Classifications

• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B62—LAND VEHICLES FOR TRAVELLING OTHERWISE THAN ON RAILS
  • B62D—MOTOR VEHICLES; TRAILERS
  • B62D57/00—Vehicles characterised by having other propulsion or other ground- engaging means than wheels or endless track, alone or in addition to wheels or endless track
  • B62D57/02—Vehicles characterised by having other propulsion or other ground- engaging means than wheels or endless track, alone or in addition to wheels or endless track with ground-engaging propulsion means, e.g. walking members
  • B62D57/032—Vehicles characterised by having other propulsion or other ground- engaging means than wheels or endless track, alone or in addition to wheels or endless track with ground-engaging propulsion means, e.g. walking members with alternately or sequentially lifted supporting base and legs; with alternately or sequentially lifted feet or skid
• • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
  • Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
  • Y10S—TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
  • Y10S901/00—Robots
  • Y10S901/01—Mobile robot

Definitions

• the present invention relates to robotics and, more specifically, to a balance controller for controlling a humanoid robot.
• a computer-implemented method controls a humanoid robot to maintain balance in response to an external disturbance.
• a robot controller receives state information of the humanoid robot.
• the robot controller determines a predicted stepping location of the robot based on the state information of the humanoid robot.
• the predicted stepping location comprising a location such that the humanoid robot will maintain balance if it steps to the predicted stepping location. Responsi ve to the predicted stepping location falling within a predefined region, the robot controller controls the robot to make a postural change without stepping to maintain balance in response to the external disturbance.
• the robot controller instead controls the robot to take a step to the predicted stepping location to maintain balance in response to the external disturbance.
• the robot can beneficially maintain balance in response to an external disturbance by either making a postural adjustment or taking a step.
• a computer-implemented method determines a stepping location on non-level ground for a humanoid robot to maintain balance in response to an external disturbance.
• the humanoid robot is modeled as a rimless wheel model.
• the rimless wheel model has a point mass corresponding to the center of mass of the humanoid robot, a first spoke corresponding to a first leg of the humanoid robot, and a second spoke corresponding to a second leg of the humanoid robot.
• a pl ane on which the rimless wheel model resides is detemiined based on a direction of the humanoid robot's center of mass projected onto the non-level ground.
• An anchor point for the rimless wheel model is determined based on the center of pressure of the humanoid robot.
• a dynamic model is applied to model motion of the rimless wheel through the plane about the anchor point.
• the robot controller selects which of a first section of the non- level ground and a second section of non-level ground to step to, where the first section of the non-level ground has a first slope and the second section of the non-level ground has a second slope.
• the stepping location is determined based on the selected section of the non- level ground such that the point mass of the rimless wheel model will come to rest above the stepping location after executing the modeled motion.
• FIG. 1A is a diagram illustrating a postural response of the robot to maintain balance following a forward push in accordance with an embodiment of the invention.
• FIG. 1 B is a diagram illustra ting a stepping response of the robot to maintain balance following a forward push in accordance with an embodiment of the invention.
• FIG. 2 illustrates a robot controller in accordance with an embodiment of the invention.
• FIG. 3 is a flowchart illustrating a process for controlling a humanoid robot in accordance with an embodiment of the invention.
• FIG. 4 is a diagram illustrating a two spoke rimless wheel model of a humanoid robot in accordance with an embodiment of the invention.
• FIG. 5 is a diagram illustrating a rimless wheel model of a humanoid robot while executing a step in accordance with an embodiment of the invention.
• FIG. 6 is a flowchart illustrating an embodiment of a process for calculating a stepping location of a humanoid robot in accordance with an embodiment of the invention.
• FIG. 7 is a diagram illustrating plane for determining a stepping location of a humanoid robot in accordance with an embodiment of the invention.
• FIG. 8 is a diagram illustrating a various stepping phases of a rimless wheel model of a humanoid robot in accordance with an embodiment of the invention.
• FIG. 9A is a diagram illustrating a rimless wheel model of a humanoid robot for a single support phase of a stepping motion in accordance with an embodiment of the invention.
• FIG. 9B is a diagram illustrating a rimless wheel model of a humanoid robot for a collision phase of a stepping motion accordance with an embodiment of the invention.
• FIG. 10 is a diagram illustrating balance recover ⁇ ' boundary conditions of a humanoid robot using a rimless wheel model accordance with an embodiment of the invention.
• FIG. 11 A is a free body diagram illustrating external forces and moments on a humanoid robot in accordance with an embodiment of the invention.
• FIG. 1 I B is a free body diagram illustrating equivalent forces and moments on a center of mass of a humanoid robot in accordance with an embodiment of the invention.
• FIG.12 is a flowchart illustrating a process for controlling a humanoid robot in accordance with an embodiment of the invention.
• FIG. 13 is a free body diagram illustrating forces on feet of the robot in
• FIG. 14 is a diagram illustrating a representation of forces applied to the feet of the robot in accordance with an embodiment of the invention.
