A New Method of Motion Coordination of a Group of Mobile Agents

Abstract

This paper presents a new method for coordinated motion planning of multiple mobile agents. The position in 2-D of each mobile agent is mapped to a complex number and a time varying polynomial contains information regarding the current positions of all mobile agents, the degree of the polynomial being the number of mobile agents and the roots of the polynomial representing the position in 2-D of the mobile agents at a given time. This polynomial is constructed by finding a path parameterized in time from the initial to the goal polynomial which represent the initial and goal positions of the mobile agents so that the discriminant variety or the set of polynomials with multiple roots is avoided in polynomial space. This is equivalent to saying that there is no collision between any two agents in going from initial position to goal position.