Closed-Form Solutions for Stable Trajectories of the Unicycle using Smooth Controllers

ANDRES GARCIA; OSVALDO ENRIQUE AGAMENNONI; JOSE LUIS FIGUEROA

Bahía Blanca

Jornada; 5tas. Jornadas Argentinas de Robótica; 2008

Universidad Nacional del Sur

This paper presents a methodology to stabilize some kind of Nonlinear Control system known as Driftless, utilizing the concept of Pseudo-Kinetic Energy introduced in this work. Once this controller is applied to the Unicycle- type robot, stability is guaranteed with the salient property that the structure of the controller allows to solve in closed-form the trajectories of the vehicle. While the proposed controller only ensures stability (not asymptotic stability) the obtained closed-form solutions will show that the wheel baseline center coordinates can be made asymptotically stable if the controller for the angle is unstable.  With such a conclusion a dissipative time varying term is added such that the modified controller endows the system with asymptotic stability providing an analytic general way to design stabilizing controllers for the Unicycle. Finally some conclusions and future directions for research are also depicted.