A variational approach to optimal nonholonomic motion planning

Nonholonomic motion planning (NMP) problems arise not only from the classical nonholonomic constraints, but also from symmetries and conservation laws of holonomic systems. In NMP problems an admissible configuration space path is constrained to a given nonholonomic distribution. Thus, NMP deals with the problem of (optimal) path finding subject to a nonholonomic distribution and possibly to additional holonomic constraints. The authors first study several representative NM systems and formulate the NMP problem. Variational principles are used to characterize optimal solutions to these problems. A simple algorithm solving an NMP problem is proposed, and simulation results are presented