Patent Grant
7270589
Not applicable.
1. Field of the Invention
The subject invention relates to legged vehicles and toys, and, more particularly, to a resilient leg and its embodiment in a robot for which it provides hopping propulsion.
2. Description of the Invention Background
Human beings and animals have remarkable abilities to walk and run over a wide variety of terrain. In running, as distinct from walking, a machine (or animal) exhibits periods of flight in which contact with the ground is completely lost. Running in general is a dynamic phenomenon where inertial forces are significant, and balance is achieved by active means, not by static equilibrium. Running allows higher speeds than walking, and exploits dynamics to negotiate widely spaced (horizontally or vertically) footholds.
There have been a number of efforts at building running robots. One running robot was a planar one-legged hopper that operated in low effective gravity on an inclined table with thrust provided by a high-force electric solenoid. A succession of machines tested one-leg, two-leg and four-leg designs both in the plane and in three dimensions (3D). Most used a telescoping leg with an internal air spring for compliance, and hydraulic actuators. Some machines have been controlled by the same basic decomposition into three independent linear controllers: forward velocity controlled by foot placement, hopping height controlled by thrust, and pitch controlled by hip torque during stance. This control involved high force and power during stance.
There have been several examples of electrically actuated hoppers. One was constructed with a one-leg electrically actuated planar hopper with a leg constructed from a four bar linkage with a tension spring. Another was built with a one-leg planar hopper with electric motors instead of hydraulics and a metal spring instead of an air spring. Others designed an electrically actuated leg with three revolute joints that used an electric motor coupled with elastic tendons to drive the foot. Others have been designed with an electrically actuated telescoping leg constrained to the vertical. It incorporated a DC motor driving a ball screw in series with a steel spring.
While research on dynamically-stabilized legged locomotion has been completed, previous hopping/running machines have been characterized by the following shortcomings: (i) inefficiency due to losses in the mechanical system and negative work; (ii) the need for large, high-powered actuators for excitation and control of motion; (iii) the requirement for excessive power via off-board power supply; (iv) large body-attitude disturbances and control effort; (v) the inability to perform precise motion control needed for reliable movement over complex terrains; (vi) control complexity; and (vii) vulnerability to damage. In short, previous concepts of running machines have been confined to laboratory environments, and have not been suitable for practical legged locomotion. Thus, there is a need for legged vehicles, which are energy efficient and simple.
There is a further need for a hopper robot that employs a pivoting hip, which minimizes the torque coupling and attitude disturbances during stance.
There is still another need for a hopping robot that is self-righting without the need for computation, actuation, or energy for pitch control.
There is yet another need for a leg that is lightweight and that can be positioned with a low-power actuator such that minimal disturbance is applied to the body.
Another need exists for a leg that has high passive restitution to minimize the energy that needs to be added for each cycle, and to make the impacts relatively repeatable and predictable.
Still another need exists for a hopping, jumping or running robot that stores energy during flight to enable the use of low-powered actuators.
In accordance with one form of the present invention, there is provided a robot leg comprising a curved spring, pivot bearing, and tension element, and a hopper robot incorporating the leg. The leg is named the “Bow Leg” for its resemblance to an archery bow, and is hereafter referred to as the “leg.” The tension element is hereafter referred to as the “bow string.”
It is a feature of the present invention to provide a simple, rugged, highly efficient leg for use in hopping, running, and walking machines. In operation a compressive force at the foot causes the leg to compress, efficiently storing, elastic energy in the bending of the spring. The leg can then return this energy by doing work on the environment as the leg extends.
It is a feature of the present invention to provide a bow string to hold the leg in compression. The bow string may be used to store elastic energy in the leg by actuating the free end of the bow string. It may also be used to retain elastic energy in the leg that was stored either by the actuation or by external forces exerted upon the foot.
It is a feature of the present invention to provide a mechanism to retract the bow string and thus store energy in the leg. As applied to a hopper robot, the retract mechanism stores energy to be delivered as thrust. The release of the energy may be automatically triggered upon contact with the ground.
It is a feature of the present invention to provide a one-legged hopper robot that is energy efficient and simple. The present embodiment is constrained to planar operation, but the leg is applicable to three dimensional (3D) operations and multilegged machines.
It is another feature of the present invention to employ a freely pivoting bearing at one end of the leg spring to accommodate the bending motion and ensure that the compressive force always acts through the pivot centerline. As embodied, this bearing serves as the hopper “hip” and this feature minimizes the torque coupling and attitude disturbances during stance. In another embodiment of a hopping machine the hip may be laterally adjustable relative to the center of mass to produce controllable body torques during stance.
