A heavy humanoid recruits its lower body to yield compliantly to external forces at arbitrary contact sites — static and dynamic force reaction, board wiping, squatting under payload, and cooperative payload transport.
Abstract
Whole-body compliant control is essential for deploying heavy humanoids under high payload, yet prior force-aware learning pipelines stop at the end-effector or upper body, leaving arbitrary-site perturbations with lower-body engagement unaddressed. CompliantWBC closes this gap with three pieces: a multi-site whole-body impedance reference controller whose per-link virtual targets supervise an RL policy, a Force Latent Encoder that infers a wrench-grounded latent of the unobserved contact state, and a bounded residual that edits the impedance equilibrium — preserving classical Cartesian-impedance passivity by construction. We validate on a real 70 kg humanoid across static and dynamic force reaction, board wiping, squat under payload, and cooperative payload transport.
Overview
Approach
An analytical controller composes centroidal-momentum impedance distributed to support contacts by a balancing QP, per-link Cartesian impedance at arbitrary sites, and an energy tank. It produces reference torques and virtual-target trajectories used as a reward signal — never cloned.
A variational latent encoder, grounded in privileged wrench supervision and clustered by perturbation class behind a gradient barrier, conditions a bounded residual that edits the impedance equilibrium — not motor commands or gains — preserving analytic compliance under sim-to-real drift.
A Phong-weighted force-origin sampler with an axis-decoupled pelvis anchor — base-relative horizontal, gravity-anchored vertical — induces multi-contact, lower-body-inclusive compliance without a hand-crafted site or magnitude curriculum.
Reference Controller
Classical Cartesian impedance couples a single end-effector to its commanded equilibrium. We extend it to a hierarchy of links — hands, elbows, knees, pelvis, torso — coupled by balance: per-link impedance is projected through a centroidal-balance null-space and realised by support contacts through a balancing QP. Knee contacts enter as extra support sites, generalising two-footed compliance to lower-body-inclusive postures. It runs only as a reference — its per-link virtual targets supervise the policy reward and are never cloned.
Force-Aware Base Policy
A variational encoder maps a 160 ms window of proprioception, torques, and motion command to a 32-D force latent. Its mean is detached before the policy — a gradient barrier so PPO never reshapes it — while four auxiliary losses (wrench reconstruction, contrastive clustering by perturbation class, a KL bottleneck, and temporal smoothness) keep it physically grounded.
The result is a wrench-grounded latent that clusters by perturbation class — none, left, right, center, mixed — as the t-SNE shows.
Residual on Impedance Targets
A second 3-layer MLP sits on top of the frozen base policy and frozen Force Latent Encoder. It reads the latent embedding and the decoded wrench estimate and outputs a bounded delta on the impedance equilibrium — a 5 cm cap on the virtual-target shift, with per-link stiffness held fixed by the curriculum. When the frozen wrench estimate is biased or noisy, the residual edits the impedance equilibrium to absorb the discrepancy without changing the base policy and without modulating gains.
Editing the equilibrium rather than the torque preserves the base controller's analytic compliance: a 5 cm shift induces at most stiffness × 5 cm of force — an explicit physical bound the residual cannot violate. Because the stiffness is fixed, the closed loop inherits classical Cartesian-impedance passivity by construction — a safety property for human–robot contact that action-residual baselines editing torque directly do not admit.
Force-Origin Sampling
Upper-body links draw force origins from a reachability point cloud; the pelvis instead draws from a continuous Phong-weighted distribution lobed on the downward axis, modelling gravity acting on a carried load.
The anchor is axis-decoupled — base-relative horizontal, gravity-pinned vertical — so the policy learns to sink under load rather than fight it, with no hand-crafted site or magnitude schedule.
Training
The pipeline deliberately avoids joint optimisation: under a single PPO loss the residual would absorb compliance behaviour the base could have learnt, making its bounded form a constraint on the joint system rather than an interpretable discrepancy compensator. The policy is deployed directly after Stage 2 with no real-rollout fine-tuning.
PPO jointly trains the latent encoder, the wrench-reconstruction head, and the base policy against the compliance-fidelity reward, internalising multi-site compliance behaviour.
