Configuration tracking for soft continuum robotic arms using inverse dynamic control of a cosserat rod model

Controlling the configuration of a soft continuum robot arm is challenging due to the hyper-redundant kinematics of such robots. We propose a new model-based, inverse dynamic control approach to this problem that is defined on the configuration state variables of the geometrically exact Cosserat rod model. Our approach is capable of controlling a soft continuum robot to track static or time-varying 3D configurations through bending, torsion, shear, and extension deformations. The controller has a decentralized structure, in which the gain matrices can be defined in terms of the physical and material properties of distinct cross-sections of the robot arm. This structure facilitates its implementation on continuum robot arms composed of independently-controllable segments that have local sensing and actuation. The controller is validated with numerical simulations in MATLAB with a hydrogel-based soft robot arm that can produce the four primary types of deformations. The simulated arm successfully tracks these configurations with average normalized root-mean-square errors (NRMSE) below 7% in all cases. To demonstrate the generality of the control approach, its performance is also validated on a larger simulated robot arm made of silicone.