Parameter estimation and optimal control of swarm-robotic systems: A case study in distributed task allocation

This paper presents a methodology for finding optimal control parameters as well as optimal system parameters for robot swarm controllers using probabilistic, population dynamic models. With distributed task allocation as a case study, we show how optimal control parameters leading to a desired steady-state task distribution for two fully-distributed algorithms can be found even if the parameters of the system are unknown. First, a reactive algorithm in which robots change states independently from each other and which leads to a linear macroscopic model describing the dynamics of the system is considered. Second, a threshold-based algorithm where robots change states based on the number of other robots in this state and which leads to a non-linear model is investigated. Whereas analytical results can be obtained for the linear system, the optimization of the non-linear controller is performed numerically. Finally, we show using stochastic simulations that whereas the presented methodology and models work best if the swarm size is large, useful results can already be obtained for team-sizes below a hundred robots. The methodology presented can be applied to scenarios involving the control of large numbers of entities with limited computational and communication abilities as well as a tight energy budget, such as swarms of robots from the centimeter to nanometer range or sensor networks.