Safe Autonomous Environmental Contact for Soft Robots using Control Barrier Functions

TL;DR

This work introduces a formal safety framework for soft robot manipulation in deformable environments by mapping force bounds to safe end-effector poses and enforcing invariance via Control Barrier Functions (CBFs). It integrates PCC-based planar soft-robot dynamics with a barrier-function-based QP to supervise a nominal controller, guaranteeing that end-effector contact forces remain within safe limits. The approach is validated through both simulation and hardware experiments on a two-segment pneumatic soft robot, demonstrating positive safety margins across tuning levels and highlighting the potential for formally verifiable safety in soft robotics. The results suggest a paradigm shift toward safety-first control in soft manipulation, with extensions to higher dimensions, time-varying environments, and more advanced CBF formulations identified as future work.

Abstract

Robots built from soft materials will inherently apply lower environmental forces than their rigid counterparts, and therefore may be more suitable in sensitive settings with unintended contact. However, these robots' applied forces result from both their design and their control system in closed-loop, and therefore, ensuring bounds on these forces requires controller synthesis for safety as well. This article introduces the first feedback controller for a soft manipulator that formally meets a safety specification with respect to environmental contact. In our proof-of-concept setting, the robot's environment has known geometry and is deformable with a known elastic modulus. Our approach maps a bound on applied forces to a safe set of positions of the robot's tip via predicted deformations of the environment. Then, a quadratic program with Control Barrier Functions in its constraints is used to supervise a nominal feedback signal, verifiably maintaining the robot's tip within this safe set. Hardware experiments on a multi-segment soft pneumatic robot demonstrate that the proposed framework successfully maintains a positive safety margin. This framework represents a fundamental shift in perspective on control and safety for soft robots, implementing a formally verifiable logic specification on their pose and contact forces.

Figures (9)

• Figure 1: This article proposes a feedback control method for a soft robot manipulator (purple) to meet a formal safety specification on its environmental contact forces. We assume the environment (black flexible plate) deforms and is known, and so safe forces map to safe poses. Control barrier functions ensure the robot remains within the set of safe poses.
• Figure 2: Our setup (A) maps a soft robot manipulator's end effector force to its pose by assuming the environment deforms, so a maximum force corresponds to a constraint on the robot's states. Our approach (B) calculates this set as a polytope $\mathbf{H}'\mathbf{r}\leq \mathbf{h}'$ given an undeformed environment surface $\mathbf{H}\mathbf{r} = \mathbf{h}$ and material parameters $\Theta$, where a supervisory controller $C_{SV}$ filters a nominal control signal to maintain the end effector $\mathbf{r}$ in the safe set. Our application (C) is a planar two-segment pneumatic robot with antagonistic actuation chambers $(p_i, p_{i+1})$. Our model (D) is piecewise constant curvature dellasantina_model_2020.
• Figure 3: The deformable environment is represented by a no-contact (free space) set, $\mathcal{N}$. We assume each face deforms in its normal direction, $\mathbf{\hat{n}}^U$ or $\mathbf{ \hat{n}}^L$ depending on inequality, upon contact with the end effector. By calculating the maximum deflection $n=n^{max}$ based on a force limit, we convert $\mathcal{N}$ into $\mathcal{P}$, the end effector poses $\mathbf{r}(\mathbf{q})$ that apply less than maximum force. Our approach also adds an additional hyperplane per vertex during the set expansion, between $\mathbf{c}_i^i$ to $\mathbf{c}_i^{i+1}$, to conservatively bound the environment's force when two hyperplanes are deflected.
• Figure 4: Simulation results with three levels of conservativeness of CBF tuning constants all show that the robot's end effector is prevented from moving out of the unsafe set, when the unsafe $\mathbf{u}_{nom}$ control (black dashed line) would violate safety.
• Figure 5: All simulations with CBF-based control show a positive safety margin on force application. The most conservative CBF tuning (green) prevents all environmental contact.

Theorems & Definitions (7)

• Definition 1
• Lemma 1
• Proof 1
• Remark 1
• Theorem 1
• Proof 2
• Remark 2