Computing good holonomic collision-free paths to steer nonholonomic mobile robots

Several schemes have been proposed in the path planning literature to plan collision-free and feasible trajectories for nonholonomic mobile robots. A classical scheme is the two-step approach which consists in first computing a collision-free holonomic path, and then in transforming this path by a sequence of feasible ones. The quality of the solution and the computational cost of the second step depend on the shape of the holonomic path. In this paper, we introduce a nonholonomic cost of the geometric path to be approximated and we propose a configuration space structuring that allows us to compute an holonomic path minimizing at best the nonholonomic cost. The algorithms have been implemented and we present simulation results which illustrate the efficacy of the planner to produce good solutions with respect to the nonholonomic constraints of a mobile robot.