On the stability of the soft pendulum with affine curvature: open-loop, collocated closed-loop, and switching control

This letter investigates the stability properties of the soft inverted pendulum with affine curvature - a tem- plate model for nonlinear control of underactuated soft robots. We look at how changes in physical parameters affect stability and equilibrium. We give conditions under which zero dynamics corresponding to a collocated choice of the output is (locally or globally) stable or unstable. We leverage these results to design a switching controller that stabilizes a class of nonlinear equilibria of the pendulum, which can drive the system from one equilibrium to another.