Trajectory-Constrained Collective Circular Motion with Different Phase Arrangements

Jain, A and Ghose, D (2020) Trajectory-Constrained Collective Circular Motion with Different Phase Arrangements. In: IEEE Transactions on Automatic Control, 65 (5). pp. 2237-2244.

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Abstract

A methodology to stabilize synchronized, balanced, or symmetric phase patterns of unicycle-type agents on a desired common circle, while restricting their trajectories to a certain region of interest, is proposed in this note. These phase patterns are characterized by the motion of the collective centroid of the group of agents and derived by optimizing the average linear momentum of the group. Under a mild assumption on initial states of the agents, we design control laws by exploiting the concept of barrier Lyapunov function in conjunction with bounded phase potential functions. We show that the agents asymptotically stabilize to a desired phase arrangement and their trajectories remain bounded during stabilization. We obtain bounds on the different quantities of interest in the postdesign analysis and show that these bounds depend on the initial conditions and can be altered by adjusting the controller gains. We also prove convergence when the control input is saturated to a prespecified value. Finally, we provide a discussion on the application and limitation of the proposed approach and characterize the feasible initial conditions. © 2020 IEEE.

Item Type:	Journal Article
Publication:	IEEE Transactions on Automatic Control
Publisher:	Institute of Electrical and Electronics Engineers Inc.
Additional Information:	The copyright for this article belongs to Institute of Electrical and Electronics Engineers Inc.
Keywords:	Accident prevention; Collision avoidance; Image segmentation; Lyapunov functions; Lyapunov methods; Stabilization; Synchronization; Trajectories, Barrier functions; Formation control; Initial conditions; Phase arrangement; Potential function; Quantities of interests; Region of interest; Robot sensing system, Multi agent systems
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited:	06 Feb 2023 09:29
Last Modified:	06 Feb 2023 09:29
URI:	https://eprints.iisc.ac.in/id/eprint/79916

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