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

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