On use of Campbell-Baker-Hausdorff-Dynkin formulas in nonholonomic motion planning

In this paper discrete and continuous Campbell-Baker-Hausdorff-Dynkin formulas are used for designing the control method to steer driftless nonholonomic systems. The formulas offer complementary properties of controls: the discrete formula produces piecewise constant controls with many switches and practically without computational effort; while the continuous formula provides piecewise continuous controls with only a few switches, in computationally involved procedure. Both of the formulas can be used in nonholonomic motion planning. A simple algorithm of motion planning based on the formulas is presented. Examples of controls obtained for exemplary motion planning of a unicycle robot in an obstacle free environment are included.