cs.ROMar 1, 2026

Minimalist Compliance Control

Authors: Haochen Shi, Songbo Hu, Yifan Hou, Weizhuo Wang, Karen Liu, Shuran Song

Organizations: Stanford University

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Abstract

Compliance control is essential for safe physical interaction, yet its adoption is limited by hardware requirements such as force torque sensors. While recent reinforcement learning approaches aim to bypass these constraints, they often suffer from sim-to-real gaps, lack safety guarantees, and add system complexity. We propose Minimalist Compliance Control, which enables compliant behavior using only motor current or voltage signals readily available in modern servos and quasi-direct-drive motors, without force sensors, current control, or learning. External wrenches are estimated from actuator signals and Jacobians and incorporated into a task-space admittance controller, preserving sufficient force measurement accuracy for stable and responsive compliance control. Our method is embodiment-agnostic and plug-and-play with diverse high-level planners. We validate our approach on a robot arm, a dexterous hand, and two humanoid robots across multiple contact-rich tasks, using vision-language models, imitation learning, and model-based planning. The results demonstrate robust, safe, and compliant interaction across embodiments and planning paradigms.

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Figure 2: Policy Inputs and Outputs. We show that Minimalist Compliance Control is plug-and-play with a range of high-level policies that benefit from compliant interaction. We illustrate the inputs and outputs of (A) a VLM-based policy, (B) an imitation policy, and (C) a model-based policy. The math symbols refer to those in Eq. ( 1 ). (A) and (C) predict only the directions of the stiffness Kp\mathbf{K}_{p} and force command fcmd\mathbf{f}_{\text{cmd}} , while their magnitudes remain fixed. For all three, the damping matrix is set for critical damping as Kd=2 Kp1/2\mathbf{K}_{d}=2\,\mathbf{K}_{p}^{1/2} , assuming an identity inertia matrix, where (⋅)1/2(\cdot)^{1/2} denotes the matrix square root. We also visualize the VLM pipeline to predict 3D contact points and normals, which are interpolated to generate xdes\mathbf{x}_{\text{des}} .
Figure 3: Comparison with Force Sensor Readings. Dashed lines ( f^\hat{f} ) denote the estimated forces, while solid lines ( ff ) show ground-truth measurements from an ATI Mini45 sensor. The mean absolute error is 0.69±0.73\penalty N0.69\pm 0.73\penalty\ \mathrm{N} for ToddlerBot with servo motors (gear ratio >200:1>200{:}1 ) and 1.05±1.60\penalty N1.05\pm 1.60\penalty\ \mathrm{N} for ARX arm with QDD motor (gear ratio ≈10:1\approx 10{:}1 ).
Figure 4: Qualitative Comparison with Baselines. In this experiment, ToddlerBot draws a heart on a whiteboard using a target trajectory generated by a VLM. All methods follow the same command, which specifies the desired end-effector position xdes\mathbf{x}_{\text{des}} , velocity x˙des\dot{\mathbf{x}}_{\text{des}} , stiffness Kp\mathbf{K}_{p} , damping Kd\mathbf{K}_{d} , and commanded wrench fcmd\mathbf{f}_{\text{cmd}} . We visualize the 3D end-effector trajectories and real-world execution results for UniFP [ 45 ] , FACET [ 36 ] , our method without f^ext\hat{\mathbf{f}}_{\text{ext}} , and our full method.
 Pos. Error ( mm\mathrm{mm} )Ori. Error ( rad\mathrm{rad} )Root Pitch ( rad\mathrm{rad} )
UniFP [ 45 ]57.8 ±\pm 30.20.147 ±\pm 0.1190.068 ±\pm 0.020
FACET [ 36 ]22.4 ±\pm 11.00.151 ±\pm 0.0870.018 ±\pm 0.008
Ours w/o f^ext\hat{\mathbf{f}}_{\text{ext}}22.5 ±\pm 9.60.082 ±\pm 0.0400.060 ±\pm 0.038
Ours15.9 ±\pm 5.10.048 ±\pm 0.0430.029 ±\pm 0.012
Table I: Quantitative Comparison with Baselines. We report position tracking errors in millimeters and orientation tracking errors in radians, defined as the deviation of x\mathbf{x} from xdes\mathbf{x}_{\text{des}} . We also report the humanoid’s root pitch as a proxy for contact force. Since the contact point is at an approximately fixed distance from the center of mass, the moment arm is nearly constant, making root pitch correlated with the applied force.
