Dynamic Locomotion For Passive-Ankle Biped Robots And Humanoids Using Whole-Body Locomotion Control

1 Introduction

• The paper targets a gap between dynamic walking methods and humanoid task-based whole-body control, which had not been extended to full humanoid systems.Earlier humanoid approaches often used task-oriented inverse kinematics and inverse dynamics with horizontal CoM control, while dynamic walking methods used foot placement without directly controlling the CoM instantaneous state.Source: §1 · pp. 1–2
• The framework achieves unsupported dynamic walking with passive-ankle and full humanoid robots using a whole-body controller and dynamic locomotion planner.The authors report testing on Mercury and DRACO, with additional simulations on humanoid robots.Source: §1 · p. 2
• TVR uncertainty analysis sets stable-locomotion accuracy targets of 1 cm for landing-foot positions and 0.5 cm for estimated CoM state.The authors report using motor-position feedback and feedforward current commands to address the required tracking accuracy and drivetrain friction and stiction.Source: §1 · p. 2
• WBLC combines kinematics-level joint-position commands with dynamics-level torque commands, while low-level motor-position feedback and feedforward current replace joint torque feedback.The authors report that joint-position control worked better than joint torque control in their system.Source: §1 · p. 2, Figure 1 · p. 3
• WBLC relaxes contact constraints into cost terms, then reduces those costs during foot detachment to smooth contact transitions and reduce movement jerk.High contact-acceleration weights emulate contact constraints; tapering the weights as a foot lifts enables smooth transitions.Source: §1 · p. 2
• The TVR planner updates foot landing locations from the CoM state during swing, supporting dynamic walking robust to control errors and external disturbances.It plans landing locations at the midpoint of swing-leg trajectories.Source: §1 · p. 2
• Experiments with Mercury cover dynamic balancing, directional walking, and rough-terrain walking; the same methods also produced dynamic walking with the new DRACO biped.The authors report deploying the methods on DRACO within a few days of developing its joint-position controllers.Source: §1 · p. 2

2 Related Work

• ATRIAS is described as a close precedent for unsupported dynamic balancing and walking, while this work emphasizes methods applicable to whole-body humanoid control on passive-ankle bipeds.The authors characterize their TVR-based planner and jerk-reducing whole-body controller as distinct contributions.Source: §2 · p. 3
• Published work made it difficult to determine how much ATLAS Dynamics (2018) and ASIMO Honda (2011) relied on ankle actuation, foot support, or particular control methods.The passage says those implementation details were not available in published work.Source: §2 · p. 3
• Prior work on passive walking and actuated planar bipeds informs locomotion research, but the cited studies do not provide the paper’s focus on feedback control for unsupported biped walking.The passage notes that Raibert et al. (1984) demonstrated unsupported single-leg hopping, while body-posture control, stance-leg ground interaction, and disturbances from other limbs were omitted in the discussed work.Source: §2 · p. 3

3.1 Whole-Body Locomotion Controller (WBLC)

• WBLC combines motor position feedback with feedforward torque commands and sequential kinematic- and dynamics-level control blocks.KinWBC computes joint commands from prioritized operational-space tasks; DynWBC computes torque commands consistent with robot dynamics and changing contact constraints.Source: §3.1 · p. 4

3.1.1 Kinematic-level Whole-Body Controller (KinWBC)

• KinWBC computes joint increments from operational-space position errors using null-space task prioritization.It derives joint position, velocity, and acceleration commands for the subsequent control block.Source: §3.1.1 · p. 4

3.1.2 Dynamic-level Whole-Body Controller (DynWBC)

• DynWBC treats contact accelerations as weighted costs rather than hard constraints, adjusting contact weights and force bounds during transitions.This formulation is termed reduced “jerk” whole-body control.Source: §3.1.2 · pp. 4–5
• The DynWBC formulation empirically produces rapidly changing but smooth torque commands compared with hard contact constraints.Passive-ankle contact changes are described as more sudden than those of robots controlling horizontal CoM movement.Source: §3.1.2 · p. 5

3.2 Joint-Level Controller

• Joint-level control combines motor-position PD feedback with feedforward torque and accounts for spring deflection when computing motor positions.The torque command is the feedforward input, and the spring constant is considered because motor-position conversion otherwise ignores spring deflection.Source: §3.2 · p. 5

3.3 Time-to-Velocity-Reversal (TVR) Planner

• The TVR planner updates foot placements from CoM position and velocity around mid-swing, using a simplified constant-CoM-height model.The planner reverses CoM velocity each step; the passage states that CoM movement is asymptotically stable.Source: §3.3 · p. 5

