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 constrains its environmental contact forces. This framework represents a fundamental shift in perspective on control and safety for soft robots, defining and implementing a formally verifiable logic specification on their pose and contact forces.

10 pages, 10 figures