from RRR while green and orange boxes (last two, i.e. rightmost two, in each cluster) are for a middle layer 310 of the embodiment being described.
In each set of box-plots in each graph 700a-c, the box plot for RRR-DCS is left-most, adjacent to the box plot for RRR-SC. The box plot for the middle layer 310-SC is right-most, adjacent to the box plot for the middle layer 310-DCS.
In
In all these cases, the middle layer 310 outperforms RRR, especially on the M3500Olson (
For more detailed results and comparison with RRR, please refer to the supplementary file referenced above.
The solid lines 802a-e are the ground truth. The dotted lines 804a-f are the model.
In each pair, the ground truth line 802 is the same.
Although the middle layer 310 was implemented with Matlab rather than C or C++ in the embodiment being described, the runtime was found to be reasonable. The skilled person would appreciate that the middle layer 310, or other implementation, may be implemented in any appropriate language.
The detailed runtime of middle layer 310 on the eight datasets is given in Table III.
The most time consuming part in the embodiment being described was found to be executing abundant spatial consistency tests while looking for a consistent subset of loop closures in the graph.
The quadratic time increase with respect to the number of loop closures is avoided in this embodiment by restricting the traversing distance of the circle in the test with a threshold which largely reduces the number of loop closures to be compared. Hence, this threshold determines runtime to some extent. However, an extremely small threshold will prevent the selected loop closure from being compared with enough other loop closures. Hence, the default value is set to 300 steps in the embodiment being described to achieve a suitable balance between runtime and performance. In the embodiment being described, each step is an actual step taken by a person carrying the device; one step corresponds to one odometry edge in this embodiment. In alternative embodiments, a “step” may correspond to a set number of steps or wheel rotations, a set distance, a set time of travel, a time between pauses, or the like.
Step 1010, artificial loop closure insertion, is performed in embodiments implementing the “GTk” approach discussed above in addition to the Outlier Removal (OR) approach common to all embodiments, but not in all embodiments. The output from step 1010 is the augmented graph 307 shown in
From the above, the skilled person will appreciate that embodiments/aspects of the invention may be thought of as providing one or more of the following:
Uses of embodiments described herein could include, but are not limited to, any of the following examples:
The skilled person will appreciate that the embodiments disclosed herein could be used for SLAM of one device's trajectories, or of trajectories of multiple devices. Further, trajectories used by a single embodiment may be a mixture of trajectories generated by different types of devices, such as some being generated by robots, some by other mobile objects and some by people.
| Number | Date | Country | Kind |
|---|---|---|---|
| 20170100360 | Jul 2017 | GR | national |
| 1718507.5 | Nov 2017 | GB | national |
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/GB2018/052188 | 7/31/2018 | WO | 00 |
