Source-linked AI summary
LAC: Linear and Angular Compliance for Humanoid Whole-body Control
Yang Liu, Zhongkai Gu, Wei Zhu, Mitsuhiro Hayashibe
TL;DR
Humanoid loco-manipulation needs compliance with external wrenches across the upper body, including independently commanded linear and angular responses. LAC synthesizes feasible compliant motions from sampled interaction events and trains a single policy with teacher-student reinforcement learning, with simulation and real-robot experiments confirming whole-body compliance, stiffness modulation, and teleoperated task utility.
Problem
Existing humanoid controllers often reject external forces or provide limited compliance without commanded angular effects across the upper body.
Method
LAC augments human-interaction motion data with force- and couple-driven virtual-admittance responses and trains one policy through teacher-student reinforcement learning.
Results
Simulation and real-robot experiments confirm whole-body wrench compliance across the upper body, monotonic modulation over both stiffness-command ranges, and applicability to loco-manipulation tasks.
Takeaways & Limitations
LAC supports adjustable compliant interaction for tasks ranging from transporting soft objects to carrying heavy boxes and pushing open spring-loaded doors.
Abstract
from arXiv · showhide
Real-world humanoid tasks involve physical interaction with objects and humans, yet current controllers either reject external forces as disturbances or restrict compliance to limited body links while ignoring angular effects. We present LAC, a general whole-body controller that simultaneously realizes commanded Linear and Angular Compliance for wrenches applied to the upper body. First, we synthesize whole-body compliant responses into a large-scale augmented dataset. Sampled force and couple events are imposed on contact frames extracted from human interaction data. At each contact link, the external force and a virtual torque from the passively yielding kinematic chain drive a virtual admittance under the commanded stiffness. Subsequently, teacher-student reinforcement learning trains a single policy to track the compliant motions under external wrenches. Finally, extensive simulation and real-world experiments demonstrate whole-body compliant responses to wrenches across the upper body, monotonic modulation over the full range of both stiffness commands, and applicability to teleoperated loco-manipulation tasks. Project website: https://lac-humanoid.github.io/
I. INTRODUCTION
LAC addresses the need for humanoid controllers that comply with external wrenches across the upper body while independently commanding linear and angular stiffness. It synthesizes feasible compliant motions and trains one policy, with simulation and real-robot validation.
- Real-world loco-manipulation requires continuous force interaction, whereas many existing controllers reject external forces as disturbances.
- Grasping and object-carrying tasks require independently adjustable linear and angular stiffness to accommodate different interaction needs.
- A single learned policy needs compliant training responses that are both physically feasible and observable from proprioception.
- LAC imposes sampled force and couple events on human-interaction contact frames, uses virtual admittance and whole-body inverse kinematics, then applies teacher-student reinforcement learning.
- LAC provides whole-body responses to wrenches at different upper-body locations and is presented as the first humanoid method with experimentally verified commanded linear and angular compliance.
II. RELATED WORK
Prior work spans classical and learned compliance methods, including quadrupedal and humanoid controllers. Existing humanoid approaches leave limitations in generality, multi-link coverage, or experimentally supported angular stiffness.
- Classical compliance methods include hybrid position/force control and impedance control, while learned policies can modulate impedance parameters for contact-rich manipulation.
- Table I is presented as a capability comparison with prior work, while an en dash denotes absent supporting experimental evidence.
- Quadrupedal reinforcement-learning controllers achieve compliance by relaxing tracking rewards, learning explicit end-effector force control, or tracking commanded virtual impedance.
- SoftMimic synthesizes compliant motion augmentation with whole-body inverse kinematics, but each policy is trained for one motion clip and one hand link at a time.
- SoftMimic lacks experimental evidence for its angular stiffness command, highlighting an unresolved humanoid compliance capability.
A. Problem Definition
The problem is to control humanoid loco-manipulation with adjustable linear and angular stiffness while maintaining commanded locomotion and posture. External upper-body wrenches produce whole-body deviations governed by the stiffness commands.
- The robot receives base velocity, base height, and upper-body reference joint-angle commands for loco-manipulation.
- A five-dimensional stiffness command specifies linear-angular stiffness for both arms and linear stiffness for the torso.
- One or more externally applied upper-body wrenches are unobserved directly by the robot, while the stiffness commands prescribe the resulting response.
- Linear stiffness controls contact-link center-of-mass displacement, whereas angular stiffness controls link rotation.
- The robot outputs 23 whole-body joint angles that maintain balanced locomotion while realizing command deviations dictated by external wrenches and stiffness.
B. Compliant Motion Augmentation
LAC synthesizes physically feasible whole-body compliant motions by applying force and couple events to retargeted human-interaction contact frames, then solving virtual admittance dynamics and whole-body inverse kinematics. The resulting dataset spans upper-body contacts and independently commands linear and angular compliance.
- Human–object and human–human interactions are retargeted into contact frames containing reference joint angles, contact points, and surface normals.
- Sampled force or couple events are applied at active contact points using shared trapezoidal time profiles.Force events use environment-spring displacement, while couple events apply torque without an external force.
- A virtual admittance balances external force, external couple, passive-chain torque, and commanded-stiffness impedance to generate target contact-link poses.The passive rotation of each link under the wrench provides the angular-response reference.
- The torso uses only linear compliance because its single waist-yaw joint permits little passive rotation.At steady state, the angular response reproduces the passive arm at κ, with smaller stiffness producing larger rotation and larger stiffness producing smaller rotation.
