Averaging approach to nonholonomic motion planning

The author considers the problem of motion planning for a nonholonomic system with drift. Open-loop and feedback solutions for nonholonomic motion planning (NMP) are constructed by using the averaging technique that is well known in applied mathematics. An algorithm for open-loop and feedback solutions of NMP is introduced. The main step in the algorithm is the case of first order Lie brackets. This case, as is shown, is equivalent to NMP for Brockett´s system considered over functional commutative algebra. Feedback solutions are constructed in the same manner. From a robotics point of view, it is shown that NMP can be reduced to the holonomic problem. As linear algebra plays a crucial role in linear control theory, polylinear algebra is crucial for NMP. The rolling disk example is used to illustrate the feedback algorithm