It is a feature of the present invention to provide a bending spring with tension constraint used for general energy storage and shock absorption. As a shock absorber the “leg” attached to one body is compressed by interaction with some other body and stores collision energy as elastic bending.
Another feature of the present invention is to provide a leg that is lightweight and that can be positioned with a low-power actuator such that minimal disturbance is applied to the body.
Yet another feature of the present invention is to provide a hopping robot that is self-righting (the body tends to remain upright due to gravitational forces) without the need for mechanism, force, or energy for pitch control.
Another feature of the present invention is to provide other techniques for body stabilization. One such method is the use of a mechanical stabilizing gyroscope attached to the hopper body to resist changes to body attitude. Another method is the use of aerodynamic control surfaces to actively generate attitude control torques during flight.
The present invention provides a mechanism, which controls the leg angle with respect to the body during flight of the hopping machine.
The present invention further provides a mechanism that limits the torque applied to the hip joint.
Accordingly, the present invention provides solutions to the shortcomings of prior design of legged hopping, walking, jumping and running machines. Those of ordinary skill in the art will readily appreciate, however, that these and other details, features and advantages will become further apparent as the following detailed description of the embodiments of the present invention proceeds.
In the accompanying Figures, there are shown present embodiments of the invention wherein like reference numerals are employed to designate like parts and wherein:
The present invention will be described below in terms of a resilient leg used in a hopping robot. It should be noted, however, that describing the present invention in terms of a resilient leg used in a hopping robot is for illustrative purposes and the advantages of the present invention may be realized using other structures and technologies that have a need for a resilient leg for a vehicle such as three dimensional machines, multi-legged machines, military applications, toys, recreational equipment, etc.
The body structure 40 comprises a base plate 42 and a mounting plate 44 that are interconnected together in a spaced-apart relationship. Two spacing members 61 are positioned between the base plate 42 and the mounting plate 44. Base plate 42 and mounting plate 44 may be fabricated from aluminum. However, one of ordinary skill will appreciate that the base plate 42 and mounting plate 44 may be fabricated from other structural materials. As can be seen in
A bow string 60 is attached to the foot member 30 by, for example, a loop through a horizontal hole in the foot and a knot. The other end of the bow string 60 is affixed to a bow string mooring block 62 that is oriented between the base plate 42 and the mounting plate 44 and is attached thereto. Mooring block 62 may be fabricated from aluminum and be attached to the base plate 42 and the mounting plate 44 by machine screws. The bow string 60 may be affixed to the mooring block 62 by, for example, a turnbuckle to allow adjustment of bow string pre-load. The bow string 60 is also supported through the hip centerline between a pair of commercially available idler pulleys 64 that are journaled on corresponding shafts (not shown) that are affixed to the hip shaft 48. The bow string 60 limits the extension of the leg 20 and allows control of the length of the leg 20 by the thrust mechanism 70 attached to the body 40 above the hip, wherein the hip is located along axis A-A.
The subject invention also comprises a thrust mechanism, generally designated as 70. The thrust mechanism 70 includes a servo disc 72 that may be fabricated from, for example, Delrin, generically known as acetal plastic. The servo disc 72 is mounted to the rotatable shaft 73 of a commercially available hobby servo 74 that is mounted to the mounting plate 44. We have found that the servos commonly used in the model airplane and hobby industry work well for this purpose. A commercially available drive pulley 76 is rotatably affixed to the servo disc 72 as shown. A face spring 80 is affixed to the thrust servo disc 72. Face spring 80 comprises a thin, flexible substantially egg-shaped member, which is pre-loaded by the side force of the bow string 60 that is pulled taut across the face of the face spring 80.
The present hopper 10 may also be provided with a leg positioning lever 81 which is a substantially rectangular bar member made from Delrin, acetal plastic, and is operably affixed to the shaft 85 of a commercially available hobby servo 86. The thrust servo 74 and the leg angle servo 86 are attached to a computer 190 (PC with I/O board) by an umbilical cord 192.
The leg angle positioning mechanism 90 comprises the leg positioning lever 81, a pair of control strings 92, and an elastic element 93 that maintains tension in the control strings. As shown in
In one embodiment, as shown in
During stance, the leg curvature increases, storing energy in elastic bending of the spring. Static equilibrium—neglecting leg inertia and bearing friction—dictates that the contact force with the ground must act through the hip. The free hip pivot allows not only free leg sweep motion but also unhindered rotation associated with the leg compression. In practice, placing the center of mass (COM) slightly below the hip produces a mild restoring effect that keeps the body structure 40 upright passively, even when subjected to significant disturbances. The body 40 then acts as a pendulum, with frequency essentially the same as a comparable statically suspended pendulum. Keeping this pendulum frequency well below the hopping frequency minimizes pitch oscillations excited by the hopping motion. This is similar to the phenomenon reported in Self-Stabilizing Running, Robert Ringrose, Proceedings of IEEE International Conference on Robotics and Automation, 1997, Vol. 1, pp. 487-93, which used a large, curved foot to stabilize the pitch of a monopod hopper.
