Nonholonomic motion planning using Stoke's theorem
Ranjan Mukherjee, David P. Anderson · 2002
An algorithm for planning admissible trajectories for nonholonomic systems that will take the system from one point in its configuration space to another is developed. In this algorithm, the independent variables are converged to their desired values. Closed trajectories of the independent variables are used to converge the dependent variables. Stoke's theorem is used in the algorithm to convert the problem of finding a closed path into that of finding a surface area in the space of the independent variables such that the dependent variables converge to their desired values as the independent variables traverse along the boundary of this surface area. The salient features of this algorithm are illustrated in the example of a disk rolling without slipping on a flat surface.>