A simulation evaluation of gCBHD formula for driftless nonholonomic systems

In this paper an accuracy of local motion planning based on the generalized Campbell-Baker-Hausdorff-Dynkin formula was evaluated for a few nonholonomic robotic systems. For a given set of controls, an exact trajectory is computable via an integration of equations of motion. This reference trajectory is compared with with a trajectory based on shrinked versions of the gCBHD formula. An impact of controls (linear time and amplitude scaling, their rotations) on the accuracy of reaching the final goal (important in motion planning) and retrieving a shape of the trajectory (important while avoiding obstacles) will be discussed and illustrated with simulations.