Numerical Determination of Optimal Non-Holonomic Paths in the Presence of Obstacles

This paper addresses the problem of numerically finding an optimal path for a robot with non-holonomic constraints. A car like robot, whose turning radius is lower bounded i s considered as an example, where the arc length and the change in steering angle are optimized. The car like robot is kinematically constrained and i s modelled as a 2 D object translating and rotating in the horizontal plane in the midst of well defined static obstacles. Given the initial and final configurations of the car and a complete description of the obstacles, our procedure directly generates a nonholonomic path as a function of the control variables in an environment of reasonable obstacle clutter. Nonholonomic paths in the midst of more complet obstacle clutter have been generated by identifying grid points on a geometric road map and by applying our procedam between successive grid points.