Limit Cycle Construction Using Bézier Curves: Application in a Mobile Robot

A methodology is proposed to design a wide range of simple closed curves not parameterized by time using second-order Bézier curves. A Hamiltonian system and a gradient system are designed, which in turn produce a velocity field that points to the closed curve. The velocity field is used as a reference for a mobile robot to follow the closed curve asymptotically. Numerical and experimental results are presented, which are implemented in a low-budget experimental platform.