In one exemplary embodiment, the bow leg length is 25 cm and the running circle of the boom 100 is 1.5 m in radius. Effective gravity, a result of the supporting elastic cord and boom geometry, is 0.35 G (3.5 m/s2). Effective machine mass is 4.0 kg, including 0.8 kg in the hopper mechanism itself, 0.2 kg of batteries, and 3.0 kg of ballast and boom weight. The leg 20 itself weighs only 30 g excluding the hip bearing. It is noteworthy that the hopper mechanism comprises only 20% of the total mass; the batteries 5%; and the leg 0.8%. A full 75% of the mass is in the “dead weight” of the weights and boom.
The operation of the thrust mechanism 70 may be appreciated from reference to
It will be appreciated by those skilled in the art that the geometry depicted in
The design of the leg 20 for a particular application depends on a number of factors, including the elastic energy storage, the force/deflection characteristics, the length and the maximum deflection. Current implementations of the leg 20 have been fabricated from unidirectional fiberglass composites as used in archery bows, and exhibit specific energies on the order of 100 N-m/N. That is, the elastic energy storage in the leg 20 is sufficient to lift the weight of the leg 20 approximately 100 meters. If the leg 20 has a weight of 1 N, it can store about 100 N-m of energy. If this leg 20 were used on a hopping machine weighing 10 N total, the elastic energy of the leg 20 could lift the whole machine (i.e., hop) about 10 meters. If the machine weighed 100 N, it should be able to hop about 1 meter high, based on the energy storage. For maximum energy storage, the leg 20 must be designed to have nearly constant bending stress along its length; this can be accomplished with a constant material thickness and a width that varies from a maximum at the mid-length to theoretically zero at the tip, with an approximately sinusoidal width profile. Alternately, thickness of the leg 20 may be varied along the length thereof to achieve constant or desirable bending stress, or a combination of width and thickness variations may be employed. Enough width must be provided near the ends to sustain the shear forces in the material. Further improvements in performance can be obtained by using light-weight core laminates; pre-stressing the laminations; tailoring the stiffness and elongation characteristics of individual laminations; and other techniques well known in the composite materials industry.
The force/deflection characteristics of the leg 20 can be affected by the laminating process and the pre-loading of the leg 20. If the leg 20 is laminated in a straight shape (according to the thickness and width constraints described above) or fabricated from a single piece of material, the compressive force is effectively that of a column in compression. The force is nearly constant, increasing by only about 20% from the initial straight shape until the spring is bent to a 180 degree curve. In this design, it behaves nearly as a constant-force spring. If the leg 20 is laminated to an initial curvature, the compressive force will be zero initially, and will increase monotonically to maximum at the maximum deflection based on the allowable bending stress. In this case, the leg 20 will behave more like a conventional compression spring with a fixed spring rate. The force/deflection characteristics can be tailored by means of the initial curvature to get approximately constant force, constant rate, or somewhere in-between.
Fabrication of the leg may be simplified using an initially flat, monolithic (single-piece) bow leg 160, as shown in
In
The designs fabricated thus far have utilized a single, unidirectional fiberglass material laminated to the desired thickness and initial curvature or in a flat monolithic structure. Because the bending strain varies from zero at the neutral axis (roughly the middle plane of the laminate) to a maximum at the outer fiber (surface), using different laminate materials in different layers, or prestressing individual laminates can produce improved energy storage, reduced weight or lowered cost. For example, a lightweight core laminate, such as wood, plastic foam or a honeycomb material, may be used for the middle laminations to reduce-weight/cost without greatly reducing energy storage. Laminations of different stiffness can be used (stiffer closer to the neutral axis) such that each laminate is stressed to its limit, maximizing energy storage. Another technique is to pre-stress each layer such that a more beneficial stress distribution is achieved at the fully loaded state; for example, laminating the leg beam in a curved shape, then flexing it past straight and operating it with the curvature reversed, can produce a more nearly constant stress profile in each laminate layer.
While the current embodiments of the invention may employ unidirectional fiberglass as the elastic energy storage material, it will be expected that other material may be used depending on the particular application such as environmental and cost factors, etc. Such material may include, but are not limited to, carbon fiber, reinforced plastics, thermoplastics with or without reinforcement, metals, or other materials.