• FIG. 15 is a diagram illustrating example trajectories for a stepping motion in accordance with an embodiment of the invention.
• FIG. 16A is a diagram illustrating a response of the robot to maintain balance following push from behind on uphill terrain in accordance with an embodiment of the invention.
• FIG. 16B is a diagram illustrating a response of the robot to maintain balance following push from behind on downhill terrain in accordance with an embodiment of the invention.
• Certain aspects of the embodiments include process steps and instructions described herein in the form of an algorithm. It should be noted that the process steps and instructions of the embodiments could be embodied in software, firmware or hardware, and when embodied in software, could be downloaded to reside on and be operated from different platforms used by a variety of operating systems. The embodiments can also be in a computer program product which can be executed on a computing system.
• the embodiments also relates to an apparatus for performing the operations herein.
• This apparatus may be specially constructed for the purposes, e.g., a specific computer, or it may comprise a general-purpose computer selectively activated or
• Such a computer program may be stored in a computer readable storage medium, such as, but is not limited to, any type of disk including floppy disks, optical disks, CD-ROMs, magnetic-optical disks, read-only memories (ROMs), random access memories (RAMs), EPROMs, EEPROMs, magnetic or optical cards, application specific integrated circuits ( AS ICs), or any type of media suitable for storing electronic instructions, and each coupled to a computer system bus.
• the memory/storage can be transitor or non-transitory.
• Memory can include any of the above and/or other devices that can store information/data/programs.
• the computers referred to in the specification may include a single processor or may be architectures employing multiple processor designs for increased computing capability.
• a robot controll er controls motion of a robot to maintain balance in response to external disturbances such as a push.
• the robot controller can selectively encourage the robot to recover its balance either with or without taking a step.
• FIGS. 1A-1B illustrate two different ways in which the robot can recover from a push.
• the robot controller fully respects the linear momentum of the robot while compromising the angular momentum (if needed). This results in postural balance change in which the robot rotates its body in response to the push to maintain balance without stepping.
• the robot instead respects the angular momentum while compromising linear momentum (if needed). This results in a stepping motion of the robot allowing it to maintain balance without changing its posture.
• the robot controller determines winch balance control technique to employ, thereby enabling human-like balance recovery in response to an external perturbation.
• FIG. 2 is a block diagram illustrating an embodiment of a robot controller 200 for controlling motion of a robot.
• the robot is a humanoid biped robot having a human-like joint configuration (e.g., six degrees of freedom in each leg and a total mass of between 40 and 60 kgs).
• the robot controller 200 receives state information of the robot. This state information can include both sensed information pertaining to the positions and/or velocities of different components of the robot and motion instructions (e.g., from an input controller) indicating how the robot should move.
• the motion instructions may direct the robot to, for example, stay stationary, w r alk in a particular direction, move or rotate its limbs or trunk according to a particular motion, etc.
• motion instructions may be irrespecti ve of balance considerations or other physical constraints on the robot. Such motion instructions may be inputted by a human through a control mechanism, or may be generated automatically by an artificial intelligence system that controls motion decisions of the robot.
• the state information 202 is defined in terms of a motion of the feet (e.g., configuration and velocity), angular momentum about the robot's center of mass, center of mass position and velocity, and joint accelerations. In some situations, the motion instructions of the state information 202 can indicate that the robot should remain stationary (i.e., the desired angular momentum and center of mass velocity should ideally be zero).
• the robot controller 200 Based on the state information 202, the robot controller 200 generates a control output 204 that controls joint actuators 250 which cause the robot to move. For example, the robot may rotate portions of its body or take a step in order to execute a motion as close as possible to the robot's motion instructions while still retaining balance.
• the control output 204 comprises a vector of joint torques indicating the torques that the actuators will apply to each of the robot's joints. If the motion instructions would not result in the robot losing balance based on the sensed data, then the control output 204 controls the joint actuators 250 to carry out the received motion instructions.
• the robot controller 200 determines that the motion instructions would cause the robot to lose its balance and topple over given the current state information 202, the robot controller 200 generates a control output 204 such that the resulting motion fan "admissible motion") is optimally close to the desired motion while still allowing the robot to maintain balance.
• the robot controller 200 is able to control the robot to maintain its balance even when the robot is subjected to external perturbations (e.g., a push) or when the robot is standing or walking on a non-level and/or non-stationary surface.
• the robot controller 200 may process the state information 202 and generate control output 204 periodically (e.g., once every millisecond) such that the robot continuously retains its balance even as its motion instructions change or when external forces acting on the robot change.
• the robot controller 200 can be based on a human motion model in one embodiment, the resulting motion of the robot can be human-like, i.e., the robot moves to maintain its balance in a manner similar to a human.
• the robot controller 200 comprises a processor 220 and a memory 210.
• the processor 220 processes data signals and may comprise various computing architectures such as a complex instruction set computer (CISC) architecture, a reduced instruction set computer (RISC) architecture, or an architecture implementing a combination of instruction sets. Although only a single processor 220 is shown in FIG. 2, multiple processors may be included.
