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CompliantWBC: Whole-Body Compliance for Heavy Humanoids via Force Latent Estimation and Residual Impedance Targets
Tan-Dzung Do, Cuc T. Trinh, Tuan Dat Phuong, Chien Le, Thanh Ly, Vien Anh Ngo, An Thai Le
TL;DR
Learning-based compliance for heavy humanoids must address forces at arbitrary contact sites while maintaining balance and tracking, but prior approaches leave whole-body perturbation training and bounded compliance insufficiently addressed. CompliantWBC combines a multi-site impedance reference, a base RL policy, a bounded residual, and whole-body force sampling; it achieves the best reported compliance fidelity and is demonstrated on a real heavy humanoid.
Problem
Learning-based humanoid compliance must handle unobserved external wrenches at arbitrary contact sites while balancing and tracking, but prior approaches leave whole-body perturbation training and bounded compliance insufficiently addressed.
Source: §I · pp. 1–2Method
CompliantWBC guides a base RL policy with multi-site impedance targets, adds a bounded residual to per-link impedance equilibria, and samples perturbations across the whole body.
Source: §I · p. 2Results
Eimp = 2.58, against ≥3.81 for every baseline and ablation; CompliantWBC also showed whole-body compliance with higher lower-body participation in simulation and the real world.
Source: B. Simulation Experiments · p. 5, §VI · p. 7Takeaways & Limitations
The pipeline demonstrates whole-body, lower-body-inclusive compliance on heavy-payload loco-manipulation tasks in simulation and on a real heavy humanoid.
Source: §VI · p. 7
Abstract
from arXiv · showhide
Whole-body compliant control is essential for deploying heavy humanoids under high payload in human-centric environments. Most prior force-aware learning-based pipelines focus on end-effector resistance, per-link upper-body springs, or end-effector stiffness modulation, leaving arbitrary-site perturbations on heavy platforms with lower-body engagement largely unaddressed. We close this gap with CompliantWBC comprising: (1) A base policy trained with RL to maximize compliance-fidelity reward, guided by a multi-site whole-body impedance reference controller, extending classical Cartesian impedance to any controlled link; (2) A bounded residual policy that edits the per-link impedance equilibrium over a frozen base, correcting the coarse but structured wrench estimate supplied by a force encoder co-trained behind a gradient barrier; (3) A Phong-weighted force-origin sampler with an axis-decoupled pelvis anchor induces lower-body-inclusive compliance curriculum training via two interpretable parameters. We evaluate CompliantWBC in simulation against both compliant and stiff baselines, achieving best compliant fidelity of 2.58cm deviation from analytical solutions, and demonstrate it on a real heavy humanoid across static/dynamic force reaction, board wiping, squat under payload, and cooperative payload transport. Project website: https://dotandung.github.io/compliantwbc/
I. INTRODUCTION
COMPLIANTWBC targets arbitrary-site, multi-contact compliance with lower-body participation, which prior learning-based approaches largely leave unaddressed. It combines a whole-body impedance reference for base-policy training with a bounded equilibrium residual and a force-origin curriculum.
I. INTRODUCTION
- Prior learning-based compliance largely restricts perturbations to end-effectors or upper-body links, leaving arbitrary-site, multi-contact compliance with lower-body impedance unaddressed.The motivating settings include pelvis bracing, hip translation, and double-support redistribution.Source: §I · p. 1
- The base policy uses virtual targets from a multi-site reference controller combining centroidal-momentum balance with per-link Cartesian impedance at arbitrary sites.A compliance-fidelity reward guides the policy instead of cloning the controller's torque, avoiding its runtime cost and contact-mode fragility at deployment.Source: §I · p. 2
- A bounded residual edits per-link impedance equilibrium over a frozen base to correct structured error in a proprioceptive wrench estimate.The residual acts on equilibrium rather than motor commands or gains.Source: §I · p. 2
- A Phong-weighted force-origin sampler with an axis-decoupled pelvis anchor trains compliance across whole-body sites, including the lower body.The paper reports simulation evaluation and demonstration on a real heavy humanoid.Source: §I · p. 2
- Table I organizes humanoid whole-body-control methods by lower-body compliance, compliance site, and residual location.Its site categories include end-effector, upper body, CoM reference, and arbitrary links.Source: Table I · p. 2
II. RELATED WORK
Prior humanoid compliance methods often limit compliance sites or lack a per-link impedance interface, while residual and latent-force methods use different correction targets. COMPLIANTWBC combines arbitrary-site impedance with a bounded residual guided by proprioceptive wrench estimation.
