Performance Bounds on Spatial Coverage Tasks by Stochastic Robotic Swarms

• 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
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2017.2747769

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.