• the processor 220 comprises an arithmetic logic unit, a microprocessor, a general purpose computer, or some other information appliance equipped to transmit, receive and process electronic data signals from the memory 210 or from external inputs.
• the memory 210 comprises a computer-readable storage medium that stores computer-executable instructions and computer-readable data.
• the instructions may comprise code for performing any and/or all of the techniques described herein.
• the memory 210 may furthermore temporarily or persistently store data inputted to the robot controller 200 (e.g., desired motion 202), data to be outputted by die robot controller 200 (e.g., control output 204 ), and any intermediate data used to carr out the process steps of the robot controller 200 described herein.
• Memory 204 may be a dynamic random access memory (DRAM) device, a static random access memory (SRAM) device. Flash RAM (non-volatile storage), combinations of the above, or some other memory device known in the art.
• the processor 220 loads the computer-executable instructions and/or data from the memory 210 to carry out the process steps described herein.
• the memory 210 stores computer-executable instructions embodied as a high-level controller 216, a postural balance controller 212, and a step controller 214.
• the high-level controller 116 determines whether motion of die robot is controlled by the postural balance controller 212 or the step controller 214.
• the high-level controller 216 gives control to the postural balance controller 212 when the high- level controller 216 determines that the robot is not taking a step and does not need to take a step to maintain balance.
• the high-level controller 216 generally gives control the step controller 216 when the robot is stepping or when it detects a trigger condition indicating that the robot cannot maintain balance without taking a step.
• the robot controller 200 may include more or less components than those shown in FIG. 2 without departing from the scope of the present invention.
• computer system 200 may include additional memory, such as, for example, a first or second level cache, or one or more application specific integrated circuits (ASICs), in other embodiments, the robot controller 200 may be implemented entirely in hardware.
• ASICs application specific integrated circuits
• FIG. 3 illustrates an embodiment of a high-level process performed by the robot controller 200 for controlling a robot.
• the robot controller 200 receives 302 the robot state information (e.g., sensed data and current motion instructions), pertaining to the positions and/or velocities of different components of the robot.
• the robot controller 200 determines 304 whether the robot is currently stepping (or about to take a step). If the robot is currently stepping, the step controller 214 is used 312 to determine and control motion of the robot. Alternatively, if the robot is not currently stepping already, the robot controller 200 periodically determines 306 a generalized foot placement estimator (GFPE) based on the current dynamic state of the robot (e.g., positions and/or velocities of its joints).
• GFPE generalized foot placement estimator
• the GFPE represents a point on the ground surface where the robot will be in a balanced position if its foot is placed there. Generally when the robot is balanced, the GFPE will already be under the robot's CoM and therefore the robot need not take any action to retain balance. However, if the robot becomes unstable (e.g., in response to an external disturbance), the G FPE: will move away from under the robot's CoM and the robot may need to take some action to retain balance, such as making a postural change (e.g., rotating about the trunk) or taking a step. Calculation of the GFPE is described in further detail below.
• the robot controller 200 uses 310 the postural balance controller 212 to control the motion of the robot such that the robot will retain balance and carry out a motion based on its motion instructions. If, on the other hand, the robot controller 200 determines 308 that the GFPE falls outside the predefined region, the robot controller 200 instead uses 312 the step controller 214 to cause the robot to take a step to the determined GFPE location.
• the predefined region comprises the area under the robot's support base (e.g., its feet). The robot controller 200 then controls 314 joint actuators of the robot to achie ve the determined motion provided by either the step controller 214 or the postural balance controller 212. Operation of the postural balance controller 212 and the step controller 214 are described in further detail below.
• the GFPE comprises a predicted ground location such that the robot will be able to maintain balance if it steps to the predicted location.
• the GFPE can exist on both level and non-level ground.
• computation of the GFPE assumes that the ground either has a constant slope or has a single discontinuous slope change from where the robot is standing (see e.g., FIG. 9B).
• the robot has knowledge of the ground layout (e.g., the slopes and location(s) of the slope change).
• the ground layout can be automatically detected by the robot using, for example, its computer vision system or via other sensors.
• the robot controller 200 determines the GFPE based on a simplified dynamic model of the humanoid robot comprising a rimless wheel with only two spokes.
• the rimless wheel model is illustrated in FIG. 4.
• the rimless wheel model has massless spokes 402, 404 of fixed length representing each of the legs of the robot.
• the rimless wheel model also has a point mass 406 at the center of the wheel corresponding to the CoM of the robot.
• the GFPE corresponds to the point on the ground where the rimless wheel model would come to a complete stop with its CoM directly above the stepping location.
• FIG. 5 illustrates an example sequence of positions that the robot may take in response to a push and the corresponding rimless wheel mode! at each stage.
• a robot in a first position 502 is subjected to a push from behind.
• the robot takes a step in response to the push arriving at a second position 504 with its swing leg landing at the determined GFPE location 508.
• the robot then takes a follow-up step to bring the robot back to a vertically upright position 506 with its CoM above the GFPE 508.
