Condensed Semi-Implicit Dynamics for Trajectory Optimization in Soft Robotics

Over the past decades, trajectory optimization (TO) has become an effective solution for solving complex motion generation problems in robotics, ranging from autonomous driving to humanoids. Yet, TO methods remain limited to robots with tens of degrees of freedom (DoFs), limiting their usage in soft robotics, where kinematic models may require hundreds of DoFs in general. In this work, we introduce a generic method to perform trajectory optimization based on continuum mechanics to describe the behavior of soft robots. The core idea is to condense the dynamics of the soft robot in the constraint space in order to obtain a reduced dynamics formulation, which can then be plugged into numerical TO methods. In particular, we show that these condensed dynamics can be easily coupled with differential dynamic programming methods for solving TO problems involving soft robots. This method is evaluated on three different soft robots with different geometries and actuation.