Motion Planning of a Group of Agents Using the Homotopy Approach
Mayank Lal, Suhada Jayasuriya, Swaminathan Sethuraman · 2007
In this paper motion planning of a group of agents is done to move the group from an initial configuration to a final configuration through obstacles in 2-D. Also we introduce a new homotopy approach which uses potential fields to find paths in polynomial space. We use the homotopy approach for changing the group shape of the mobile agents and at the same time treat the group as a single agent by finding a bounding disc for it to plan the motion of the group through obstacles. A time varying polynomial is constructed, the roots of which represent the current positions of the mobile agents in a frame attached to the bounding disc. The real and imaginary parts of the roots of this polynomial represent the x and y coordinates of the mobile agents in this frame. This polynomial is constructed such that it avoids the discriminant variety or the set of polynomials having multiple roots. This is equivalent to saying that the mobile agents do not collide with each other at all times. The bounding disc is then used to plan the motion of the agents through obstacles such that the group avoids the obstacles at all times.