Exact Robot Navigation Using Artificial Potential Functions

Elon Rimon, Mechanical Engineering, Technion (Currently on sabbatical at Caltech)

The purpose of this talk is to serve as a trigger on the possible use of potential fields for multi-agent control. In addition to technical material detailed below, I will attempt to communicate informal thoughts shared by colleagues in the robotics community on this subject.

In this talk I will report on research conducted with Dan Koditschek, on the application of artificial potential functions to solve the robot navigation problem. A class of suitable potential functions - *navigation functions* - is defined and shown to represent an exact solution to the problem. Once a navigation function is constructed for a given environment and desired destination, there is a natural and automatic way to derive from it a bounded-torque feedback control law for the robot. The resulting closed-loop robot system is guaranteed to approach the desired destination without hitting the obstacles.

This technique suggests the following paradigm for robot navigation. The high-level planner needs to provide the desired destination and the obstacles' geometrical description; then, a collision-free path as well as a control input to drive the robot are computed without the operator intervention. In fact, this methodology constitutes the only provably correct and, in principle, completely general alternative to the currently used method of first planning a collision-free path and then ``forcing'' the robot to follow it.

I will show how to construct navigation functions on almost any geometrically complicated robot configuration space which is topologically equivalent to a simple disc punctured by disjoint smaller discs, representing obstacles. This work is a precursor to a much larger program of research committed to construction of navigation functions for progressively more realistic robotic situations. Time permitting, I will also mention subsequent research by colleagues on application of navigation functions to multi-part assembly.