A navigation function for a simple rigid body

A provably correct navigation algorithm for a simple rigid body in a planar environment cluttered with disc obstacles is presented. The algorithm specifies a collision-free path by subjecting the robot to the influence of a navigation function, a special artificial potential function whose most crucial property is the absence of undesired local minima. Unlike other unknown algorithms, it specifies a feedback control law that is guaranteed to move the physical robot to the goal without it hitting obstacles, subject to the bounded-torque capability of the robot's actuators. Previous work has shown that navigation functions are guaranteed to exist. Construction of navigation functions for a realistic situation is proposed. The implementation of the algorithm reveals a numerical difficulty, which is effectively corrected by making a slight heuristic modification to the navigation function. This is discussed and illustrated