Performance Bounds on Spatial Coverage Tasks by Stochastic Robotic Swarms

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 main contribution of this paper is the analysis of the dependence of this error on two key parameters: t...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2018-06, Vol.63 (6), p.1563-1578
Main Authors: Fangbo Zhang, Bertozzi, Andrea L., Elamvazhuthi, Karthik, Berman, Spring
Format: Article
Language:English
Subjects:
Advection
Advection-diffusion-reaction (ADR) partial differential equation (PDE)
Analytical models
Computational modeling
Computer simulation
Error detection
Mathematical model
Mathematical models
Optimal control
Parameters
Partial differential equations
Robot sensing systems
Robot sensors
Robotics
Robots
Spatial distribution
Stochastic processes
stochastic systems
swarm robotics
Switching
Velocity distribution
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Summary: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 main contribution of this paper is the analysis of the dependence of this error on two key parameters: the number of robots in the swarm and the robot sensing radius. 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 in [13] 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.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2017.2747769