期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 63, 期 6, 页码 1563-1578出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2017.2747769
关键词
Advection-diffusion-reaction (ADR) partial differential equation (PDE); optimal control; stochastic systems; swarm robotics
资金
- National Science Foundation [CMMI-1435709, CMMI-1436960]
- Div Of Civil, Mechanical, & Manufact Inn
- Directorate For Engineering [1436960] Funding Source: National Science Foundation
- Div Of Civil, Mechanical, & Manufact Inn
- Directorate For Engineering [1435709] Funding Source: National Science Foundation
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 advectiondiffusion- 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.
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