The basic philosophy for controlling a bow leg hopper (or multi-legged machine) is to set the actuators during flight to achieve the desired response during stance. Based on the output of a high-level planner in response to a desired task specification (such as travel from A to B while avoiding obstacle C), the leg angle and elastic energy increment are set by the leg angle servo and retract actuator. This is done once during each flight phase to prepare the machine for the next bounce. During stance, no control action is taken; the machine behaves as a passive, spring-mass oscillator. This determines the height and direction of the next hop. With the center-of mass of the body 40 slightly below the hip, body attitude is maintained passively without control action, assuming the parameters are properly tuned (body pendulum frequency well below the hopping frequency). In the case where a mechanism is present to adjust the location of the hip relative to the center-of-mass, this is adjusted prior to landing and held during stance to produce a desired impulse on the body angular momentum.
In the above discussion, the position of the hip is adjusted with respect to the center of mass (COM) of the machine. It will be appreciated that other means may be used to adjust the relative positions of the hip and COM. For example, a weight on the body, such as batteries, motors, electronic components, ballast, etc. could be moved to achieve a relative movement of the COM.
The subject invention includes a novel design for a locomoting robot that bounces passively on a flexible, efficient leg. It is controlled by adjusting the leg angle and stored leg energy during flight in preparation for impact. The body pitch rotation is passively stabilized by locating the center of mass slightly beneath the hip. During stance, the actuators are automatically decoupled and the bounce proceeds passively. The trajectory is determined by the impact state and the spring-mass physics of the robot. This design is energy efficient and moves the energy demand from the stance interval to the longer flight interval, reducing the required peak power. This design also imposes novel requirements on a locomotion controller, since the maximum control rate is one update per hopping cycle.
The bow leg mechanical design permits only one control cycle per bounce and this defines the properties of the controller. The controller function takes the following form:
(φn+1,ΔEn+1)=ƒ(xnyn{dot over (x)}n) (1)
In this function the variables (φn+1, ΔEn+1) are the leg angle and stored leg energy at impact and (xn,yn,{dot over (x)}n) define the trajectory preceding the impact. This function summarizes the control and comprises the physical model used for feedforward, terrain data, the task being performed, and error feedback. The discrete form can be justified by examining the effect of each actuator and the definition of state.
The leg servomotor determines the angle of the leg prior to impact. During flight, the leg carries no load and can be positioned quickly. This motion only slightly affects body pitch since the leg mass is approximately 1% of the body mass. During stance, the leg positioning motor is physically decoupled from the leg. It is conceivable the leg servo could be repositioned during stance in order to exert horizontal ground forces as the bow string regains tension at liftoff, but we consider this unreliable and ignore this possibility. Thus the leg motion can be entirely described as φn, the leg angle in world coordinates at impact n.
The thrust motor determines the energy stored in leg tension prior to impact. During flight, the motor performs positive work on the leg spring. It is conceivable for it to immediately reverse and dissipate some stored energy but the net work during flight is always non-negative. During stance, the thrust motor becomes physically decoupled from the leg as the now-slack string is released. The leg then extends to full length, and all stored energy is released. The thrust action can be entirely described as ΔE, a non-negative potential energy added to the kinetic energy.
The full physical state of the planar embodiment nominally has ten dimensions: three body DOF, two actuator DOF, and the corresponding velocities. We make several assumptions to define a trajectory using only three dimensions. First, pitch and pitch velocity may be neglected since the body is designed to passively stabilize pitch and rotates like a slow pendulum. This axis is decoupled from the other coordinates since body rotations only slightly affect the direction of leg forces and the leg position is independently defined in world coordinates. Second, on the time scale of the hopping cycle the actuators have insignificant dynamics and may be treated simply as outputs.
The hopper may thus be treated as a point particle with four state variables (x, y, {dot over (x)}, {dot over (y)}). However, all constraints are assumed to be time-invariant and so only the geometry of the trajectory matters. Since the free flight physics is known, each trajectory can be described by only three parameters; we use the set (xnyn,{dot over (x)}n), which are the position and velocity at the apex of the trajectory.
Note that the leg and thrust values are a function of time during flight (φ(t), ΔE(t)), but only the final values (φn,ΔEn) affect the impact. The abstract control problem is described with discrete functions but the implementation does require control over time. The abstract control values closely correspond to the mechanical freedoms: the stored energy is a monotonic function of the thrust servo angle, and the leg angle φ is the sum of the body attitude θ and the leg servo angle.
