  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.
