Performance Bounds on Spatial Coverage Tasks by Stochastic Robotic Swarms

Fangbo Zhang, Andrea L. Bertozzi, Karthik Elamvazhuthi, Spring Berman

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

This paper presents a novel procedure for computing parameters of a robotic swarm that guarantee coverage performance by the swarm within a specified error from a target spatial distribution. The robots cannot localize or communicate with one another, and they exhibit stochasticity in their motion and task-switching policies. We model the population dynamics of the swarm as an advection-diffusion-reaction partial differential equation (PDE) with time-dependent advection and reaction terms. We derive rigorous bounds on the discrepancies between the target distribution and the coverage achieved by individual-based and PDE models of the swarm. We use these bounds to select the swarm size that will achieve coverage performance within a given error and the corresponding robot sensing radius that will minimize this error. We also apply the optimal control approach from our prior work to compute the robots' velocity field and task-switching rates. We validate our procedure through simulations of a scenario in which a robotic swarm must achieve a specified density of pollination activity over a crop field.

Original languageEnglish (US)
JournalIEEE Transactions on Automatic Control
DOIs
StateAccepted/In press - Aug 31 2017

Fingerprint

Robotics
Advection
Robots
Partial differential equations
Population dynamics
Spatial distribution
Crops

Keywords

  • advection-diffusion-reaction PDE
  • Analytical models
  • Computational modeling
  • Mathematical model
  • optimal control
  • Robot sensing systems
  • Stochastic processes
  • stochastic systems
  • Swarm robotics

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

Cite this

Performance Bounds on Spatial Coverage Tasks by Stochastic Robotic Swarms. / Zhang, Fangbo; Bertozzi, Andrea L.; Elamvazhuthi, Karthik; Berman, Spring.

In: IEEE Transactions on Automatic Control, 31.08.2017.

Research output: Contribution to journalArticle

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