• the GFPE can exist even on non- levei ground. Assuming that the robot knows the ground slopes, this GFPE exists in most cases unless stepping is physically not feasible due to the fixed length of the spokes or a steep slope.
• FIG. 6 illustrates an embodiment of a process for determining the GFPE based on the rimless wheel model described above. Since the rimless wheel model is defined in two- dimensional space and the robot exists in three-dimensional space, the high-level controller 216 determines 602 a plane on which the simplified rimless model resides. This
• the robot controller 200 estimates that the robot will move in the same direction as the velocity of the robot CoM, , just after a push. Consequently, the GFPE will be located on the line of projected on the ground.
• the two- dimensional plane 702 for the rimless wheel is therefore defined by two vectors: and the vertical through the CoM.
• the magnitude and direction of the push do not necessarily need to be known in order to compute the GFPE. Rather, in one embodiment, the selected plane is solely dependent on the states of the robot (i.e., joint angles and velocities) after the push.
• P' is the actual CoP of the robot and P is the projected CoP located on the wheel plane about which the wheel rotates.
• the region enclosed by the dotted black lines is the support, convex hull for the robot.
• the two feet of the robot are drawn disproportionally large in FIG. 7 to clearly show the convex hull and the points.
• an anchor point is determined 604 upon the two- dimensional plane where the rimless wheel touches the ground and rotates about. Setting an appropriate anchor point is important since the robot has extended feet while the rimless wheel model has a point, contact.
• the location of the anchor point affects the GFPE location and the decision for taking a step.
• the projected CoP P is used as the anchor point, as shown in FIG. 7.
• the CoP P' of the robot is projected on the two- dimensional plane and it is approximated that the rimless wheel rotates about the projected CoP, P, For several reasons, the projected CoP may make a better anchor point than another possible choice, the ground projection of the CoM.
• the CoP better represents the state of the robot for the purpose of push recovery, in part because its computation includes acceleration. For example, just after a push from behind, the CoP will be ahead of the CoM as in FIG. 7. If the projected CoM is instead used as the anchor point, even a small push may result in a big step which may not be necessary at all. For instance, if the robot is pushed from behind and the projected CoM is used as the anchor point, the push may make the CoM of the rimless wheel pass over the vertical. This would imply that the robot would topple forward and stepping would become necessary.
• the projected CoP P is used as the anchor point and is ahead of the projected CoM, the kinetic energy from a small push would be dissipated before the CoM rotates and passes over the vertical line through the projected CoP P. This implies that no step is necessary since the robot would not topple forward from that small push.
• a dynamic model is then applied 606 to model motion of the rimless wheel based on the determined plane and anchor point.
• the rotational inertia of the rimless wheel model is equal to the rotational inertia of the robot about the anchor point P.
• FIG. 8 illustrates four stages of motion of a rimless wheel model modeling a push from behind. Although FIG. 8 illustrates a case where the ground is flat, the described model is also valid for general non- level ground.
• the CoM is behind the anchor point but will pass over the anchor point since the robot has enough kinetic energy.
• the robot takes a step.
• the robot stops with the CoM above the foot contact.
• the fourth phase 808 models a follow-up step of the robot in which the swing spoke takes a step at the same step location of the support spoke.
• the first phase 802 and third phase 806 can be modeled as an inverted pendulum model.
• the second phase 804 is modeled as an instantaneous phase of collision where the wheel energy is lost.
• FIG.9A illustrates an inverted pendulum model modeling the first phase 802 and third phase 806 where only one of the support legs is in contact with the ground.
• the equation for motion is given by:
• ⁇ is the angle made by the support spoke and the vertical
• P is the rotational inertia of the rimless wheel about P
• m is mass
• g is the acceleration due to gravity
• / is the length of the support leg.
• the GFPE is next determined for non-level ground, i?. Whether to step on the next slope
• the robot determines 608 if it should take a step on the first slope or the second slope .
• Eqs. (6) and (7) together are the conditions for the robot to take a step on the second slope.
• the robot next determines 610 where to step. In the case of non-level ground where the conditions given by Eqs. (6) and (7) are satisfied, the robot takes a step on the second slope. In this case, the robot controller 100 determines the leg angle . which will stop the robot at the vertically upright configuration at the end of the stepping.
• FIGS. 10A-B The robot controller 200 first checks the geometrically possible range of a given the initial configuration. This detemiination is illustrated in FIGS. 10A-B.
• FIG. 1 OA shows a first limiting case.
• the robot based on the rimless wheel model
• camiot physically step between the two points P 2 and P3 in FIG 10A which are the points of intersection of the /- radius circle centered at ⁇ and the second slope.
• FIG. 10B shows a second limiting case.
• the distance from O to the stepping point, P 2 in FIG. 9B can be computed as:
• ⁇ is given as:
• the duration of stepping is an important parameter.
• One of the benefits from using the GFPE is that the robot can estimate the time during which the robot can take a step because the robot has dynamics and the stepping motion takes a certain amount of time.
