Minimalist Compliance Control

TL;DR

Minimalist Compliance Control is proposed, 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.

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.

Figures (7)

• Figure 1: Minimalist Compliance Control (A) requires no force sensors or learning, estimating external wrenches $\hat{\mathbf{f}}_{\text{ext}}$ directly from motor current or voltage signals using a motor torque model and Jacobians. These estimates drive a spring--mass--damper model to update task-space position references. (B) This minimalist approach generalizes across embodiment, from robot arm and dexterous hand to humanoid robot, and (C) remains plug-and-play with any policy such as VLM-based policy, imitation policy, and model-based policy, and across diverse tasks such as wiping, drawing, scooping, and in-hand manipulation.
• 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. \ref{['eq:smd']}. (A) and (C) predict only the directions of the stiffness $\mathbf{K}_p$ and force command $\mathbf{f}_{\text{cmd}}$, while their magnitudes remain fixed. For all three, the damping matrix is set for critical damping as $\mathbf{K}_d = 2\,\mathbf{K}_p^{1/2}$, assuming an identity inertia matrix, where $(\cdot)^{1/2}$ denotes the matrix square root. We also visualize the VLM pipeline to predict 3D contact points and normals, which are interpolated to generate $\mathbf{x}_{\text{des}}$.
• Figure 3: Comparison with Force Sensor Readings. Dashed lines ($\hat{f}$) denote the estimated forces, while solid lines ($f$) show ground-truth measurements from an ATI Mini45 sensor. The mean absolute error is $0.69 \pm 0.73~\mathrm{N}$ for ToddlerBot with servo motors (gear ratio $>200{:}1$) and $1.05 \pm 1.60~\mathrm{N}$ for ARX arm with QDD motor (gear ratio $\approx10{:}1$).
• 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 $\mathbf{x}_{\text{des}}$, velocity $\dot{\mathbf{x}}_{\text{des}}$, stiffness $\mathbf{K}_p$, damping $\mathbf{K}_d$, and commanded wrench $\mathbf{f}_{\text{cmd}}$. We visualize the 3D end-effector trajectories and real-world execution results for UniFP zhi2025learning, FACET xu2025faceta, our method without $\hat{\mathbf{f}}_{\text{ext}}$, and our full method.
• 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.