Departmental Papers (ESE)


We present a new methodology for exact robot motion planning and control that unifies the purely kinematic path planning problem with the lower level feedback controller design. Complete information about the freespace and goal is encoded in the form of a special artificial potential function - a navigation function - that connects the kinematic planning problem with the dynamic execution problem in a provably correct fashion. The navigation function automatically gives rise to a bounded-torque feedback controller for the robot's actuators that guarantees collision-free motion and convergence to the destination from almost all initial free configurations. Since navigation functions exist for any robot and obstacle course, our methodology is completely general in principle. However, this paper is mainly concerned with certain constructive techniques for a particular class of motion planning problems. Specifically, we present a formula for navigation functions that guide a point-mass robot in a generalized sphere world. The simplest member of this family is a space obtained by puncturing a disc by an arbitrary number of smaller disjoint discs representing obstacles. The other spaces are obtained from this model by a suitable coordinate transformation that we show how to build. Our constructions exploit these coordinate transformations to adapt a navigation function on the model space to its more geometrically complicated (but topologically equivalent) instances. The formula that we present admits sphere-worlds of arbitrary dimension and is directly applicable to configuration spaces whose forbidden regions can be modeled by such generalized discs. We have implemented these navigation functions on planar scenarios, and simulation results are provided throughout the paper.

Document Type

Journal Article

Subject Area

GRASP, Kodlab

Date of this Version



Copyright 1992 IEEE. Reprinted from IEEE Transactions on Robotics and Automation, Volume 8, Issue 5, October 1992, pages 501-518.

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.

NOTE: At the time of publication, Daniel Koditschek was affiliated with the University of Michigan. Currently, he is a faculty member at the School of Engineering of the University of Pennsylvania.

Included in

Robotics Commons



Date Posted: 12 March 2008

This document has been peer reviewed.