Tracking under the nonholonomic constraint using cubic navigation laws

This paper deals with the problem of mobile robot tracking an unpredictably moving target in the presence of obstacles. We suggest a new family of navigation laws that consists of cubic navigation functions. These laws depend on various external parameters that can be used to adjust the robot´s path, especially to avoid collision with obstacles. The suggested method allows an easy combination between the global aspects of target tracking and the local aspects of obstacle avoidance. A method is suggested to tune and adjust the parameters of the navigation laws and derive a locally optimal path. The method is illustrated using an extensive simulation.