Departmental Papers (ESE)


In this paper, we present a computational framework for automatic generation of provably correct control laws for planar robots in polygonal environments. Using polygon triangulation and discrete abstractions, we map continuous motion planning and control problems, specified in terms of triangles, to computationally inexpensive problems on finite-state-transition systems. In this framework, discrete planning algorithms in complex environments can be seamlessly linked to automatic generation of feedback control laws for robots with underactuation constraints and control bounds. We focus on fully actuated kinematic robots with velocity bounds and (underactuated) unicycles with forward and turning speed bounds.

Document Type

Journal Article

Subject Area


Date of this Version

October 2005


Copyright 2005 IEEE. Reprinted from IEEE Transactions on Robotics, Volume 21, Issue 5, October 2005, pages 864-874.

This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to By choosing to view this document, you agree to all provisions of the copyright laws protecting it.


Bisimulation, control, discrete abstraction, hybrid system (HS), motion planning, triangulation



Date Posted: 25 February 2006

This document has been peer reviewed.