Soft robots can execute tasks with safer interactions. However, control techniques that can effectively exploit the systems' capabilities are still missing. Differential dynamic programming (DDP) has emerged as a promising tool for achieving highly dynamic tasks. But most of the literature deals with applying DDP to articulated soft robots by using numerical differentiation, in addition to using pure feed-forward control to perform explosive tasks. Further, underactuated compliant robots are known to be difficult to control and the use of DDP-based algorithms to control them is not yet addressed. We propose an efficient DDP-based algorithm for trajectory optimization of articulated soft robots that can optimize the state trajectory, input torques, and stiffness profile. We provide an efficient method to compute the forward dynamics and the analytical derivatives of series elastic actuators (SEA)/variable stiffness actuators (VSA) and underactuated compliant robots. We present a state-feedback controller that uses locally optimal feedback policies obtained from DDP. We show through simulations and experiments that the use of feedback is crucial in improving the performance and stabilization properties of various tasks. We also show that the proposed method can be used to plan and control underactuated compliant robots, with varying degrees of underactuation effectively.

翻译：软体机器人能够以更安全的方式执行任务，然而，能有效利用系统能力的控制技术仍显不足。差分动态规划（DDP）已成为实现高动态任务的有前景工具，但现有文献大多通过数值微分将DDP应用于关节式软体机器人，并采用纯前馈控制执行爆发性任务。此外，欠驱动柔性机器人公认难以控制，而基于DDP的算法对其控制尚未得到充分研究。我们提出了一种高效的DDP算法，用于关节式软体机器人的轨迹优化，可同步优化状态轨迹、输入力矩及刚度曲线。我们提供了一种高效方法，用于计算串联弹性致动器（SEA）/可变刚度致动器（VSA）及欠驱动柔性机器人的正向动力学及其解析导数。我们提出了一种基于DDP局部最优反馈策略的状态反馈控制器。通过仿真与实验证明，反馈机制对提升各类任务的性能与稳定特性至关重要。同时表明，所提方法能有效规划与控制不同欠驱动程度的柔性机器人。