With the base policy and wrench estimator frozen, PPO trains the bounded residual; the only way to reduce the reward is to edit the impedance interface to absorb wrench-prediction error.
Evaluation
Positioning
CompliantWBC is the only pipeline that combines lower-body compliance, multi-site contact, an explicit learned force latent, structured force sampling, and a residual on the impedance equilibrium. It admits both FALCON and GentleHumanoid as restrictions.
| Method | Lower-body compliance | Multi-site | Force latent | Residual architecture | Humanoid platform |
|---|---|---|---|---|---|
| FALCON | – | EE | – | – | G1/Booster |
| GentleHumanoid | – | upper only | implicit | – | G1 |
| FACET | quadruped | CoM | – | impedance ref. | Go2/G1 |
| SoftMimic | ✓ | whole-body | – | – | G1 |
| CHIP | – | EE | – | hindsight goal | G1 |
| ResMimic | – | – | – | on motion | G1 |
| ASAP | – | – | – | on action | G1 |
| CompliantWBC (ours) | ✓ | ✓ | ✓ | on equilibrium | in-house, 70 kg |
Ablation Study
We compare the full method against two baselines — the stiff whole-body tracker TWIST2 and the upper-body-compliant Gentle Humanoid — and two ablations, removing one component at a time. Each controller runs 100 paired rollouts under a ramp–hold–release force protocol across a fixed pool of contact sites (wrist, elbow, torso, pelvis, hip, knee), split evenly between static and dynamic motions.
| Controller | Ecmdfree ↓ | Ecmdforce ↓ | ρτ ↓ | RLB ↑ | S ↑ |
|---|---|---|---|---|---|
| ×10−2 | ×10−2 | ×10−2 | |||
| TWIST2 | 2.18±0.31 | 3.14±0.42 | 2.74±0.38 | 0.16±0.04 | 0.59 |
| Gentle Humanoid | 5.22±0.47 | 7.86±0.61 | 2.12±0.29 | 0.14±0.03 | 0.91 |
| Ours w/o pelvis force sampling | 4.12±0.38 | 5.89±0.51 | 1.87±0.24 | 0.16±0.03 | 0.93 |
| Ours w/o residual policy | 3.89±0.35 | 5.43±0.47 | 1.56±0.21 | 0.20±0.03 | 0.94 |
| CompliantWBC (full) | 4.65±0.41 | 6.57±0.53 | 0.93±0.15 | 0.31±0.04 | 0.98 |
TWIST2 tracks best in free space but fights every perturbation (S = 0.59). Gentle Humanoid yields with its upper body but shows the lowest whole-body engagement. CompliantWBC (full) more than doubles lower-body participation RLB over Gentle Humanoid, attains the lowest joint saturation ρτ and the highest success S = 0.98, at only a modest free-tracking cost. Removing pelvis force sampling collapses RLB toward the upper-body-only regime; removing the residual hurts force-aware tracking Ecmdforce the most.
Qualitative Results
Two short simulated demonstrations make the compliance behaviour visible. First, a side-by-side comparison of our compliant policy against a stiff tracker under the same upward arm force; second, the same single policy yielding to forces applied at three different contact sites.
Under an identical upward force at the arm, the compliant policy recruits the whole body to yield, while the stiff policy resists and is driven off balance.
A single policy yields compliantly to forces applied at the shoulder, the wrist, and the pelvis — no per-site tuning.
Real-World
We deploy the trained policy on a real heavy humanoid via teleoperation across five hardware tasks. Static and dynamic force reaction are quantitative and directly comparable to the simulation ablation; board wiping, squat under payload, and cooperative payload transport are qualitative demonstrations of sustained whole-body compliance and lower-body participation.
Measured, ramped pushes at wrist, torso, and pelvis while the robot holds a fixed pose — the primary quantitative real-world result.
Static and dynamic force reaction mirror the simulation ablation; full quantitative hardware tables are reported in the paper and will be added here for the camera-ready version.
Cite
Reference
BibTeX will be available once the paper is published.