A. Compliance Control for Humanoids
- Classical operational-space compliance handles multiple frames through task-priority projection and a balancing QP, but depends on accurate dynamics, hand-crafted hierarchies, and contact-mode reasoning.Whole-body tracking controllers may enable agile loco-manipulation but do not expose an impedance interface.Source: A. Compliance Control for Humanoids · p. 2
- Most learning-based compliance methods restrict behavior to end-effectors or upper-body chains, while some lower-body methods target a single motion and require per-motion augmentation.Heavy-payload multi-policy and trajectory-reference approaches also lack a per-link impedance interface; COMPLIANTWBC composes centroidal-momentum balance with arbitrary-site per-link impedance inside RL.Source: A. Compliance Control for Humanoids · p. 2
B. Residual Policies and Latent Force Estimation
- Unlike residuals on motor commands, tracked motions, or goals, COMPLIANTWBC applies a bounded residual to per-link impedance equilibrium over a frozen base.The equilibrium shift times fixed link stiffness upper-bounds the residual's effect.Source: B. Residual Policies and Latent Force… · p. 3
- The method adopts proprioceptive external-wrench estimation rather than improving it, using its deliberately coarse estimate to guide the equilibrium residual.Because link stiffness is fixed, the residual's effect is bounded by the virtual-target shift times stiffness.Source: B. Residual Policies and Latent Force… · p. 3
III. WHOLE-BODY IMPEDANCE HEURISTIC
The heuristic extends single-end-effector Cartesian impedance to a hierarchy of frames coupled by balance. Its per-link virtual targets carry wrench-dependent displacement corrections into training, with estimated and ground-truth wrenches serving distinct policy and reward roles.
III. WHOLE-BODY IMPEDANCE HEURISTIC
- The heuristic extends single-end-effector Cartesian impedance to a hierarchy of frames coupled by balance.The humanoid model is expressed with configuration, generalized velocity, and floating-base dynamics.Source: §III · p. 3
- For a perturbed link, the per-link virtual target is the single signal carried into training.The external wrench is applied at a body site and transported to the link frame; inverse anisotropic Cartesian stiffness gives the correction displacement.Source: §III · p. 3
- The ground-truth-wrench target anchors the reward, the estimated-wrench target is commanded to the policy, and the zero-wrench target is nominal.The realized link position is denoted without a wrench argument.Source: §III · p. 3
- Restricting the heuristic to upper-body links with scalar isotropic stiffness recovers GentleHumanoid's spring response, while restricting perturbations to end-effectors gives FALCON's model as a special case.The GentleHumanoid correspondence is qualified as holding up to its motion-data-driven guiding contacts.Source: §III · p. 3
A. Pipeline Architecture
COMPLIANTWBC trains a force-aware base policy for whole-body compliance, then adds a bounded residual to compensate for wrench-estimation error. Its force encoder is trained with auxiliary objectives, while a gradient barrier keeps policy rewards from redirecting the encoder.
