On Computing Complex Navigation Functions

This paper addresses the problem of efficiently computing robot navigation functions. Navigation functions are potential functions free of spurious local minima that present an exact solution to the robot motion planning and control problem. Although some methodologies were found in the literature, none of them are easy to implement and generalize for complex shaped workspaces and robots. We discuss some of the difficulties encountered in the current methodologies and propose a novel approach using a Finite Element method for potential field computation.