CompliantBot: Learning Whole-Body Compliance across Task Interfaces for Humanoid Control

Haoyang Li; Keqi Zhu; Zhanxiang Cao; Yang Zhang; Yizhi Chen; Xuekang Yang; Yue Gao

cs.RONov 1, 2026

CompliantBot: Learning Whole-Body Compliance across Task Interfaces for Humanoid Control

Authors: Haoyang Li, Keqi Zhu, Zhanxiang Cao, Yang Zhang, Yizhi Chen, Xuekang Yang, Yue Gao

Organizations: Department of Automation, Shanghai Jiao Tong University, Shanghai, China · Shanghai Innovation Institute, Shanghai, China · Department of Computer Science, Shanghai Jiao Tong University, Shanghai, China · MoE Key Lab of Artificial Intelligence and AI Institute, Shanghai Jiao Tong University, Shanghai, China

Abstract

Humanoid controllers need the ability to yield to external forces while retaining the capacity to resume their original tasks. However, tracking objectives penalize the deviations needed for yielding, while relaxing tracking goals persistently can make task recovery harder. Existing approaches often rely on task-specific interaction command interfaces or constructed compliant motion data and reference trajectories, limiting the direct reuse of their compliance-training mechanisms across different task interfaces. We introduce CompliantBot, a compliance-training framework for motion tracking and velocity-command locomotion. It preserves the original task inputs and requires no preconstructed compliant data or target trajectories. A state-dependent interaction force field couples applied loads to the robot's motion, enabling local articulation and whole-body movement to change the forces experienced. A complementary force-magnitude reward encourages lower interaction loads, while task rewards are downweighted during loading and restored after release to coordinate yielding and task resumption. The trained policies use task inputs and proprioceptive history without explicit external-force measurements. Across both task interfaces, CompliantBot yields farther under constant pulls and experiences lower spring interaction loads than matched baselines, while resuming task tracking after force removal. CompliantBot achieves the highest task completion among the compared methods under stronger pulls. Power evaluations further show that CompliantBot has the lowest mean joint mechanical power among the compared methods. Real-robot demonstrations further illustrate compliant responses through arm motion, stepping, and body reorientation.

Figures & tables

Figure 2: CompliantBot framework. (a) The actor generates joint-position targets for a PD controller. (b) A state-dependent interaction force field acts on a sampled body link. (c) The force objective and task rewards are weighted according to the interaction stage. (d) Torso and wrist responses; orange arrows indicate external forces.

Figure 3: Interaction-stage reward allocation. Solid curves show the task and interaction weights under external force; the dotted line shows the task weight during unforced execution.

Parameter	Value
Actor/critic hidden widths	512, 256, 128
Activation	ELU
Observation history length $H$	10
Parallel environments	4,096
Rollout steps per environment	24
PPO updates	10,000

Table 1: Network and PPO settings for the motion-tracking comparison.

Group	Reward	Expression	Weight
Compliance	Force target	$\chi_{t}e^{-\\|\,\|\boldsymbol{F}_{t}\|-\boldsymbol{f}^{\star}\\|_{1}/\beta_{c}}$	2.0
Task	Anchor pos.	$e^{-\\|\Delta\boldsymbol{p}_{a}\\|_{2}^{2}/s_{ap}^{2}}$	0.5
	Anchor ori.	$e^{-\theta_{a}^{2}/s_{aR}^{2}}$	0.5
	Rel. body pos.	$e^{-\langle\\|\Delta\boldsymbol{p}_{b}\\|_{2}^{2}\rangle_{b}/s_{p}^{2}}$	1.0
	Rel. body ori.	$e^{-\langle\theta_{b}^{2}\rangle_{b}/s_{R}^{2}}$	1.0
	Body lin. vel.	$e^{-\langle\\|\Delta\boldsymbol{v}_{b}\\|_{2}^{2}\rangle_{b}/s_{v}^{2}}$	1.0

Table 2: Reward functions for motion tracking.

