Technical Reports (CIS)

Document Type

Technical Report

Subject Area

GRASP

Date of this Version

1-1-2003

Comments

University of Pennsylvania Department of Computer and Information Science Technical Report No. MS-CIS-07-16.

NOTE: At the time of publication, author Dan Koditschek was affiliated with the University of Michigan. Currently (October 2007), he is a faculty member in the Department of Electrical and Systems Engineering at the University of Pennsylvania.

NOTE: Updated PDF has been uploaded on June 26, 2014.

Abstract

This paper addresses the coordinated navigation of multiple independently actuated disk-shaped robots - all placed within the same disk-shaped workspace. Assuming perfect sensing, shared centralized communications and computation, as well as perfect actuation, we encode complete information about the goal, obstacles and workspace boundary using an artificial potential function over the cross product space of the robots’ simultaneous configurations. The closed-loop dynamics governing the motion of each robot take the form of the appropriate projection of the gradient of this function. We show, with some reasonable restrictions on the allowable goal positions, that this function is an essential navigation function - a special type of artificial potential function that is ensured of connecting the kinematic planning with the dynamic execution in a manner that guarantees collision-free navigation of each robot to its destination from almost all initial free placements. We summarize the results of an extensive simulation study investigating such practical issues as average resulting trajectory length and robustness against simulated sensor noise.

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Date Posted: 07 October 2007