• the duration of stepping is important also for the robot controller 200. If the estimated duration of step is too short for the robot to physically take a step, the robot controller 200 may switch to an emergency protocol such as fall-avoidance or damage minimization from fall, instead of trying to take a step. Since the robot is modeled as a two-dimensional inverted pendulum, an incomplete elliptic integral of the first kind is used to obtain the stepping duration.
• GFPE is predictive. It yields a future stepping point and duration for the step. This contrasts with other foot placement estimators that are state-dependent, and therefore may result in the estimated point moving away by the time the robot takes the step, in addition, the GFPE exists on the non-level ground as long as the slopes change discretely. In contrast, prior foot placement estimators assume a flat ground and cannot make foot placement predictions for non-level ground.
• a generalized balance control technique is now described for controlling motion of the robot.
• These general principles can be used to implement both the postural balance controller 212 and the step controller 214.
• the postural balance controller 212 balance parameters described below are configured such that the robot will attempt to preserve its desired linear momentum o ver angular momentum, and is therefore likely to respond to an external perturbation by making a postural change to maintain balance.
• the step controller 214 different parameters are configured such that the robot will instead respond to the push by taking a step to the GFPE location.
• the GFPE location therefore acts as an additional constraint on the robot's motion so that the robot will attempt to maintain its balance while stepping to the GFPE location.
• YQ is the CoM location and p is the CoP location.
• the spatial centroidal momentum, h may also be referred to as spatial momentum, or simply the momentum of the robot 1100.
• FIG. 1 I B depicts the robot's rate of change of angular momentum about the CoM, k , and linear momentum, / , respectively.
• the (spatial) momentum rate change has a one- to-one relationship with the GRF and CoP.
• the external forces illustrated in FIG. 11 A are solely responsible for the centroidal momentum rate change illustrated in FIG. 1 I B.
• I is completely determined by f and vice versa.
• the centroidal angular momentum rate change k is determined by both GRF ' f and the CoP location p.
• the CoP location p depends on both k and / . This implies that complete control of p requires control of both linear and angular momentum.
• the robot controller 200 maintains balance of the robot by control ling both the linear and angular components of the spatial momentum.
• behavior of the robot controller 200 is defined in terms of the desired momentum rate change.
• the desired momentum rate change may not always be physically realizable due to several constraints on the foot-ground contact.
• the CoP is constrained in that it cannot be located outside the robot's support base.
• the support base In the single support case (i.e., the robot's feet are positioned such that they provide a single support), the support base is identical to the foot contact area, whereas in the double support case on level ground, the support base is equivalent to the convex hull of the support areas of the two feet.
• the GRF must be unilateral in nature, and must not attract the robot towards the ground.
• the GRF must satisfy the friction limit of the foot-ground surface, so as not to cause slip.
• the robot controller 200 determines the admissible or physically realizable values of the momentum rate change that are as close as possible to the desired values while satisfying the above physical constraints. Subsequently, whole body joints are controlled to generate the admissible momentum rate change.
• the robot controls the external forces.
• the gravity force g cannot be manipulated, and the effect of T n is typically small. Therefore, the GRF J assumes substantial importance in momentum control, and its magnitude, line of action and the point of application (i.e., the CoP) have unique effect on the momentum.
• the desired GRF and CoP Due to the one-to-one correspondence between momentum rate change and GRF-CoP pair, the desired GRF and CoP are directly determined from the desired spatial momentum rate change.
• the desired GRF and CoP uniquely define the contact force and its location on the support foot. However, for double support, there can be infinitely many combinations of contact forces at the two feet that can create the desired momentum rate change.
• the individual foot GRF and foot CoP are instead computed directly from the desired momentum rate change. Assuming planar contact between the ground and each foot, the foot GRF is the ground reaction force acting on an individual foot and foot CoP is the location where its line of action intersects the foot support plane. These are contrasted from the more traditional net GRF and the net CoP, which are applicable when the two feet are taken together during double support.
• foot GRF and foot CoP are not only a choice of convenience, but a natural choice for balance control.
• the foot GRF and foot CoP are directly obtained as sensor data, whereas net GRF and net CoP are computed only as a subsequent step.
• ankle torques may be minimized while generating the desired momentum rate change. As will be described in further detail below, this may be achieved by solving two simple constrained linear least- squares problems. Minimizing ankle torque is important because typically the ankle torque is more constrained than others in that it should not cause foot tipping.
• the robot controller 200 controls both angular and linear momentum of the robot for balance maintenance.
• the control policy is defined in terms of the desired momentum, which allows for different control variations. Under different circumstances, the robot controller 200 can satisfy linear and angular momentum in different proportions as the situation demands.
• the postural balance control ler 212 is configured to preserve linear momentum in favor of making angular momentum changes.
• the step controller 214 is configured to preserve angular momentum in favor of changing linear momentum by executing a step to the GFPE location. Desired foot GRF and foot CoP are directly computed without requiring the robot controller 200 to compute the net G R F and net CoP.
