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Variable curvature modeling tools provide an accurate means of controllinginfinite degrees-of-freedom deformable bodies and structures. However, theirforward and inverse Newton-Euler dynamics are fraught with high computationalcosts. Assuming piecewise constant strains across discretized Cosserat rodsimposed on the soft material, a composite two time-scale singularly perturbednonlinear backstepping control scheme is here introduced. This is to alleviatethe long computational times of the recursive Newton-Euler dynamics for softstructures. Our contribution is three-pronged: (i) we decompose the system'sNewton-Euler dynamics to a two coupled sub-dynamics by introducing aperturbation parameter; (ii) we then prescribe a set of stabilizing controllersfor regulating each subsystem's dynamics; and (iii) we study the interconnectedsingularly perturbed system and analyze its stability.

Singularly Perturbed Layered Control of Deformable Bodies