Mean-Field Stabilization of Markov Chain Models for Robotic Swarms: Computational Approaches and Experimental Results

Vaibhav Deshmukh, Karthik Elamvazhuthi, Shiba Biswal, Zahi Kakish, Spring Berman

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this letter, we present two computational approaches for synthesizing decentralized density-feedback laws that asymptotically stabilize a strictly positive target equilibrium distribution of a swarm of agents among a set of states. The agents' states evolve according to a continuous-time Markov chain on a bidirected graph, and the density-feedback laws are designed to prevent the agents from switching between states at equilibrium. First, we use classical linear matrix inequality (LMI)-based tools to synthesize linear feedback laws that (locally) exponentially stabilize the desired equilibrium distribution of the corresponding mean-field model. Since these feedback laws violate positivity constraints on the control inputs, we construct rational feedback laws that respect these constraints and have the same stabilizing properties as the original feedback laws. Next, we present a sum-of-squares (SOS)-based approach to constructing polynomial feedback laws that globally stabilize an equilibrium distribution and also satisfy the positivity constraints. We validate the effectiveness of these control laws through numerical simulations with different agent populations and graph sizes and through multirobot experiments on spatial redistribution among four regions.

Original languageEnglish (US)
Pages (from-to)1985-1992
Number of pages8
JournalIEEE Robotics and Automation Letters
Volume3
Issue number3
DOIs
StatePublished - Jul 1 2018

Fingerprint

Swarm Robotics
Feedback Law
Markov Chain Model
Mean Field
Markov processes
Robotics
Stabilization
Feedback
Experimental Results
Equilibrium Distribution
Positivity
Multi-robot
Mean-field Model
Continuous-time Markov Chain
Strictly positive
Sum of squares
Redistribution
Violate
Graph in graph theory
Swarm

Keywords

  • distributed robot systems
  • multirobot systems
  • optimization and optimal control
  • probability and statistical methods
  • Swarms

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Human-Computer Interaction
  • Biomedical Engineering
  • Mechanical Engineering
  • Control and Optimization
  • Artificial Intelligence
  • Computer Science Applications
  • Computer Vision and Pattern Recognition

Cite this

Mean-Field Stabilization of Markov Chain Models for Robotic Swarms : Computational Approaches and Experimental Results. / Deshmukh, Vaibhav; Elamvazhuthi, Karthik; Biswal, Shiba; Kakish, Zahi; Berman, Spring.

In: IEEE Robotics and Automation Letters, Vol. 3, No. 3, 01.07.2018, p. 1985-1992.

Research output: Contribution to journalArticle

Deshmukh, Vaibhav ; Elamvazhuthi, Karthik ; Biswal, Shiba ; Kakish, Zahi ; Berman, Spring. / Mean-Field Stabilization of Markov Chain Models for Robotic Swarms : Computational Approaches and Experimental Results. In: IEEE Robotics and Automation Letters. 2018 ; Vol. 3, No. 3. pp. 1985-1992.
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