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.

翻译：变曲率建模工具为控制无限自由度的变形体与结构提供了精确手段，但其正向与逆向牛顿-欧拉动力学面临计算成本高昂的难题。针对施加于软材料上离散柯瑟拉杆的逐段常应变假设，本文提出一种复合双时间尺度奇异摄动非线性反推控制方案，旨在缓解软结构递归牛顿-欧拉动力学的长计算时间。本文贡献包含三方面：（i）通过引入摄动参数，将系统的牛顿-欧拉动力学分解为两个耦合的子系统动力学；（ii）进而设计一组镇定控制器以调控各子系统动力学；（iii）研究互联奇异摄动系统并分析其稳定性。