4.1 Formulation of the Planner

• The planner computes a stance-foot location to reverse CoM velocity after a chosen time, then adds a bias term to steer the robot toward the origin.It models the CoM with a linear inverted pendulum and updates foot landing locations step by step.Source: §4.1 · pp. 5–6
• With eigenvalue magnitudes set to 0.8, simulated phase trajectories from three initial states converge toward the origin over eight steps.The feedback policy has a PD form, and its parameters are tuned so the closed-loop eigenvalues are below one.Source: §4.1 · p. 6, Figure 2 · p. 7

4.2 Uncertainty Analysis

• The uncertainty analysis models foot-landing error as a scalar and CoM state-estimation error as a vector, under a 0.5 m step limit and ignored state-dependent errors.It evaluates convergence over two steps because the CoM velocity changes sign at each step.Source: §4.2 · p. 6
• The uncertainty ball marks states without guaranteed asymptotic stability, while the light-blue region marks states recoverable in one step without violating foot-placement limits.The ball’s radius grows with observation and control errors; the analysis compares it with the feasible CoM-state region.Source: §4.2 · p. 7, Figure 2 · p. 7
• After hardware and control improvements, the uncertainty region lies within the feasible CoM-state region, so the foot policy can find stabilizing landing locations.The analysis describes this region using the TVR planner’s landing-error and state-estimation-error bounds.Source: §4.2 · p. 7

5 Mercury Experimental Robot

• Mercury has six actuated hip and knee joints, series-elastic actuators, virtual floating-base joints, and LED sensors for motion-capture-based body sensing.Joint encoders also provide relative position with respect to the stance foot for foot-landing control.Source: §5 · p. 8, §5.1 · p. 8

5.2 Hardware Upgrades

• Mercury’s upgrades replaced its low-performance IMU, weak structure, and quasi-pointed feet that had contributed to poor orientation estimates, buckling, and yaw rotation.The redesign added a tactical IMU, reinforced leg structures, and spring-loaded passive feet with contact switches.Source: §5.2 · pp. 8–9, Figure 4 · p. 9

5.3 Challenges in Passive-Ankle Locomotion

• Mercury’s mass distribution resembles humanoids such as Valkyrie and Atlas, with torso CoM near the body center and a leg-to-torso mass ratio of about 0.4.ATRIAS differs, with its torso CoM near the hip and a leg-to-torso ratio below 0.1.Source: §5.3 · p. 9, Figure 5 · p. 10
• Mercury’s humanoid-like mass distribution makes body-orientation control harder than ATRIAS’s, while its significant leg mass also perturbs the body during swing.Mercury’s torso CoM is above the hip, increasing the moment arm, and its swing leg requires whole-body compensation for Coriolis and gravitational effects.Source: §5.3 · pp. 9–10

6.1 Walking Control

• The swing phase can end early on detected contact, and the TVR planner updates the next foot placement midway through swing.The walking cycle proceeds through swing, double stance, and contact transition.Source: §6.1 · p. 10, Figure 6 · p. 10, Table 2 · p. 10

6.2 Task and Weight Setup of WBLC

• WBLC prioritizes body posture over swing-foot motion and assigns stance- and swing-leg actuators distinct roles to limit task coupling.During contact transitions, DynWBC relaxes contact conditions through weights, while KinWBC interpolates joint commands to reduce jerk.Source: §6.1 · p. 10, §6.2 · p. 11

6.3 Base State Estimation

• The controller uses the robot’s base state as a proxy for CoM state; base and CoM velocities were nearly indistinguishable, supporting sensor fusion with a Kalman filter.Encoder-derived velocity fluctuates, so the implementation uses filtered motion-capture velocity data and fuses motion-capture and encoder measurements.Source: §6.3 · pp. 11–12

6.4 Kinematic Model Verification With MoCap Data

• Motion-capture calibration of Mercury’s kinematic model produced a final model with less than 5 mm error.The model parameters were tuned by comparing motion-capture LED positions with positions computed from the kinematic model during leg swings.Source: §6.4 · p. 12, Figure 8 · p. 12

7 Results

• Unsupported Mercury experiments showed stable directional walking, push recovery, and mildly irregular-terrain walking; the same schemes also achieved dynamic balancing on DRACO and were simulated on other humanoids.The simulations included dynamic walking and Valkyrie locomanipulation.Source: §7 · p. 12

7.1 Directional Walking

• Mercury followed commanded cardinal-direction paths relatively well, but converged slowly laterally; joint torques transitioned smoothly across contact changes.Spring-deflection compensation also brought sensed knee positions close to commands when the knees supported body weight.Source: Figure 9 · p. 13, §7.1 · p. 13

