Motion Planning by Piecewise Constant or Polynomial Inputs

Abstract

Abstract In this paper we present an algorithmic solution of the “Exact Motion Planning Problem” for nilpotent systems, by piecewise constant or polynomial inputs. By using an identification process, we improve here the solution earlier given by Lafferiere and Sussmann, for systems without drift. So we obtain a much smaller number of pieces (in case of piecewise constant inputs), we get also able to identify polynomial inputs, and finally we give also elements of a solution in case of systems with drift.