Optimal control, stability and numerical integration analysis of unicycle

This paper addresses the problem of the study of controllability and stability analysis of an elementary but useful example of unicycle. We have considered a three dimensional control system of a unicycle. The control system on unicycle is related to a group, which has a Lie group structure. Here we show how concepts of differential geometry and Lie algebra can be elegantly applied to explain the behavior of such a system. Controllability and a minimum effort problem for the system are studied using well known theorems and necessary optimality conditions. The two unconventional integrators, namely Kahan and Lie–Trotter integrators have been implemented for numerical integration and the results are compared with the conventional Runge-Kutta integrator.