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 is considered as an example, where the arc length and the change in steering angle are optimized. The car like robot is kinematically constrained and is 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 non-holonomic path as a function of the control variables in an environment of reasonable obstacle clutter. Non-holonomic paths in the midst of more complex obstacle clutter have been generated by identifying grid points on a geometric road map and by applying our procedure between successive grid points