P-satI-D Shape Regulation of Soft Robots

Soft robots are intrinsically underactuated mechan- ical systems that operate under uncertainties and disturbances. In these conditions, this letter proposes two versions of PID-like control laws with a saturated integral action for the particularly challenging shape regulation task. The closed-loop system is asymptotically stabilized and matched constant disturbances are rejected using a very reduced amount of system information for control implementation. Stability is assessed on the under- actuated dynamic model through the Invariant Set Theorem for two relevant classes of soft robots, i.e., elastically decoupled and elastically dominated soft robots. Extensive simulation results validate the proposed controllers.