A. Pipeline Architecture
- The base policy maps proprioception, joint targets, nominal per-link targets, and an estimated wrench to joint-position targets, trained against analytical impedance targets without deploying the balancing QP.A fixed-gain joint-space PD law executes online; the analytical controller and balancing QP do not run at deployment.Source: A. Pipeline Architecture · p. 3
- The force encoder maps observation history to a latent, using wrench reconstruction, contrastive, bottleneck, and temporal-smoothness objectives to produce a coarse, structured signal.Its wrench estimate is detached before entering the policies, preventing PPO gradients from redirecting the encoder toward reward-hacking features.Source: A. Pipeline Architecture · pp. 3–4
- The two-stage pipeline jointly trains a force-aware base policy and encoder, then trains a bounded residual on the impedance equilibrium to compensate for wrench-estimation error.The residual is trained over a frozen base policy.Source: A. Pipeline Architecture · p. 3, Figure 2 · p. 4
- The residual edits per-link impedance equilibria by bounded displacements, equivalent to correcting the estimated wrench, without changing the base policy or modulating gains.The equilibrium edit and wrench correction are equivalent because the impedance target is affine in the wrench.Source: A. Pipeline Architecture · p. 4
B. Compliant virtual targets via external-force sampling
Force-origin sampling extends perturbations beyond the upper body by using a downward-biased Phong distribution for the pelvis. An axis-decoupled anchor and compliance-aware height target make pelvis loading compatible with locomotion and lower-body yielding.
B. Compliant virtual targets via external-force sampling
- Upper-body links use force origins from a kinematic reachability cloud, while pelvis origins are sampled inside a 0.5 m-radius ball with a downward-focused Phong lobe and isotropic mixing.The lobe has exponent n=2 and isotropic mixing weight ϵ=0.1; the distribution is gap-free and sampled by inverse CDF.Source: B. Compliant virtual targets via… · pp. 4–5
- The pelvis anchor co-moves horizontally with the floating base but pins its vertical component to commanded base height, avoiding a self-chasing load or an unbounded force as the robot walks away.The anchor height is a per-chunk gravity-aligned datum that does not sink with the robot.Source: B. Compliant virtual targets via… · p. 5
- A compliance-aware pelvis-height target interpolates between rigid tracking and anchor-following according to the relative anchor and leg stiffnesses, allowing lower-body sinking without an explicit compliance offset.The gain is αz = k/(k + kleg): a stiff anchor pulls the comfortable pose toward the load, while a stiff stance resists it.Source: B. Compliant virtual targets via… · p. 5
V. EXPERIMENTS
The evaluation asks whether multi-site whole-body compliance improves on aggressive tracking and end-effector-only compliance, how the wrench estimate and residual behave, and how the method performs on real contact-rich tasks.
V. EXPERIMENTS
- The evaluation tests whether multi-site wrist, elbow, torso, pelvis, hip, and knee perturbations improve over aggressive tracking and end-effector-only compliance, especially away from the hands.This is the first of the three stated evaluation questions.Source: §V · p. 5
- A second evaluation question examines learned wrench-estimation accuracy and what the bounded residual on virtual targets corrects.The passage assigns this question to Section V-B.Source: §V · p. 5
- The real-world evaluation asks how COMPLIANTWBC behaves on contact-rich tasks.This is the third stated question and is addressed in Section V-C.Source: §V · p. 5
A. Settings and Metrics
The settings compare full COMPLIANTWBC with stiff and upper-body-only baselines and residual/pelvis-sampling ablations. The section also defines measures of tracking, compliant response, and lower-body participation.
A. Settings and Metrics
- The comparison includes a stiff whole-body tracker, an upper-body-only compliant reimplementation, and ablations removing pelvis force sampling or the residual; variants share training budgets and paired seeds.The full method adds the bounded residual to the Stage-1 base policy, with per-link stiffness fixed by the curriculum.Source: A. Settings and Metrics · p. 5
- Compliance fidelity Eimp measures the distance between the perturbed link's realized pose and the analytical impedance response anchored to the ground-truth wrench.Both overly stiff and overly soft responses score poorly against this target.Source: A. Settings and Metrics · p. 5
- Torque reaction ρτ reflects the fraction of near-saturated joints, while lower-body participation RLB measures the lower-body share of perturbation-induced torque deviation and is a behavioral diagnostic, not a standalone success criterion.Task success and free-motion tracking are also reported; Figure 4 shows t-SNE projections of force-latent embeddings across contact sites.Source: A. Settings and Metrics · p. 5, Figure 4 · p. 5
B. Simulation Experiments
COMPLIANTWBC achieves the best reported compliance fidelity while combining high success, lower-body participation, and low joint saturation. Ablations, pelvis-push behavior, and wrench-estimation results characterize how its components contribute to compliant response.
