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具有无限自由度的可变形体及结构提供了精确手段。然而，其正向与逆向牛顿-欧拉动力学存在高计算成本问题。本文针对软材料上离散化柯瑟拉杆假设的常应变分段特性，引入了一种复合双时间尺度奇异摄动非线性反步控制方案，以缓解软结构递归牛顿-欧拉动力学的冗长计算时间。本文贡献包含三方面：（i）通过引入摄动参数，将系统牛顿-欧拉动力学分解为两个耦合子动力学；（ii）针对每个子系统的动力学设计一组镇定控制器；（iii）研究互联奇异摄动系统并分析其稳定性。