Motion planning of nonholonomic systems using highly oscillatory series

In this paper a nonholonomic motion planning task was solved using an algorithm proposed by Sussmann and Liu [8] and based on controls in the form of highly oscillatory series (HOS). Outputs of the algorithm were evaluated with respect to energy expenditure on controls and speed of its convergence. Based on characteristic features of the task, two modifications of the algorithm were proposed. Simulations were carried out on the unicycle model and an exemplary nilpotent nonholonomic system. Finally, the relevance of the algorithm to possible applications was discussed.