B. Simulation Experiments
- Eimp = 2.58 for OURS (FULL), versus ≥3.81 for every baseline and ablation; it also has the highest lower-body participation and lowest joint saturation at the highest success rate.Its free-tracking gap to TWIST2 is described as modest.Source: B. Simulation Experiments · p. 5, Table II · p. 6
- Removing pelvis sampling collapses lower-body participation toward the GENTLEHUMANOID regime, while removing the residual slightly improves tracking precision but worsens compliance and robustness.The no-residual variant has the worst joint saturation, lower-body participation, and success rate.Source: B. Simulation Experiments · p. 6, Table III · p. 6
- During pelvis pushes, the compliant policy keeps lower-body torques smaller and remains stable, especially at peak force.Figure 5 bins normalized lower-body joint effort in 0.1 s intervals; red marks effort above 0.9 τ_max.Source: B. Simulation Experiments · p. 6, Figure 5 · p. 6
- Across 242k samples, wrench direction sharpens with load, while amplitude is biased: the median norm ratio is 2.35 → 0.97 → 0.80 across load ranges.Direction error falls from 33° in the 1–5 N bin to 19° above 100 N; amplitude crosses calibration in the 10–25 N bin and underestimates heavier loads.Source: B. Simulation Experiments · pp. 6–7, Figure 7 · p. 7
- With an estimated wrench, the residual improves Eimp by 1.23 cm and ρτ by 0.63, versus 0.13 on each metric with an oracle wrench.The mean equilibrium edit falls 5.3×, from 2.1 cm with the estimated wrench to 0.4 cm with the oracle.Source: Table III · p. 6, B. Simulation Experiments · p. 7
C. Real-World Experiments
The trained policy was deployed on a real humanoid across five force-aware tasks. Demonstrations include balanced responses to dynamic pushes and whole-body load redistribution during sustained contacts.
C. Real-World Experiments
- Real-world deployment covered static and dynamic force reaction, cooperative payload transport, board wiping, and squatting under payload.The first two mirror simulation perturbations; the remaining tasks use sustained, structured contacts.Source: C. Real-World Experiments · p. 7
- Under large pushes during dynamic walking, the robot stays balanced in a regime where stiff TWIST2 collapses in simulation (S = 0.59).Source: C. Real-World Experiments · p. 7
- In payload transport, the robot yields at the wrists, redistributes load through its torso and hips, and resumes a stable gait; squatting spreads sustained pelvis load across the chain.Source: C. Real-World Experiments · p. 7
- During board wiping, the humanoid leans its trunk back and shifts its center of mass over the support polygon under hand-applied pressure.The paper notes this response is not trained by an upper-body-only policy with no lower-body perturbations.Source: C. Real-World Experiments · p. 7
VI. CONCLUSIONS
COMPLIANTWBC is a two-stage RL pipeline using a multi-site whole-body impedance reference controller as a compliance-fidelity reward. On heavy-payload loco-manipulation tasks, it exhibits better whole-body compliance and significantly higher lower-body participation in simulation and on a real humanoid.
VI. CONCLUSIONS
- COMPLIANTWBC exhibits better whole-body compliance and significantly higher lower-body participation in simulation and in the real world.The validation covers heavy-payload loco-manipulation tasks requiring lower-body and multi-contact compliance.Source: §VI · p. 7
- The two-stage RL pipeline trains a force-aware base against a compliance-fidelity reward, then adds a bounded residual to the impedance equilibrium.The residual compensates for the discrepancy between the frozen wrench estimator and the true external wrench.Source: §VI · p. 7
- A multi-site whole-body impedance reference controller supplies the compliance-fidelity reward signal for the base policy.Source: §VI · p. 7