Statics and Dynamics of Continuum Robots Based on Cosserat Rods and Optimal Control Theories

This paper explores the relationship between op- timal control and Cosserat beam theory from the perspective of solving the forward and inverse dynamics (and statics as a subcase) of continuous manipulators and snake-like bio- inspired locomotors. By invoking the principle of minimum potential energy, and the Gauss principle of least constraint, it is shown that the quasi-static and dynamic evolution of these robots, are solutions of optimal control problems (OCPs) in the space variable, which can be solved at each step (of loading or time) of a simulation with the shooting method. In addition to offering an alternative viewpoint on several simulation approaches proposed in the recent past, the optimal control viewpoint allows us to improve some of them while providing a better understanding of their numerical properties. The approach and its properties are illustrated through a set of numerical examples validated against a reference simulator.