Jorge Cortés

Professor





Network connectivity maintenance via nonsmooth control barrier functions
P. Ong, B. Capelli, L. Sabattini, J. Cortés
IEEE Conference on Decision and Control, Austin, Texas, 2021, submitted


Abstract

This paper considers the connectivity maintenance problem for multi-robot systems and proposes a continuous optimization-based controller with Nonsmooth Control Barrier Functions to achieve it. The design is based on the concept of algebraic connectivity of the interaction graph. When viewed as a function of the network state, the algebraic connectivity is not continuously differentiable, a fact neglected in previous controller designs. To illustrate the importance of this observation, we present an example of a simple multi-robot system that fails to maintain connectivity under such controllers. The insights gained allow us to synthesize an optimization-based controller that prescribes that all the nontrivial eigenvalues of the Laplacian remain positive. Using tools from nonsmooth analysis and set-valued theory, we show that the proposed controller is continuous, thereby guaranteeing the existence of the robot trajectories for the closed-loop system and ensuring network connectivity is maintained along them.

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Mechanical and Aerospace Engineering, University of California, San Diego
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