Gauss's Principle with Inequality Constraints for Multi-agent Navigation and Control

Journal Article (Journal Article)

Multi-agent navigation systems present opportunities for many applications due to their agility and cooperation. In any multi-agent navigation system, it is critical that actual inter-agent collisions are strictly prevented. In this paper, we present a solution for the 2-D multi-agent navigation problem with collision avoidance. Our solution to this problem is based on a novel extension to Gauss's Principle of Least Constraint (GPLC) in which a fixed set of strict equality constraints are replaced by time-varying sets of active inequality constraints. To the best of our knowledge, this is the first instance that extends GPLC with dynamic incorporation and stabilization of active inequality constraints and with actuator delay and saturation. Herein, the dynamics of a collision-free multi-agent system satisfies the Karush-Kuhn-Tucker conditions. Active inequality constraints enforce collision avoidance, leader following and agglomeration behaviors, and they are stabilized using Baumgarte's error stabilization approach. We show that in dense configurations the positional arrangement of the agents can lead to linearly dependent constraints, and we propose specialized solutions involvin

Full Text

Duke Authors

Cited Authors

  • Zhang, B; Gavin, HP

Published Date

  • January 1, 2021

Published In

Electronic International Standard Serial Number (EISSN)

  • 1558-2523

International Standard Serial Number (ISSN)

  • 0018-9286

Digital Object Identifier (DOI)

  • 10.1109/TAC.2021.3059677

Citation Source

  • Scopus