7.2 Robustness Of Balance Controller

• A 0.32 kg football impact disturbed Mercury at step 28; it fully recovered balance by step 30 and returned to its nominal regime at step 31.During recovery, the planner limited a foot placement to 10 cm from the stance leg to avoid collision, then commanded a 48 cm step to reverse velocity.Source: §7.2 · pp. 13–14, Figure 10 · p. 14
• Outside recovery steps, Mercury’s landing-location errors were below 0.5 cm in the reported steps and consistently below 0.5 cm in extended data.The recovery steps were 29 and 30.Source: §7.2 · p. 14
• With κx set to 0.25, Mercury traversed mildly irregular mats despite terrain variations and feet sometimes catching on mat edges.The experiment involved no terrain-topology knowledge or sensing.Source: §7.2 · p. 14, Figure 12 · p. 15

7.3 Experimental Evaluation On New Biped Robot DRACO

• DRACO balanced unsupported using WBLC and TVR with its ankle pitch made soft to emulate a passive joint; testing also demonstrated transfer of the framework across robots.The experiment used planner parameters similar to Mercury’s, with adjusted feedback gains.Source: Figure 13 · p. 15, §7.3 · p. 15

7.4 Simulation Results in Assorted Platforms

• Simulations showed dynamic walking for Mercury, DRACO, and Atlas, and locomanipulation for Valkyrie using additional hand- and head-orientation tasks.Atlas and Valkyrie were full-body humanoids with actuated ankles, so their tasks and contact constraints were modified.Source: §7.4 · pp. 15–16, Figure 14 · p. 16

8 Conclusions

• WBLC and TVR achieved robust dynamic walking across bipeds, including one without ankle actuation, with hardware demonstrations on Mercury and DRACO and humanoid simulations on Atlas and Valkyrie.The uncertainty analysis identified allowable estimator and controller errors and informed redesign and tuning.Source: §8 · p. 16
• The authors describe the presented controller as their best-performing formulation after system-level integration and extensive testing of task specifications and feedback options.Source: §8 · p. 16
• DRACO’s dynamic locomotion exploration was initial; future work includes turning and cluttered-environment robustness tests, while Mercury cannot change heading without yaw actuation.Source: §8 · p. 16

Appendix 1: Index to multimedia extensions

• The multimedia extension is a video of experimental and simulation results from Section 7.Source: Appendix 1: Index to multimedia… · p. 18

• Raibert, capture-point, Rezazadeh, and TVR planners express foot placement as a weighted sum of CoM state, using position and velocity feedback gains.The equation’s p, x, and ˙x denote foot landing position and sensed CoM position and velocity, respectively.Source: Appendix 2: Difference Among Footstep… · p. 18
• Raibert’s hopping foot-placement equation is a variation of Eq. (42), with kp = KKp and kv = K(Kv + 1) + Tst/2.Source: Appendix 2: Difference Among Footstep… · p. 18
• Capture point (CP), using the LIP model, computes the foot’s center of pressure (CoP) to drive the CoM velocity to zero at the CoP location given the current CoM state.The cited text says its expression uses Eq. (42) with kp set to 1; g is gravitational acceleration and h is CoM height.Source: Appendix 2: Difference Among Footstep… · p. 18
• Capture point places the CoP so CoM velocity reaches zero and the robot stops over it; TVR places a footstep to reverse CoM velocity before it reaches that location.Source: Appendix 2: Difference Among Footstep… · p. 18
• Rezazadeh’s in-place planner includes previous-step CoM velocity, but its velocity-error effect is not very significant for in-place walking; TVR is also a variation of Eq. (42).TVR uses kp = (1 + κ) and kd = w−1 coth(ωt′).Source: Appendix 2: Difference Among Footstep… · p. 18
• TVR’s parameter t′ should be close to half the designated swing time, with further asymptotic-stability tuning possible by checking the eigenvalues of A + BK.Source: Appendix 2: Difference Among Footstep… · p. 18

• F is given as the sum of three norm terms: ||(AcB)⊤P AcB||, 2||B⊤P AcB||, and ||B⊤P B||.Source: Appendix 3: Definition of g(ζ⊤P ζ) · p. 18
• The displayed expression F is a sum of three norm terms; its middle additive term is exactly 2||B⊤P AcB||, between ||(AcB)⊤P AcB|| and ||B⊤P B||.Source: Appendix 3: Definition of g(ζ⊤P ζ) · p. 18
• F is expressed as three additive norm terms: the first is ||(AcB)⊤P AcB||, the middle is twice ||B⊤P AcB||, and the last is ||B⊤P B||.Source: Appendix 3: Definition of g(ζ⊤P ζ) · p. 18