The low motor power does impose timing constraints. The minimum time required to store leg energy depends on the magnitude of ΔE and the maximum motor power. In practice, the entire flight time is required to store a large impulse, so energy storage for impact n must typically begin immediately after takeoff n−1; that energy will affect the trajectory following impact n. In contrast, the leg servo can typically position the leg shortly before impact since it is moving an unloaded low mass leg.
The controller uses a model of the hopper physics for planning paths and for feedforward control. The physics function is a discrete map from one trajectory to the next given the control parameters of the intervening impact. It combines the physics of the hopper and geometric information about the terrain.
Although the controller views the physical model as a discrete function, the physics is a continuous time system and could be modeled using differential equations. However, the hopper is designed to have dynamics similar to idealized models, so a discrete closed form model was chosen based on idealized analysis, combined with ad hoc but physically motivated corrections.
The various parameters in the model are determined by a least squares fit to a set of recorded trajectories. Some parameter values and statistics are shown in Table 1. The errors listed are the residual; i.e., the distribution of the differences between the predicted and actual trajectory parameters on the same data set with which the model was fitted.
ΔE vs. thrust, linear term
ΔE vs. thrust, quadratic term
The analytic portion of the model is based on the assumption of a massless leg and instantaneous impact. The leg is attached with a pin joint at the hip and an effective pin joint where the foot makes point contact with the ground. With no leg inertia, the free body equilibrium dictates that the ground force applied to the toe lies along the axis of the leg and is balanced by an opposing hip force. The total force on the body is the sum of gravity and the leg spring force. The spring has restitution ε that defines the ratio of impulse released to impulse absorbed. The hopper bounces like a ball on a paddle perpendicular to the leg axis. With no thrust, the tangential velocity is unchanged and the normal velocity is mirrored with a loss:
νn1=−ενn0
νt1=νt0 (2)
This may be modified to include the effect of thrust. The energy stored in the leg is a function of thrust motor angle and is independent of the impact state. Assuming perfect transfer from spring storage into kinetic energy, the impact may be modeled as follows:
νn1=√{square root over (ε2νn02+(pt1θt+pt2θt2))}
νt1=νt0 (3)
The two terms involving the thrust motor angle θt form a quadratic approximation of the energy stored in the leg. The normal impact velocity νn0 is always negative and normal takeoff velocity νn1 is always positive.
In reality, the stance is not instantaneous and the leg sweeps a small arc while in contact. This angle is a function of stance time and the tangential velocity, but we simply lump the effect into a single parameter and approximate the actual leg sweep as follows:
Δφ≅ps·−νt (4)
The leg angle at liftoff is the sum of the angle at impact and the sweep angle (φn+Δφ). Since the leg angle is not constant during stance the idealized reflection model is only an approximation. However, if the midpoint of the sweep (φn+1/2Δφ) is used as the effective leg angle in computing the idealized model, the result is good enough to be a useful predictor of takeoff velocity.
The flight model assumes constant gravity and a constant lateral friction force. The effective gravity produced by the constraint boom and gravity compensation spring varies slightly with altitude, but the effect is negligible. The measurable but low horizontal deceleration is presumably due to bearing friction and tether drag.
An experimental task was defined to travel to a destination while obeying gait constraints. The basic constraints on this task are the location of footholds, contact friction, and obstacles. The gait constraints might include a desired velocity or hopping height, task constraints such as “land exactly on foothold x,” or arbitrary constraints such as “alternate between short and long steps.”
The role of the planner in the control system is to plan sequences of steps that attain the goal while satisfying the constraints. It is desirable that the planner operates in real time, be able to use terrain data obtained on-line, and produce plans tolerant of terrain and control uncertainty.
The planner performs a best-first search of a graph of possible foot placements to explore sequences of trajectories. At every search step, a set of new foot placements (i.e., search nodes) is selected by sampling the continuum of available leg angles at a given impact.
For each leg angle chosen, the trajectory that results is computed; the impact point at the end of the trajectory defines the new foot placement. The sampling procedure guarantees at least one choice of leg angle is selected for each reachable terrain segment. The branching factor of the best-first search is thus a function of the number of terrain segments reachable from a given liftoff and the sample spacing of the selection procedure.
The path is defined as a sequence of foot placements rather than a sequence of states or leg angles. This observes the terrain constraints, but a consequence is that adding a new foot placement to a path involves adjusting previous leg angles. This is performed by a numerical optimization that adjusts the leg angles to minimize the sum of absolute distances between the predicted foot contacts and the desired foot placements.
