  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.
