Continuum soft robots, composed of flexible materials, exhibit theoretically infinite degrees of freedom, enabling notable adaptability in unstructured environments. Cosserat Rod Theory has emerged as a prominent framework for modeling these robots efficiently, representing continuum soft robots as time-varying curves, known as backbones. In this work, we propose viewing the robot's backbone as a signal in space and time, applying the Fourier transform to describe its deformation compactly. This approach unifies existing modeling strategies within the Cosserat Rod Theory framework, offering insights into commonly used heuristic methods. Moreover, the Fourier transform enables the development of a data-driven methodology to experimentally capture the robot's deformation. The proposed approach is validated through numerical simulations and experiments on a real-world prototype, demonstrating a reduction in the degrees of freedom while preserving the accuracy of the deformation representation.

We introduce a novel reconfigurable passive joint (RP-joint), which has been implemented and tested on an underactuated three-finger robotic gripper. RP-joint has no actuation, but instead it is lightweight and compact. It can be easily reconfigured by applying external forces and locked to perform complex dexterous manipulation tasks, but only after tension is applied to the connected tendon. Additionally, we present an approach that allows learning dexterous grasps from single examples with underactuated grippers and automatically configures the RP-joints for dexterous manipulation. This is enhanced by integrating kinaesthetic contact optimization, which improves grasp performance even further. The proposed RP-joint gripper and grasp planner have been tested on over 370 grasps executed on 42 IKEA objects and on the YCB object dataset, achieving grasping success rates of 80% and 87%, on IKEA and YCB, respectively.

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.