The best-first search is guided by the following heuristic function in which x and {dot over (x)} are trajectory parameters, p is the number of bounces from the start, kv and k1 are constant gains, and xd is the goal position:
Currently, the energy of the hopper is regulated using a feedback loop that varies thrust to maintain a constant total energy. The hopper is designed so that the dissipation is relatively independent of forward speed. The planner estimates the operation of this controller so that initial energy ramp-up or ramp-down will be correctly treated, but otherwise only needs to plan leg angles.
The toe is assumed to contact the ground with Coulomb friction with coefficient μ. To avoid slip the leg force must lie inside the friction cone within the angle φμ=arctan μ of the surface normal. Since the leg force is always along the leg axis, leg angles within the friction cone satisfy the friction constraint.
The plan is consistent with the model of the physics but is not naturally stable. The sources of uncertainty that lead the hopper off the plan include systematic error in the physical model, mechanical backlash in the leg servo, error in the state estimation, and friction and backlash in the constraint boom. After each impact the controller computes an adjustment to the plan for the next two impacts intended to return to the planned trajectory. If the error is too large, the controller abandons the plan and begins creating a new one from the measured state.
The leg angles φ1 . . . φn at n successive impacts may be considered a vector that defines the reachable trajectories. In general, a trajectory is defined by three parameters and three successive impacts may span the trajectory space. However, hopping at constant energy reduces the trajectory space to two dimensions. Thus a deviation from the path can be corrected by adjusting two successive leg angles to reattain the planned trajectory. The correction combines linear feedback and feedforward computed using the physical model.
If the corrected foot placement falls outside a safe region defined around the planned foothold, the controller cannot guarantee the safety of that bounce and a new plan is generated. Planning occurs concurrently with execution; the planning system is an anytime planner and computes usable partial plans immediately. When starting from scratch, the best plan available before impact is used, but is then refined during the remainder of the hopping cycle. Once completed, the plan is used until accumulated error forces a replan.
The controller views the hopper as a system controlled once each bounce by supplying values for φ and ΔE. The physical hardware does require real time attention to implement these commands. The underlying control software reads sensors and computes state estimates, controls the leg and thrust servo positions, and schedules the control computations. The prototype hopper uses hobby servos for the leg and thrust motors, so the lowest level of position control is implemented in hardware.
The leg actuator controls the leg angle relative to the body. Since φ is specified in world coordinates the actuator command is actually a function of body pitch. The thrust actuator angle is computed using the inverse of the thrust model presented hereinabove.
It is desirable for the control to complement the mechanism in order to take full advantage of every possible motion. Thus, it is desirable to choose an unbiased solution method which can produce the best motion for a task from the space of possible motions. This is manageable in the case of the bow-leg hopper since the discrete control opportunities limit the space of possibilities to a continuous valued choice at discrete intervals.
However, the space of possible motions is vast and redundant and the search must be guided by sensible heuristics. It is important to note that at the heart of the planner is a linear controller that guides the search by choosing desired velocities with a linear function. By embedding this in a planning framework the linear control becomes a recommendation. This has several advantages: the terrain model is easily included, obstacles can be anticipated by looking forward in time, and arbitrary constraints can be observed to allow for a richer expression of tasks without specially programming new algorithms.
The hopper robot 10 is controlled by configuring the leg angle and stored leg energy during flight, which determine two initial conditions for the passive bounce. The new trajectory is a function of the impact state, the two control outputs, and the spring-mass physics of the hopper robot 10 and leg 20. Unlike previous work, the mechanical design requires only one control cycle per bounce and the controller (not shown) takes a discrete form that computes the desired leg angle and stored energy at touchdown (φ, ΔE) from the apex position and horizontal velocity (x, y, x).
A variety of methods might be employed to compute this control function. So far, we have implemented two methods, a linear controller and a planning approach. The linear control is similar to the Raibert three part control: the touchdown leg angle is analogous to foot placement and controls forward speed, and the leg retraction at impact controls total energy, roughly equivalent to hopping height. Because body attitude is passively controlled as a result of the body mass distribution, the need to exert pitch torques during stance is eliminated. Currently, the controller seeks to maintain constant energy in the system by varying the leg retraction performed before each stance period.
The planning approach uses graph search to explore possible sequences of steps that satisfy the constraints of the terrain. The leg angle is selected to produce the desired takeoff angle, based on a numerical solution of the impact physics. The thrust output is chosen to maintain approximately constant total energy. The plan is executed by a controller that evaluates the result of each bounce and adjusts the following two steps to return to the plan.
