Motion planning for nonlinear systems using hybridizations and robust controllers on simplices

In this paper, we consider a motion planning problem for a class of constrained nonlinear systems. In each simplex of a triangulation of the set of states, the nonlinear dynamics is conservatively approximated by an affine system subject to disturbances. This results in a hybrid abstraction, called hybridization, of the nonlinear control system. Except for the disturbance, this hybridization can be seen as a piecewise affine hybrid system on simplices for which motion planning techniques have been developed by Habets and van Schuppen in a series of papers. We extend these techniques to handle the disturbances by synthesizing robust affine controllers on the simplices of the triangulation. Our approach, though conservative, can be fully automated and is computationally tractable. We illustrate our method on an example.