Analyzing human-swarm interactions using control Lyapunov functions and optimal control

Jean-Pierre de la  Croix; Magnus  Egerstedt

doi:10.3934/nhm.2015.10.609

Article Contents

2015, Volume 10, Issue 3: 609-630. Doi: 10.3934/nhm.2015.10.609

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Analyzing human-swarm interactions using control Lyapunov functions and optimal control

Jean-Pierre de la Croix^1, and
Magnus Egerstedt^1,

1.
School of Electrical and Computer Engineering, Georgia Institute of Technology, 777 Atlantic Drive NW, Atlanta, GA 30332-0250

Received: October 31, 2014

Revised: January 31, 2015

Published: August 2015

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Abstract

A number of different interaction modalities have been proposed for human engagement with networked systems. In this paper, we establish formal guarantees for whether or not a given human-swarm interaction (HSI) strategy is appropriate for achieving particular multi-robot tasks, such as guiding a swarm of robots into a particular geometric configuration. In doing so, we define what it means to impose an HSI control structure on a multi-robot system. Control Lyapunov functions are used to establish feasibility for a user to achieve a particular geometric configuration with a multi-robot system under some selected HSI control structure. Several examples of multi-robot systems with unique HSI control structures are provided to illustrated the use of CLFs to establish feasibility. Additionally, we also uses these examples to illustrate how to use optimal control tools to compute three metrics for evaluating an HSI control structure: attention, effort, and scalability.

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Mathematics Subject Classification: Primary: 93C85; Secondary: 37B25, 49N05.

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