Numerical determination of optimal non-holonomic paths in the presence of obstacles

The problem of numerically finding an optimal path for a robot with nonholonomic constraints is addressed. A carlike robot whose tuning radius is lower bounded is considered as an example, where the arc length and the change in steering angle are optimized. The carlike robot is kinematically constrained and is modeled 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, the 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 complex obstacle clutter have been generated by identifying grid points on a geometric road map and by applying the procedure between successive grid points