This approach requires accurately modeling the physics of the hopper robot 10. However, the simple mechanical design creates dynamics that may be well modeled. So far, we have used a closed form model of stance that combines an idealized, instantaneous, impact model with empirically determined adjustments for leg losses and the finite stance time. The flight model similarly combines a uniform acceleration model with adjustments for various disturbances and departures from ideality. The parameters in the model are determined from data by minimizing the least squares difference between the predicted and actual trajectory parameters over sets of approximately 400 bounces.
The hopper control still has a real time component to read sensors, issue servo commands, and cycle through states representing ascent, descent, and stance. At the lowest level, the hobby servos use position feedback to reach commanded positions encoded as PWM (pulse-width-modulated) signals from the control computer.
We have found that a hopper robot 10 constructed in the above-described manner loses only about 15% of its energy each hop. The machine has hopped as high as 50 cm; 80 cm is theoretically possible based on leg elastic energy capacity, with the present machine mass and reduced gravity. A running speed 1.0 m/s has been observed and higher speeds should be achievable. The inherent, passive pitch stabilization has effectively damped pitch errors of about 0.5 radians; larger angles could be tolerated with increased leg-sweep travel. Energy consumption is surprisingly low: the machine runs for 45 minutes on a single charge (approximately 5 w-hr) of the four sub-C cell nickel cadmium batteries, which comprise only 5% the total machine mass.
Experiments with the machine include hopping in place, running at low velocities across level ground, and crossing obstacles composed of “stepping stones” separated by “holes” in which the hopper robot 10 must not land. An experimental run is presented in
In the present embodiment, the precision of the motion is limited by the inaccuracies and uncertainties in the flight and stance models, and the precision of actuator control. In particular, the motion is very sensitive to errors in the leg angle at touchdown: a 0.04 radian error in leg angle (1.0 cm lateral error in foot position) translates to a 17 cm error in lateral position at the next touchdown, based on typical hopping conditions (0.3 m hopping height and 0.2 m/s forward speed).
Thus, from the foregoing discussion, it is apparent that the present invention solves many of the problems encountered by prior running robot designs. For example, the present invention addresses the problem of hip torque. That is, because the leg is allowed to pivot freely at the hip during stance, and the body center of mass (COM) is located at or slightly below the hip, generation of torques on the body by the leg is precluded. This approach leads to the following benefits: (i) effort and energy loss in attitude control are minimized; (ii) leg/hip need not accept/produce large torques; (iii) hip actuators can be small; (iv) the leg can be very light; (v) the model and control are simplified (body treated as point mass); and (vi) vulnerability to damage is minimized because of the leg's lateral compliance. Locating the COM below the hip allows the body to be self righting, so no control effort or energy is needed for pitch control. Also, because the leg can be very lightweight, it can be positioned with a low-power actuator, and its motion causes minimal disturbance on the body. The leg also has high passive restitution, minimizing the energy that needs to be added each cycle, and making the impacts relatively repeatable and predictable. These factors simplify the model of the machine dynamics and flight and stance phases, leading to simpler, potentially more precise control. The present invention also differs from prior designs in the manner in which thrust is applied to the device. That is, by storing energy during flight the power demand is distributed across flight, so low-powered, electric actuators are suitable.
Those of ordinary skill in the art will further appreciate that the hopper of the present embodiment is adaptable for crossing rugged, natural and manmade terrains. The efficiency and low power requirements of the present invention are well suited for use by self-contained, electrically powered designs. Further, the high energy storage capacity of the leg permits vertical and horizontal hopping distances on the order of meters, allowing mobility on very rugged terrain. In addition, the natural control of body attitude greatly simplifies modeling and control of the machine. Also, it is expected that, because losses and control effort are small, that dynamic behavior will be quite repeatable and predictable (compared to previous systems with lower efficiency). While the present invention has been described herein as a single leg machine, it will be appreciated that the present invention leg is equally applicable to multi-leg designs. The subject invention is suitable for operation on real terrains, including small footholds spaced irregularly and separated by large horizontal and vertical distances.
Those of ordinary skill in the art will additionally appreciate that the bow leg of the present invention is adaptable for application in three dimensional (3D) hopping, running, and jumping machines with one or more legs. Applications for these machines include but are not limited to the following: robots, vehicles, toys, planetary exploration, and recreational equipment.
While walking machines are bounded by their kinematic limits, running, walking, jumping and hopping machines are bounded only by dynamic limits. A high strength composite spring can have a specific energy of 100 meters or more; that is, it can store enough energy to lift its own weight more than 100 meters. Thus, a machine having 5% of its mass in the leg could theoretically hop 5 meters or more. Of course, this performance is dependent upon allowable accelerations and ground forces, and the ability to control body attitude. Lateral hopping distance is twice the height capability, assuming an ideal trajectory. In reality, the hopper may be able to store substantial additional energy due to its horizontal motion. This energy could be employed for hill climbing or long jumping, or converted to vertical motion in a “pole vaulting” mode.
