On Periodic Control Laws for Mobile Robots

This paper deals with the control of differentially driven wheeled mobile robots. Two families of wheeled mobile robots are considered: those that are capable of forward motion only and those that can perform forward and backward motion. A unified framework for the control law analysis and design of both robot types is proposed. The control laws are developed within a Lyapunov stability analysis framework. Periodic Lyapunov functions are proposed, and the constructive procedure leads to periodic control laws. These laws are very natural for wheeled mobile robots since they are inspired by the periodic nature of a robot´s orientation. The simple form of the control laws enables their easy implementation in practical applications. Global convergence is proven based on the usual requirements for reference velocities. Some important properties of these systems are also treated, such as continuity and the presence of unstable equilibria. Some guidelines for how to choose a suitable control law and its parameters are also given. An extensive simulation study was performed, and the results of the proposed control laws are compared with some control laws from the literature. The algorithms were also validated using the Mirosot-type robot soccer robot and a vision-based system.