• the balance control framework is applicable to non-level ground at each foot without any special treatment.
• the robot controller 200 computes foot GRFs and foot CoPs that minimize the ankle torques,
• the robot controller 200 generates a control signal 204 that enables a single or double-supported robot to maintain balance when subjected to pushing various directions. Furthermore, the robot can maintain balance when two feet are on separate moving supports with different inclinations and velocities. Furthermore, the robot controller 200 can be used for stepping motions.
• FIG. 12 is a flowchart illustrating the high-level process performed by the robot controller 200, details of which are described in further detail below. From the desired motion 202, the robot controller 200 determines 1202 desired angular momentum rate change
• the desired linear momentum rate change * d may include the linear momentum rate change ' d for enabling the robot to step to the determined GFPE location.
• the robot controller 200 determines 1204 admissible foot ground reaction forces (GRFs) and foot center of pressures (CoPs) from the desired momentum rate change.
• GRFs foot ground reaction forces
• CoPs foot center of pressures
• the admissible foot GRF and foot CoPs are constrained based on balance constraints (e.g., the admissible CoP may be constrained to the area under the support base or the robot may topple over).
• the admissible foot GRF and foot CoPs may not precisely result in the desired momentum rate change if the robot is not physically capable of producing the desired momentum rate change while still maintaining balance.
• the admissible foot GRF and foot CoPs result in an admissible momentum rate change that is optimally close to the desired momentum rate change under the imposed constraints.
• the admissible momentum rate change is determined 1206 from the admissible foot GRF and foot CoPs.
• the robot controller 200 determines 1208 joint accelerations that will achieve the admissible momentum rate change based on the desired motion of joints and feet.
• the robot controller 200 determines 1210 joint torques to achieve the joint accelerations and the admissible foot GRF.
• a iR ⁇ denotes the base frame (trunk) configuration and n is the total number of joint DoFs.
• the subscripts 0 and s denote the base frame and joints, respectively, with 5 implying "shape" associated with the joint angles in geometric dynamics.
• the total DoFs of the robot is thus 6 + n, because the floating base has 6 DoFs.
• ⁇ G K b denotes the generalized forces
• H is the joint space inertia matrix
• c includes Coriolis, centrifugal, and damping forces
• T G is the gravity torque.
• c is a vector representing external "constraint" forces from the ground, determined by foot GRFs and CoPs, and the Jacobian / transforms f c to the generalized forces.
• the dimension of j c depends on the nature of constraint at the foot-ground contact. For example, for single support. f c is 6 x 1 (3 for force and 3 for torque) whereas for double support, when a non- slipping planar contact between the foot and the ground is maintained, it is 12 x 1.
• (21) can be divided into two parts, one corresponding to the base, denoted by the subscript 0, and the other, subscripted with s, for the joints. Then (20) and (21) are rewritten as follows:
• the postural balance controller 112 determines the control torques T s to control dynamics of the robot and maintain balance.
• the postural balance controller 112 solves an optimization problem.
• the computational cost of the optimization increases rapidly as the dimension of the search space increases.
• the simplest optimization problem such as the least-squares problem has order O (n j ) time complexity. Therefore, for improved computational efficiency, a sequential approach may be used.
• the balance control problem is divided into smaller sub-problems, which can be solved serially, Moreover, by computing f c and ⁇ first, an efficient linear-time algorithms for inverse dynamics can be used, without having to compute the joint space equations of motion (21) which has a quadratic time complexity.
• the robot controller 200 determines 1202 the desired angular and linear momentum rate changes and
• the desired rotational behavior may be defined in terms of the CoP instead of angular momentum.
• the GRF-CoP combination has a one-to-one relationship with momentum rate changes, their significance regarding balance are ver different. Whereas the GRF and CoP charac terize the magnitude, direction and point of application of the external forces, the momentum rate changes describe the resulting motion of a robot.
• the unilateral nature of robot-ground contact and friction limits impose important direct constraints on the range of GRF and CoP. These influence the achievable range of momentum rate change, but only indirectly.
• the controller 200 uses momentum as control objectives and uses GRF and CoP as constraints.
• the overall behavior of the robot against external perturbations is determined by the desired momentum rate change.
• the robot controller 200 employs the following feedback control policy:
• Id/m T 2 i (r G ⁇ r G ) + r c)
• a " and are the desired rates of change of centroidal angular and Imear momentum, respectively, m is the mass of the robot, FQJ is the desired CoM position, k is the actual angular momentum of the robot, YQ is the actual CoM position of the robot, and f " G is the actual CoM velocity of the robot.
• Y)j represents a 3 x 3 diagonal matrix of feedback gain parameters that may be experimentally determined.
• the feedback parameters ⁇ /? ⁇ vary between the postural balance controller 212 and the step controller 214 to achieve the different push recover ⁇ ' behaviors.
• a small value of 1 3 1 and large values of f 21, 1 22 will generate the motion shown in FIG. 1 A after a push from behind.
• postural balance controller 212 tries to respect linear momentum with higher priority over angular momentum.