A critical issue in controlling a three dimensional (3D) hopping machine is maintaining body attitude. This problem is minimized with the free hip pivot of the bow leg, but additional fine control of body pitch, roll, and yaw may be required. One mechanism to control body attitude is a mechanical stabilizing gyroscope attached to the hopper body to resist changes in body attitude. Another such mechanism is the use of aerodynamic control surfaces attached to the hopper body.
The bow leg 201 with foot 202 contacts the ground and the freely pivoting hip bearing 203 allows the leg 201 to rotate about the y-axis. The hip yoke 205 and yoke bearing 206 connect the bow leg 201 to the body 204 and allow the leg 201 to rotate about x-axis. The bow string 207 is attach to the foot 202 and is routed around the hip pulley 208 and terminates at a thrust mechanism (not shown) that may retract the bow string 207 to compress the leg 201 and add energy to the system. The pair of leg control actuators 209 and 210 with drive pulleys 211 and 212 are mounted on the body 204. The primary control string pulleys 215 and 216 are mounted concentrically with the hip pulley 208 on the hip shaft 219 on the yoke 205. The intermediate control string pulleys 217 and 218 are mounted on the yoke 205. Each control string 213 or 214 originates at the foot 202, wraps one revolution around one of the primary idler pulleys 215 or 216, wraps partially around one of the intermediate idler pulleys 217 or 218, and terminates on one of the drive pulleys 211 or 212.
The hip joint and leg control mechanism enable the leg to be swung along the y-axis as well as along the x-axis, allowing the machine 200 to move in any direction on the ground surface. While the machine 200 is in flight and the foot 202 is not in contact with the ground, the bow string 207 provides a tension force that compresses the leg 201 to a degree depending on the state of the thrust mechanism (not shown). It will be appreciated that the tension in the bow string 207 provides a torque on the leg 201 about the hip shaft 219 equal to the string tension force times the radius (r) of the hip pulley 208. This torque tends to swing the leg 201 in the M direction. This torque is balanced by the combined tensions of the left and right control strings 213 and 214 passing around the primary control string pulleys 215 and 216 of radius R. Based on a standard static torque balance, the ratio of the combined control string tensions to the bow string 207 tension is equal to the ratio of the radii of the pulleys (r/R). The maximum torque available to swing the leg 201 in the M direction occurs when the control string actuators 209 and 210 move their respective drive pulleys 211 and 212 to extend the two control strings 213 and 214, allowing them to go slack. Similarly, if both control strings 213 and 214 are retracted, control string torque will exceed the bow string torque and the leg 201 will swing in the P direction. The radius of the hip pulley and the tension in the bow string 207 determine the torque available to swing the leg in the M direction. The control string actuators and primary control string pulleys would normally be designed to produce an equivalent net torque for swinging the leg in the P direction. A preloaded torque mechanism (not shown) built into the drive pulleys 211 and 212, limits the control string tension to the nominal value. In order to minimize the disturbance torques on the body during stance (i.e., when the foot is in contact with the ground), these torques should be designed to the minimum values needed for effective control of the leg 201 in flight.
The swing motion along the y-axis of the leg 201 is affected by moving the two control actuators 209 and 210 in opposite directions (e.g., if the left control string 214 is retracted and the right control string 213 is extended, the leg 201 will move in the L direction). The location of the intermediate control string pulley 217 or 218 affects the relationship between the control string tension and lateral torque applied to the leg 201 (e.g., if the left control string 214 is retracted and the right control string 213 is extended such that the right control string 213 becomes slack and the tension in the left control string 214 is twice the nominal value). The lateral swing torque will be equal to the left control string tension times the moment arm of the intermediate control string pulley 218 (a) about the yoke bearing 203. In the design of the machine, this moment arm (a) would be selected to provide the desired lateral sensitivity of the control and the range of angular travel.
Those of ordinary skill in the art will, of course, appreciate that various changes in the details, materials and arrangement of parts which have been herein described and illustrated in order to explain the nature of the invention may be made by the skilled artisan within the principle and scope of the invention as expressed in the appended claim.
This application claims priority under 35 U.S.C. § 119(e) to provisional U.S. Patent Application Ser. No. 60/134,366 filed May 14, 1999.
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| Number | Date | Country | |
|---|---|---|---|
| 60134366 | May 1999 | US |
