Singularly Perturbed Layered Control of Deformable Bodies

Variable curvature modeling tools provide an accurate means of controlling infinite degrees-of-freedom deformable bodies and structures. However, their forward and inverse Newton-Euler dynamics are fraught with high computational costs. Assuming piecewise constant strains across discretized Cosserat rods imposed on the soft material, a composite two time-scale singularly perturbed nonlinear backstepping control scheme is here introduced. This is to alleviate the long computational times of the recursive Newton-Euler dynamics for soft structures. Our contribution is three-pronged: (i) we decompose the system's Newton-Euler dynamics to a two coupled sub-dynamics by introducing a perturbation parameter; (ii) we then prescribe a set of stabilizing controllers for regulating each subsystem's dynamics; and (iii) we study the interconnected singularly perturbed system and analyze its stability.