Contact-Aware Safety in Soft Robots Using High-Order Control Barrier and Lyapunov Functions

TL;DR

This work tackles safety for soft robots operating near humans by ensuring distributed contact forces across the body remain bounded via a safety framework that integrates HOCBFs with HOCLFs. It introduces a unified $HOCBF$+$HOCLF$ controller that optimizes a safety‑constrained QP on top of a differentiable $PCS$ model and a novel differentiable conservative polygon distance metric, $h_{ ext{DCSAT}}$, to enable real‑time, whole‑body collision reasoning. Safety constraints include a barrier enforcing $F_{ ext{c}} \,\le\, F_{ ext{c,max}}$ and a clearance barrier from forbidden regions, while HOCLFs shape operational‑space goals; collision detection uses differentiable DCSAT to provide smooth proximity information for the controller. Planar simulations demonstrate safe interactions and accurate task‑space regulation across baselines, illustrating a practical path toward provable safety for human‑centric soft‑robot deployments.

Abstract

Robots operating alongside people, particularly in sensitive scenarios such as aiding the elderly with daily tasks or collaborating with workers in manufacturing, must guarantee safety and cultivate user trust. Continuum soft manipulators promise safety through material compliance, but as designs evolve for greater precision, payload capacity, and speed, and increasingly incorporate rigid elements, their injury risk resurfaces. In this letter, we introduce a comprehensive High-Order Control Barrier Function (HOCBF) + High-Order Control Lyapunov Function (HOCLF) framework that enforces strict contact force limits across the entire soft-robot body during environmental interactions. Our approach combines a differentiable Piecewise Cosserat-Segment (PCS) dynamics model with a convex-polygon distance approximation metric, named Differentiable Conservative Separating Axis Theorem (DCSAT), based on the soft robot geometry to enable real-time, whole-body collision detection, resolution, and enforcement of the safety constraints. By embedding HOCBFs into our optimization routine, we guarantee safety, allowing, for instance, safe navigation in operational space under HOCLF-driven motion objectives. Extensive planar simulations demonstrate that our method maintains safety-bounded contacts while achieving precise shape and task-space regulation. This work thus lays a foundation for the deployment of soft robots in human-centric environments with provable safety and performance.

Figures (5)

• Figure 1: Contact Safety-Aware Control of Soft Robots with HOCBF and HOCLF. Illustration of compliant contact control with safety bounds guaranteed by HOCBF. By respecting contact force limits, the robot can intentionally engage with its surroundings without sacrificing safety. Task goals are shaped through HOCLF, while constraint satisfaction is upheld by HOCBF. This approach enables the secure use of soft robots in demanding settings—from search‑and‑rescue missions to delicate medical procedures.
• Figure 2: Illustration of SAT Polygon Distance Metrics. Visualization of SAT-based polygon distance metrics used for collision detection between the soft robot body and convex polygonal obstacles. Specifically, we illustrate the definition of the signed distance $h_{\mathrm{SAT}}(A, B)$ between convex polygons $A$ and $B$. The right panel shows projection intervals $I_{A,a}$ and $I_{B,a}$ along the maximizing axis $a_{\max}$ in both separation (top) and overlap (bottom) scenarios.
• Figure 3: Qualitative Benchmarking of DCSAT. Comparison of zero-level contours between smoothed / differentiable polygon distance metrics and the classical SAT. Specifically, we compare the position of the square polygon at a zero distance with the 8-sided polygon according to the respective distance metric. In both cases, we report the resulting contours for various sharpness parameters $\alpha$, and the gray dashed curve represents the true zero-level set of the classical, but not differentiable SAT (i.e., the ground-truth), where the centroid of polygon $B$ is in contact with polygon $A$.
• Figure 4: Search & Rescue Sequence of Stills. Sequence of stills for the system evolution in the search & rescue scenario for five different control paradigms. Contact interaction states are visualized with color cues: blue indicates no contact, green denotes safe contact, and red highlights contact above the maximum allowable force. The green cross denotes the task-space goal for this task. Safety Unaware HOCLF: Only optimizing for the task objective encoded in the HOCLF and disregarding safety constraints. Contact Avoidance Artificial Potential: Fully avoiding contact, which is the common paradigm in rigid robotics, using an artificial potential field khatib1986potential, Contact Avoidance HOCBF+HOCLF: Fully avoiding contact using the HOCBF+HOCLF framework. Contact Force-Limit HOCBF Filter: Embracing contact with the environment while ensuring that the contact forces remain within safe bounds via an HOCBF-based safety filter applied to a nominal operational-space controller della2020modelstolzle2024guidingstolzle2025phdthesis. Contact Force-Limit HOCBF+HOCLF (proposed): Also ensuring that the contact forces remain within safe bounds, but instead of a safety filter, directly solving a QP with HOCBF and HOCLF constraints.
• Figure 5: Search & Rescue Time Evolution. The contact force value, regulation error value across the robot for different controllers during a search & rescue scenario. Refer to the caption of \ref{['fig:search_rescue_sequence_of_stills']} for more details about the experiment and the considered controllers.

Theorems & Definitions (11)

• Definition 1: High-Order Control Barrier Function xiao2021highclbf
• Definition 2: High-Order Control Lyapunov Function
• Definition 3: Separating axis
• Theorem 1: Separating Axis Theorem dyn4jSAT
• Lemma 1: Sufficiency of Edge Normals in $\mathbb{R}^2$
• proof
• Definition 4: Differentiable Conservative SAT (DCSAT)
• Lemma 2: Bounds for DCSAT
• proof
• Theorem 2: Conservative Approximation via DCSAT