Figure 5: ToddlerBot Results . We demonstrate that Minimalist Compliance Control works on a floating-base humanoid robot and integrates seamlessly as a plug-and-play module across diverse high-level planners. Tasks include drawing and wiping on a whiteboard with a VLM-based policy, placing an egg on bread with a spatula using an imitation policy, and rotating a ball with a model-based policy. Odd rows (Ours) present successful executions of our method, while even rows (Position Control) illustrate representative failure cases of the baseline. Our controller maintains appropriate contact forces and stable interaction, whereas the position-control baseline frequently loses contact, applies insufficient force, or exerts excessive force, leading to task failure. Insufficient force typically fails to establish or maintain contact, while excessive force increases tangential friction and leads to larger tangential tracking errors.
Figure 6: LEAP Hand Results . We show that Minimalist Compliance Control generalizes across embodiments, including dexterous manipulation. We evaluate two high-level strategies: a VLM-based policy for multi-finger drawing and wiping on a whiteboard, and model-based planning for in-hand reorientation of various objects. Both tasks demand precise contact force regulation. Each also includes a position-control baseline, which fails due to contact loss, insufficient force, or excessive force.
CommandRange
Left handxdes←0fext←0fcmd←0\begin{aligned} \mathbf{x}_{\text{des}}&\leftarrow\mathbf{0}\\ \mathbf{f}_{\text{ext}}&\leftarrow\mathbf{0}\\ \mathbf{f}_{\text{cmd}}&\leftarrow\mathbf{0}\end{aligned}
Right hand position xdespos\mathbf{x}_{\text{des}}^{\text{pos}}x∈[0.00,0.10]\penalty my∈[0.00,0.09]\penalty mz∈[0.00,0.15]\penalty m\begin{aligned} \mathbf{x}&\in[0.00,0.10]\penalty\ \mathrm{m}\\ \mathbf{y}&\in[0.00,0.09]\penalty\ \mathrm{m}\\ \mathbf{z}&\in[0.00,0.15]\penalty\ \mathrm{m}\end{aligned}
Right hand orientation xdesrot\mathbf{x}_{\text{des}}^{\text{rot}}rx∈[0.00,0.10]\penalty radry∈[0.2,0.34]\penalty radrz∈[0.00,0.00]\penalty rad\begin{aligned} \mathbf{r_{x}}&\in[0.00,0.10]\penalty\ \mathrm{rad}\\ \mathbf{r_{y}}&\in[0.2,0.34]\penalty\ \mathrm{rad}\\ \mathbf{r_{z}}&\in[0.00,0.00]\penalty\ \mathrm{rad}\end{aligned}
Right hand fext\mathbf{f}_{\text{ext}}fext,x∈[0,5]\penalty Nfext,y∈[0,3]\penalty Nfext,z∈[0,3]\penalty N\begin{aligned} \mathbf{f}_{\text{ext},x}&\in[0,5]\penalty\ \mathrm{N}\\ \mathbf{f}_{\text{ext},y}&\in[0,3]\penalty\ \mathrm{N}\\ \mathbf{f}_{\text{ext},z}&\in[0,3]\penalty\ \mathrm{N}\end{aligned}
Right hand fcmd\mathbf{f}_{\text{cmd}}fcmd,x∈[0,5]\penalty Nfcmd,y∈[−1.5,1.5]\penalty Nfcmd,z∈[−2,0]\penalty N\begin{aligned} \mathbf{f}_{\text{cmd},x}&\in[0,5]\penalty\ \mathrm{N}\\ \mathbf{f}_{\text{cmd},y}&\in[-1.5,1.5]\penalty\ \mathrm{N}\\ \mathbf{f}_{\text{cmd},z}&\in[-2,0]\penalty\ \mathrm{N}\end{aligned}
Right hand Kp\mathbf{K}_{p} and Kd\mathbf{K}_{d}Kp,xpos∈[120,400]Kp,ypos∈[350,400]Kp,zpos∈[350,400]Kprot∈[20,40]3Kd=2 Kp1/2\begin{aligned} \mathbf{K}_{p,x}^{\mathrm{pos}}&\in[120,400]\\ \mathbf{K}_{p,y}^{\mathrm{pos}}&\in[350,400]\\ \mathbf{K}_{p,z}^{\mathrm{pos}}&\in[350,400]\\ \mathbf{K}_{p}^{\mathrm{rot}}&\in[20,40]^{3}\\ \mathbf{K}_{d}&=2\,\mathbf{K}_{p}^{1/2}\end{aligned}
Table II: Command ranges to train UniFP and FACET.
TermDefinitionUniFPFACET
eef_site_posexp⁡ ⁣(−σpos∥xpos−xrefpos∥2)\exp\!\left(-\sigma_{\text{pos}}\lVert\mathbf{x}^{\text{pos}}-\mathbf{x}^{\text{pos}}_{\text{ref}}\rVert^{2}\right)10.06.0
eef_site_velexp⁡ ⁣(−σlinvel∥x˙pos−x˙refpos∥2)\exp\!\left(-\sigma_{\text{linvel}}\lVert\dot{\mathbf{x}}^{\text{pos}}-\dot{\mathbf{x}}^{\text{pos}}_{\text{ref}}\rVert^{2}\right)1.00.6
eef_site_rotexp⁡ ⁣(−σrot∥xrot⊖xrefrot∥2)\exp\!\left(-\sigma_{\text{rot}}\lVert\mathbf{x}^{\text{rot}}\ominus\mathbf{x}^{\text{rot}}_{\text{ref}}\rVert^{2}\right)3.04.0
motor_posexp⁡(−∥q−qref∥2)\exp(-\lVert q-q_{\text{ref}}\rVert^{2})4.00.5
energy−mean(∥τq˙∥2)-\mathrm{mean}(\lVert\tau\dot{q}\rVert^{2})0.11.0
action_rate−mean(∥at−at-1∥2)-\mathrm{mean}(\lVert a_{\text{t}}-a_{\text{t-1}}\rVert^{2})0.082.0
Table III: Reward terms and weights for UniFP and FACET.
Figure 7: VLM prompt template. For the wiping task, the task description is: “Wipe up the black ink on the whiteboard using an eraser,” where the default target object is “black ink.” For the drawing task, the task description is: “Draw the {object_label} on the whiteboard using a pen,” where the target object corresponds to the provided {object_label}.
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