Browsing by Author "Boddu, Adithya"
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Item Multi-agent navigation functions: Have we missed something?(Department of Mechanical Engineering, University of Delaware, 2010-08) Tanner, Herbert; Boddu, AdithyaThis paper presents a methodology for designing (centralized) control laws which can probably steer a group of robotic agents to fall into a formation of arbitrary shape, while following collision free trajectories. The scheme is based on the concept of navigation functions, a special type of artificial potential functions without local minima, and the paper describes how this idea can be generalized from its original formulation for single-robot systems, to multi-robot formations. We indicate why existing solutions that have appeared in literature, although potentially functional, may not have been accompanied with sufficient guarantees against the possibility of the system ever getting stuck in non-optimal configurations. The problem is therefore revisited here under a new set of assumptions, a new construction is proposed, and the properties of this new centralized potential function are analytically demonstrated.Item Nonsmooth multi-agent navigation functions(University of Delaware, 2012) Boddu, AdithyaThis 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.