Feedback Regulation of Elastically Decoupled Underactuated Soft Robots

The intrinsically underactuated and nonlinear nature of continuum soft robots makes the derivation of provably stable feedback control laws a challenging task. Most of the works so far circumvented the issue either by looking at coarse fully-actuated approximations of the dynamics or by imposing quasi-static assumptions. In this letter, we move a step in the direction of controlling generic soft robots taking explicitly into account their underactuation. A class of soft robots that have no direct elastic couplings between the dynamics of actuated and unactuated coordinates is identified. Considering the actuated variables as output, we prove that the system is minimum phase. We then propose regulators that implement different levels of model compensation. The stability of the associated closed-loop systems is formally proven by Lyapunov/LaSalle techniques, taking into account the nonlinear and underactuated dynamics. Simulation results are reported for two models of 2D and 3D soft robots.