Wheeled mobile robot navigation using proportional navigation

We present a method for wheeled mobile robot navigation based on the proportional navigation law. This method integrates the robot's kinematics equations and geometric rules. According to the control strategy, the robot's angular velocity is proportional to the rate of turn of the angle of the line of sight that joins the robot and the goal. We derive a relative kinematics system which models the navigation problem of the robot in polar coordinates. The kinematics model captures the robot path as a function of the control law parameters. It turns out that different paths are obtained for different control parameters. Since the control parameters are real, the number of possible paths is infinite. Results concerning the navigation using our control law are rigorously proven. An extensive simulation confirms our theoretical results.