Group	Reward	Expression	Weight
Compliance	Force target	$\chi_{t}e^{-\\|\boldsymbol{F}_{t}\\|_{1}/\beta_{c}}$	2.0
Task	Linear vel.	$e^{-\\|\boldsymbol{v}_{xy}^{\rm yaw}-\boldsymbol{v}_{xy}^{\rm cmd}\\|_{2}^{2}/\sigma_{v}^{2}}$	1.0
	Angular vel.	$e^{-(\omega_{z}^{\rm b}-\omega_{z}^{\rm cmd})^{2}/\sigma_{\omega}^{2}}$	0.5
Regularization	Alive	$\mathbb{I}[\text{not terminated}]$	0.15
	Vertical vel.	$(v_{z}^{\rm b})^{2}$	$-2.0$
	Roll/pitch vel.	$\\|\boldsymbol{\omega}_{xy}^{\rm b}\\|_{2}^{2}$	$-0.05$

Table 3: Reward functions for velocity-command locomotion.

	Constant force			Spring ( $k=20$ N/m)				Spring ( $k=50$ N/m)
Method	Survival (%) $\uparrow$	$Y_{w}$ (cm) $\uparrow$	$\Delta E$ (mm) $\downarrow$	Survival (%) $\uparrow$	$Y_{w}$ (cm) $\uparrow$	$\Delta E$ (mm) $\downarrow$	$\bar{F}$ (N) $\downarrow$	Survival (%) $\uparrow$	$Y_{w}$ (cm) $\uparrow$	$\Delta E$ (mm) $\downarrow$	$\bar{F}$ (N) $\downarrow$
BS	97.54 $\pm$ 0.32	9.96 $\pm$ 0.30	0.58 $\pm$ 0.10	97.54 $\pm$ 0.32	2.54 $\pm$ 0.07	0.63 $\pm$ 0.03	7.04 $\pm$ 0.02	97.54 $\pm$ 0.32	0.86 $\pm$ 0.04	0.64 $\pm$ 0.06	7.27 $\pm$ 0.02
DR	97.32 $\pm$ 0.63	6.80 $\pm$ 0.12	0.24 $\pm$ 0.03	97.32 $\pm$ 0.63	1.57 $\pm$ 0.04	0.35 $\pm$ 0.02	7.06 $\pm$ 0.01	97.32 $\pm$ 0.63	0.39 $\pm$ 0.13	0.34 $\pm$ 0.03	7.29 $\pm$ 0.02
CB	99.78 $\pm$ 0.32	18.75 $\pm$ 0.29	0.19 $\pm$ 0.03	99.78 $\pm$ 0.32	10.25 $\pm$ 0.35	$-$ 0.10 $\pm$ 0.50	6.56 $\pm$ 0.07	99.78 $\pm$ 0.32	9.48 $\pm$ 0.46	0.00 $\pm$ 0.49	6.75 $\pm$ 0.03
SoftMimic	90.89 $\pm$ 0.40	21.69 $\pm$ 1.42	0.38 $\pm$ 0.44	91.43 $\pm$ 2.01	11.48 $\pm$ 0.87	0.40 $\pm$ 0.42	6.95 $\pm$ 0.06	90.62 $\pm$ 2.07	6.73 $\pm$ 2.05	0.41 $\pm$ 0.33	7.27 $\pm$ 0.04
GentleHumanoid	95.27 $\pm$ 1.16	13.42 $\pm$ 0.52	0.22 $\pm$ 0.04	95.18 $\pm$ 0.97	6.52 $\pm$ 0.24	0.14 $\pm$ 0.02	6.89 $\pm$ 0.03	95.36 $\pm$ 1.08	3.74 $\pm$ 0.31	0.16 $\pm$ 0.03	7.24 $\pm$ 0.02

Table 4: Motion-tracking performance under external forces. Bold and underlined means indicate the best and second-best values within each condition, respectively.

Figure 4: Yielding across body sites. Bars and error bars show means and sample standard deviations across training seeds, respectively. Yielding is the displacement of the loaded link relative to the same policy’s unforced rollout, projected onto the force direction.

