Control oriented modeling of soft robots: the polynomial curvature case

The complex nature of soft robot dynamics calls for the development of models specifically tailored on the control application. In this letter, we take a first step in this direction by proposing a dynamic model for slender soft robots, taking into account the fully infinite-dimensional dynamical structure of the system. We also contextually introduce a strategy to approximate this model at any level of detail through a finite dimensional system. First, we analyze the main mathematical properties of this model in the case of lightweight and non lightweight soft robots. Then, we prove that using the constant term of curvature as control output produces a minimum phase system, in this way providing the theoretical support that existing curvature control techniques lack, and at the same time opening up to the use of advanced nonlinear control techniques. Finally, we propose a new controller, i.e., the PD-poly, which exploits information on high order deformations, to achieve zero steady state regulation error in presence of gravity and generic nonconstant curvature conditions.