A Global Approach to Nonholonomic Motion Planning

The kinematic path planning problem of a nonholonomic system can be posed as a point-to-point control problem of a nonlinear system. This system has the property that it is not locally stabilizable but is globally controllable. The authors present a new algorithm for constructing a feasible path between specified initial and final configurations. The algorithm iteratively warps the entire path until all the constraints are satisfied. Polyhedral constraints in both configuration and nonconfiguration spaces (possibly nonconvex) can also be incorporated in this framework. The algorithm is based on the assumption that the system is usually controllable about a nontrivial trajectory, which is true for many cases. An initial trajectory is iteratively warped until the desired final configuration is reached. Examples of a front-wheel driven car and of tractors with one, two, and three trailers are included to illustrate the efficacy of the proposed algorithm.<>