Feedback control of a two wheeled mobile robot with obstacle avoidance using potential functions

This paper deals with the feedback stabilization problem for a two-wheeled mobile robot which moves in the presence of obstacles. A state feedback controller is proposed based on Lyapunov control. First, we choose a potential function (Lyapunov function) whose value is minimum at a desired point and maximum on the surfaces of obstacles. And then, we construct a control input by multiplying the gradient vector of the potential function by a matrix composed of a negative definite symmetric one and a skew-symmetric one. It is shown that the system with the controller converges to one of critical points of the potential function. When the potential function has some critical points other than the minimum at the desired point, in order to avoid convergence to those points, the controller is modified. As a result, the controlled system converges to the desired point avoiding collision with obstacles.