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

cs.ROSep 27, 2026

CompliantWBC: Whole-Body Compliance for Heavy Humanoids via Force Latent Estimation and Residual Impedance Targets

Authors: Tan-Dzung Do, Cuc T. Trinh, Tuan Dat Phuong, Chien Le, Thanh Ly, Vien Anh Ngo, An Thai Le

Organizations: VinRobotics · National University of Singapore · VinUniversity · TU Darmstadt

Abstract

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/

Figures & tables

Method	LB	Sites	Residual	Platform
FALCON [ 8 ]	–	EE	–	G1/Booster
GentleHumanoid [ 11 ]	–	upper	–	G1
FACET [ 10 ]	quad.	CoM	impedance ref.	Go2/G1
SoftMimic [ 12 ]	per-motion	whole	–	G1
CHIP [ 9 ]	–	EE	hindsight goal	G1
ResMimic [ 14 ]	–	–	on motion	G1

TABLE I: Humanoid whole-body-control landscape. LB : lower-body compliance (✓), quadruped only (quad.), or none (–). Sites : where compliance is realized—end-effector (EE), upper body, CoM reference, or arbitrary links (whole). Residual : where a learned correction is applied.

Fig. 2: Two-stage training of CompliantWBC : (i) a base policy jointly trained with the force encoder to induce whole-body compliance; (ii) a bounded residual on the impedance equilibrium that compensates for wrench-estimation error.

Fig. 3: Phong-weighted sampling generates downward-biased force origins, decoupled by axis.

	Tracking quality		WB compliance and robustness
Controller	$E_{\rm cmd}^{\rm free}\!\downarrow$	$E_{\rm imp}\!\downarrow$	$\rho_{\tau}\!\downarrow$	$R_{\rm LB}\!\uparrow$	$S\!\uparrow$
	$[\times 10^{-2}]$	$[\times 10^{-2}]$	$[\times 10^{-2}]$
TWIST2	$2.18{\scriptstyle\,\pm\,0.31}$	$6.79{\scriptstyle\,\pm\,0.72}$	$2.74{\scriptstyle\,\pm\,0.38}$	$0.16{\scriptstyle\,\pm\,0.04}$	$0.59$
GentleHumanoid	$5.22{\scriptstyle\,\pm\,0.47}$	$3.92{\scriptstyle\,\pm\,0.35}$	$2.12{\scriptstyle\,\pm\,0.29}$	$0.14{\scriptstyle\,\pm\,0.03}$	$0.91$
Ours w/o pelvis force sampling	$4.12{\scriptstyle\,\pm\,0.38}$	$4.22{\scriptstyle\,\pm\,0.21}$	$1.87{\scriptstyle\,\pm\,0.24}$	$0.16{\scriptstyle\,\pm\,0.03}$	$0.93$
Ours w/o residual policy	$4.29{\scriptstyle\,\pm\,0.35}$	$3.81{\scriptstyle\,\pm\,0.29}$	$1.56{\scriptstyle\,\pm\,0.21}$	$0.20{\scriptstyle\,\pm\,0.03}$	$0.94$

TABLE II: Performance of CompliantWBC versus both compliant and non-compliant baselines over 100 paired rollouts. Arrows indicate the preferred direction; bracketed columns are in units of

10^{-2}

. Metrics are defined in Section V-A .

Fig. 4: Force latent embedding projections via t-SNE of different force profiles across contact sites.

Fig. 5: Lower-body joint effort $|\tau_{j}|/\tau_{j}^{\max}$ under two trapezoidal pelvis pushes (up $1$ – $2$ s and $9$ – $10$ s, down $7$ – $8$ s); L/R rows per joint, $0.1$ s bins. Red: above $0.9\,\tau_{j}^{\max}$ ; bars: fraction of time above it.

Fig. 6: We deploy CompliantWBC in the real world on five force-aware tasks: (a) Static Force Reaction; (b) Dynamic Force Reaction; (c) Cooperative Payload Transport; (d) Board Wiping; and (e) Squat Under Payload.

Variant	$\\|\boldsymbol{f}-\hat{\boldsymbol{f}}\\|$	$E_{\rm imp}\!\downarrow$	$\rho_{\tau}\!\downarrow$	$\\|\Delta\boldsymbol{x}\\|$	$S\!\uparrow$
	[N]	[cm]	$[\times 10^{-2}]$	[cm]
A ( $\hat{\boldsymbol{f}}$ , off)	$10.1{\scriptstyle\,\pm\,2.1}$	$3.81{\scriptstyle\,\pm\,0.29}$	$1.56{\scriptstyle\,\pm\,0.21}$	–	$0.94$
B ( $\boldsymbol{f}$ , off)	$0$	$2.44{\scriptstyle\,\pm\,0.22}$	$1.02{\scriptstyle\,\pm\,0.17}$	–	$0.97$
C ( $\boldsymbol{f}$ , on)	$0$	$2.31{\scriptstyle\,\pm\,0.21}$	$0.89{\scriptstyle\,\pm\,0.14}$	$0.4$	$0.98$
D ( $\hat{\boldsymbol{f}}$ , on)	$10.1{\scriptstyle\,\pm\,2.1}$	$2.58{\scriptstyle\,\pm\,0.24}$	$0.93{\scriptstyle\,\pm\,0.15}$	$2.1$	$0.98$

TABLE III: Residual ablation: equilibrium source

\times

residual on/off, over the same 100 paired rollouts.

\hat{\boldsymbol{f}}

is the estimated wrench,

\boldsymbol{f}

the simulator ground truth (oracle); D is Ours (full) and A is Ours w/o residual.

\|\Delta\boldsymbol{x}\|

is the mean magnitude of the residual’s equilibrium edit.

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