• the desired angular momentum is set to zero to keep the robot upright, and the bending motion generates angular momentum which contributes to the error in k .
• the generated angular momentum helps to pull the CoM backward and the small
• ⁇ I makes the controller almost ignore the angular momentum error.
• the step controller 214 applies a large Y n that causes the robot to respect angular momentum more strictly. When the desired angular momentum is zero, which is reasonable for stepping motion, the controller would move the robot CoM position rather than bend the upper body. The robot generates linear momentum by stepping to the
• the step controller 214 uses gains
• ⁇ 11 diag ⁇ 20, 20, 20 ⁇ , ⁇ 21 ::: diag ⁇ 2, 2, 5 ⁇ , and ⁇ 22 :::: diag ⁇ 3, 3, 8 ⁇ .
• Various sensors may be used to directly measure k, YQ , and ⁇ c , or the controller
• each joint of the robot has a position encoder which supplies joint position data (e.g., joint angle) to the controller 200.
• the controller 200 may apply time differentiation to the joint position data to obtain joint velocities (e.g., angular velocities),
• the robot's trunk may be equipped with an internal gyroscope and accelerometer. The gyroscope measures trunk angular velocity, which the controller 200 can integrate to obtain the trunk's angular position.
• the accelerometer generates linear acceleration of the trunk, which the controller 200 can integrate to obtain the trunk's linear velocity, and twice integrate to obtain the trunk's linear position.
• the controller 200 can compute k, YQ , and YQ from one or more the various types of sensed data, in alternative embodiments different types of sensors may be used to derive the measured quantities.
• the robot may be equipped with force sensitive skin that can directly measure applied forces, and these measured forces can be used to determine k, TQ , and FQ .
• the robot also has a force sensor in each foot.
• Each force sensor measures the GRF, which includes three components of linear force and three components of torque.
• the controller 200 can compute GRF indirectly through the observed dynamics.
• the robot controller 200 determines 1204 admissible foot GRF and CoP such that the resulting momentum rate change (i.e., the admissible momentum rate change) is as close as possible to the desired values.
• a desired momentum rate change may not be admissible, for example, because it would require a desired CoP, J? ⁇ , that is outside the robot's support base, and attempting to implement the desired momentum rate change would therefore cause the robot to topple over.
• the GRF must be unilateral in nature, and must not attract the robot towards the ground.
• the robot may not be able to achieve desired momentum rate changes, k d and I it that are outside the robot's physical capabilities (e.g., if the desired momentum rate changes, k d and l d would require an actuator to produce a torque greater than it is capable of producing or a limb would be required to demonstrate a motion outside its physical range).
• the robot is constrained by its admissible CoP and its admissible GRF, which in turn may limit the desired momentum rate change to an admissible momentum rate change.
• the robot controller 200 determines the optimal foot GRF and foot CoP that will create the admissible momentum rate change, as close as possible to the desired momentum rate change.
• the robot controller 200 may strike a compromise and determine whether to attempt to preserve k or more strictly.
• the desired CoP location, j3 ⁇ 4 is translated to the closest point of the support base resulting in an admissible CoP location, J?.
• the magnitude and line of action of the desired GRF f j is unchanged in the resulting admissible GRF .
• the linear momentum objective of the desired motion 202 is satisfied (i.e., the CoM remains stationary) but the angular momentum objective is somewhat compromised.
• the robot may topple over because the desired CoP location p c i is outside the support base.
• the behavior emerging from this solution is characterized by a trunk rotation (see e.g., FIG. 1 A). This strategy can be obsen'ed in the human when the trunk yields in the direction of the push to maintain balance.
• the step controller 214 in addition to translating the desired CoP, P d , to the support base resulting in an admissible CoP, J?, as before, the direction of the desired GRF fj can be rotated resulting in the admissible GRF f.
• the angular momentum objective is satisfied (i.e., the robot does not perform a trunk rotation), and the linear momentum is controlled to achieve a step to the GFPE location.
• the robot moves linearly along the direction of the applied force due to the residual linear momentum and prevents falling by taking the step (see, e.g., FIG. I B).
• ankle torques may be taken into account in determining foot GRFs.
• f r and fi are the GRFs at the right and left foot, respectively, and T r , ⁇ /are the positions of the body frames of the foot, located at the respective ankle joints.
• M i is the orientation of the foot
• d is the foot CoP in body frame
• FIG. 14 A diagram illustrating this representation is shown in FIG. 14.
• the pressure from the ground to the right foot is representing using CoP, denoted by d r in the right foot frame ⁇ R ⁇ , a vertical moment T ' ⁇ - ; r and the GRF f r .
• f r is represented with four basis vectors ⁇ r J( j
• ankle torques are meaningful because they are limited more severely than other joint torques due to the unilateral nature of contact.
