Nonsmooth multi-agent navigation functions

Tanner, Herbert G.This work presents a path planning methodology for designing centralized control laws which can provably steer a group of robotic agents to fall into a free-floating formation of arbitrary shape, while following collision free trajectories. The planning scheme is based on the concept of navigation functions, a special type of artificial potential functions without local minima. In this thesis, we describe how this idea can be generalized from its original formulation for single-robot systems, to multi-robot formations. Further, we indicate why existing solutions that have appeared in literature, although potentially functional, have not unequivocally established the non-degeneracy of undesirable critical points of the potential function. The problem is therefore reconsidered here, and a new (nonsmooth) potential function is proposed along with the associated control strategy. We show that the new construction of the multi agent navigation function allows analytic proofs for the convergence of the closed loop system and the non-degeneracy of the critical points of the underlying potential field.University of Delaware, Department of Mechanical EngineeringM.S