Figure 5: Learning curves of task survival and compliance. (a) Task survival and (b) yielding under constant forces; (c) mean interaction force under a spring. Lines and shaded bands show means and sample standard deviations across training seeds, respectively. CB achieves high task survival while retaining substantial yielding and lower spring interaction loads.

Figure 6: Interaction force and torso height during dance imitation. Under a sustained wrist spring pull, the baseline’s resistance increases the interaction force and leads to a fall, while CompliantBot yields to reduce the load and maintain stability.

Constant force (5 N)

Constant force (10 N)

Spring (

k=20

N/m)

Method

Y_{w}

(cm)

\uparrow

\Delta E_{v}

(mm/s)

\downarrow

\bar{F}

(N)

\downarrow

Survival (%)

\uparrow

Y_{w}

(cm)

\uparrow

\Delta E_{v}

(mm/s)

\downarrow

\bar{F}

(N)

\downarrow

Survival (%)

\uparrow

Y_{w}

(cm)

\uparrow

\Delta E_{v}

(mm/s)

\downarrow

\bar{F}

(N)

\downarrow

Survival (%)

\uparrow

\underline{13.75}

\pm 0.04

2.85

\pm 0.39

5.000

\pm 0.000

\mathbf{100}

\underline{27.10}

\pm 0.06

1.82

\pm 0.28

10.000

\pm 0.000

\mathbf{100}

14.82

\pm 0.12

21.33

\pm 0.29

\underline{13.485}

\pm 0.006

\mathbf{100}

9.85

\pm 0.08

-0.02

\pm 0.10

5.000

\pm 0.000

\mathbf{100}

20.03

\pm 0.06

\mathbf{-0.27}

\pm 0.09

10.000

\pm 0.000

\mathbf{100}

\underline{16.90}

\pm 0.05

\underline{10.30}

\pm 0.15

14.366

\pm 0.001

\mathbf{100}

\mathbf{17.62}

\pm 0.08

\underline{-0.06}

\pm 0.04

5.000

\pm 0.000

\mathbf{100}

\mathbf{39.38}

\pm 0.50

\underline{1.64}

\pm 0.49

10.000

\pm 0.000

\mathbf{100}

\mathbf{19.78}

\pm 0.18

\mathbf{9.55}

\pm 1.10

\mathbf{10.283}

\pm 0.010

\mathbf{100}

MPC

1.49

\pm 2.26

1.40

\pm 4.32

5.000

\pm 0.000

\underline{75}

2.26

\pm 2.25

12.77

\pm 8.37

10.000

\pm 0.000

\underline{75}

2.22

\pm 2.35

15.15

\pm 8.87

15.714

\pm 0.082

\underline{75}

MPC+Adm

11.52

\pm 2.18

\mathbf{-0.82}

\pm 4.44

5.000

\pm 0.000

\underline{75}

18.92

\pm 1.79

31.80

\pm 67.75

10.000

\pm 0.000

50

15.62

\pm 2.00

39.80

\pm 48.68

13.964

\pm 0.074

50

Table 5: Velocity-command locomotion under external forces. Bold and underlined means indicate the best and second-best values among all five methods within each condition, respectively. Fully tied columns are unmarked.

Figure 7: Task completion and mechanical power under external forces. (a,b) Task survival rates over time; final values indicate task completion rates. (c) Mean joint mechanical power across force magnitudes. Gray shading marks force application; colored bands and error bars show sample standard deviations across evaluation resets. CB achieves the highest final task completion and the lowest mean mechanical power among the compared methods.

Figure 8: Real-robot compliant responses during walking. (a) Arm yielding and lateral stepping under wrist pulls. (b) Stepping in place and backward stepping under torso pulls. (c) Higher force-magnitude targets $\boldsymbol{f}^{\star}$ require stronger pulls to stop forward motion. (d) A sustained wrist pull turns the robot around the fixed hand. These demonstrations show that CompliantBot coordinates local and whole-body motion to yield while continuing the task.

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Open paper AskPDF arXiv

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/

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