- Whole-body inverse kinematics converts admittance targets into augmented trajectories while anchoring the base and regularizing upper-body joints toward the reference.Locomotion commands are zero during synthesis, and walking is reintroduced during policy training.
- 378,051 accepted episodes produce about 1,050 hours of augmented data, including 278,258 force-event and 99,793 couple-event episodes.Hands and torso receive 88% of events; couple events target arm links, while force events reach all eleven upper-body links.
C. Reinforcement Learning with Augmented Samples
Teacher–student reinforcement learning trains a deployable policy to track augmented compliant motions while preserving locomotion behavior. Curriculum scheduling, symmetry augmentation, and rare-contact reweighting address the structure of the synthesized training data.
- Training replays augmented episodes with external wrenches, commands, and motion targets represented in command–residual form.
- The deployable policy receives proprioception and commands, while privileged training observations include external wrenches, base state, and motion residuals.The actor consumes a 10-frame deployable history, and the estimator uses a 64-frame history.
- A two-stage RMA-style teacher–student scheme trains a privileged encoder–actor first, then regresses its latent representation from proprioceptive history for deployment.The deployed estimator–actor pair runs at 50 Hz and outputs targets for all 23 joints.
- Rewards combine augmented-motion tracking with bipedal gait shaping, stance constraints, and auxiliary terms.
- Wrench curriculum bins unlock stronger events as tracking rewards improve, with the full curriculum enabled in the second training stage.
- Symmetry augmentation and reweighted episode sampling compensate for left–right imbalance and underrepresented elbow and shoulder contacts.The sampling scheme up-samples rare contacts and improves performance at those links.
A. Effectiveness of Linear and Angular Compliance
LAC continuously modulates whole-body pose responses through independently commanded linear and angular stiffness. Across simulated and real tests, linear stiffness primarily changes displacement, while angular stiffness primarily changes attitude.
- Linear stiffness: The linear-stiffness figure plots hand-link CoM displacement and attitude change against commanded arm stiffness on logarithmic axes.Displacement uses dashed lines with hollow markers, while attitude uses solid lines with filled markers.
- Angular stiffness: The angular-stiffness figure plots attitude change and CoM displacement against commanded arm stiffness on logarithmic axes.Attitude uses solid lines with filled markers, while displacement uses dashed lines with hollow markers.
- Angular stiffness: Angular stiffness from 10 to 100 N m/rad produces monotonically decreasing attitude change while largely preserving the position response.In the couple test, attitude change falls from 60° at 10 to 17° at 100.
- Sim-to-real transfer: The real angular-stiffness curve matches simulation in both trend and range during the lateral-pull test.This indicates transfer of the policy from simulation to the real robot.
B. Comparison with Baseline Methods
Against baseline controllers, LAC provides compliant, balanced responses and the only monotonic stiffness modulation across all tested scenarios. It also spans a wider displacement range than the compared methods.
- Qualitative comparison: Under a forward and downward palm force, LAC steps forward, extends the arm, lowers its height, and moves back toward the initial state as the force decreases.Its motion remains compliant, natural, and balanced throughout the force event.
- Quantitative comparison: LAC is the only compared method whose CoM displacement decreases monotonically with its stiffness command in all three scenarios.The comparison averages force-peak contact-link displacement over three trials.
- Quantitative comparison: LAC’s torso displacement decreases from 49 cm at the low end to 8 cm at the high end.SoftMimic and GentleHumanoid cover narrower ranges, while FALCON provides one fixed response.
C. Performance in Real-World Tasks
Real-world tests show whole-body compliance to wrenches at multiple upper-body locations and independent angular-stiffness effects. VR teleoperation uses stiffness commands to adapt compliance to soft-object and force-demanding tasks.
- Whole-body interaction: External wrenches at the hand, elbow, shoulder, and torso elicit whole-body compliant responses on the real robot.Responses include arm extension and stepping, elbow raising with base motion, recovery movement, and knee bending.
- Angular compliance: At angular stiffness 10, a full-strength hand twist produces an 84° attitude change, versus 15° at stiffness 100.The same modulation determines whether a 4 kg object falls from tilting arms or is carried steadily.
- Teleoperated loco-manipulation: Low linear and angular stiffness on both arms facilitates transporting a yoga ball during VR teleoperation.The robot picks the ball from a low chair and hands it to another person without fine motion adjustment.
- Teleoperated loco-manipulation: High stiffness commands on both arms support carrying a heavy box to a table and pushing open a spring-loaded door.The operator provides both motion commands and stiffness commands through VR teleoperation.
V. CONCLUSION
LAC realizes commanded linear and angular compliance across the humanoid upper body through compliant motion augmentation and teacher–student reinforcement learning. Experiments confirm compliant wrench responses, monotonic stiffness modulation, and utility for loco-manipulation, while stiffness selection remains operator-controlled and the approach may extend to other mobile bases.
- LAC realizes commanded linear and angular compliance through large-scale compliant motion augmentation and teacher–student reinforcement learning.
- Simulation and real-robot experiments confirm whole-body compliant responses to wrenches across the upper body and monotonic modulation over the full command range.
- The controller demonstrates utility in loco-manipulation tasks.
- Stiffness commands are currently set by the operator rather than adjusted autonomously from task context.
- Because the lower body is commanded through base velocity and height, the method may extend to quadrupedal or wheeled mobile-manipulation platforms.