• the ankle torques (k T ⁇ 0) f 00 t GRFs J r and J should create as close to the desired angular momentum rate change k,() as possible while satisfying * fl - . If k ⁇ ⁇ ⁇ & d > the ankle torques can vanish. If k ⁇ k d , the ankle torques are determined to account for the residual angular momentum rate change, d — k - ,
• Each loot GRF is modeled using four basis vectors ⁇ ' ⁇ ⁇ '. ' /and their magnitudes ' ⁇ that approximate the friction cone (an inverted pyramid in FIG. 14) on the ground:
• T r and Fi are detennined by the configuration of the robot; they are constants when solving this problem. Therefore becomes a linear equation of Pi when
• [0117] (38) can be solved using a Non-Negative Least-Squares algorithm, which has the merit of not requiring parameter tuning.
• I is chosen such that ⁇ 1 is zero, i.e., the line of action of J" , ⁇ intersects the ankle.
• Eq, (43) may be sol ved using an appropriate method, such as, for example, the Levenberg-Marquardt method, or other known methods. Note that both the least squares problems have a small number of variables, so the optimization can be carried out quickly.
• the robot controller 200 determines 1108 the joint accelerations that will generate the admissible momentum rate change as well as the foot contact constraints.
• (47) is used because the balance controller defines its objectives in terms of centroidal momentum. Specifically, the robot controller 200 computes the output accelerations a such that they minimize the following objective function:
• (48) can be viewed as an inverse kinematics problem with three task objectives: momentum rate change, style, and contact constraints.
• (22) By treating (22) as a hard constraint, it has a higher priority over the others.
• (48) is solved by converting it to a least- squares problem with linear equality constraints.
• the feedforward torque input ⁇ ⁇ $ is computed from ⁇ « and the admissible external forces by performing inverse dynamics.
• the hybrid system dynamics algorithms may be used, which is useful for performing inverse dynamics for floating base mechanisms. Since external forces are explicitly specified for all the links contacting the ground, the robot can be treated as an open loop system even when multiple links are in contact with the ground, thereby making it possible to use the inverse dynamics algorithm for open-loop systems.
• the desired motion of the feet acts as an input to the balance controller.
• the desired foot accelerations . are set such that each foot has the desired configuration c ⁇ Ei 3) and velocity v ⁇ ⁇ se ⁇ 3)_ Specifically, for each foot, zwe use for * k p and / are proportional and derivative feedback gains, respectively.
• the ' * se l ⁇ j function computes the twist coordinates corresponding to a transformation matrix.
• the configuration T and velocity v of a foot can be computed from the forward kinematics operation assuming that the robot can estimate the configuration and velocity of the trunk, e.g., from an accelerometer and a gyroscope.
• the robot controller 200 controls a humanoid robot to maintain balance on non- level, non-continuous, and non-stationary grounds.
• the robot controller 200 allows the robot to maintain balance under relatively large perturbations and respond to such perturbations with human-like balancing behavior.
• the robot controller 200 can deal with different ground geometry and ground frictions at each foot.
• each trajectory is a quadratic Bezier curve defined as:
• planar CoM trajectory uses current CoM, FQ, pivot foot position 7 / and the half-
• Tj is a pivot foot position
• T r is a swing foot position
• T t is a target stepping point for the swing foot.
• the reason for using the center of the pivot foot is to achieve the CoP moving inside of the pivot foot print so that a robot can make a stable step.
• the height of CoM trajectory can be designed by modeling a robot as a rimless wheel model on the slope.
• velocities of the trajectories are parameterized so that it has zero velocity at the start and the end.
• the duration of the trajectory comes from the duration of stepping multiplied by a safety factor (70%) considering the discrepancy between the simplified model and the real humanoid.
• FIGS. 16A-16B illustrate motion of the robot when subjected to various perturbations and/or when standing on non-level or non- stationary supports.
• the initial desired motion 202 of the robot is stationary, but the robot decides to take a step in response to a push.
• FIG. 16A for example, the robot is subjected to a push from behind when standing in front of uphill sloping ground.
• the robot determines a GFPE location 1602 indicated by the cross. Because the GFPE location 1602 is determined to be outside of the foot, the robot takes a step to maintain balance
• FIG. 16B illustrates a similar situation for downhill sloping ground. Due to the downhill slope, the GFPE 1604 is further away from the robot, thereby causing the robot to take a bigger step.
• the robot can maintain balance in response to external disturbances such as a push by selectively using momentum-based postural balance control and reactive stepping, By switching By switching between controllers for respecting linear momentum and angular momentum, a biped robot can choose to take a step or re-balance without stepping according to the magnitude of external disturbance,
• the GFPE beneficially provides a stepping location for stepping on non-le vel ground. Desirable properties of the GFPE include: 1 ) The point is predictive so that the controller may start stepping early. 2) The point may exist on the non- level ground while many previously proposed reference points for stepping do not. 3) Computation of the point y ields both the time required for stepping as well as the location of the point itself.

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• 2012
  • 2012-03-20 US US13/425,383 patent/US8849454B2/en active Active
  • 2012-03-20 WO PCT/US2012/029848 patent/WO2012129250A2/en not_active Ceased
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