This paper studies the density regulation problem for a large-scale robotic swarm with homogeneous agents. A novel robust model predictive mean-field control method is proposed to significantly improve the control performance and the algorithm scalability with the population size. To that end, a top-down control philosophy is first employed, under which the physical space is divided into finite disjoint bins and the actual density distribution (ADD) over these bins is taken as the macrostate. The system dynamics of ADD is then established by including a stochastic disturbance in the mean-field model, which describes the evolution process of each agent’s probability density distribution over the bins. Next, an optimization-based model predictive control method is developed to efficiently overcome the performance degradation raised by the disturbance term. Furthermore, the conditions ensuring the algorithm feasibility are strictly developed. We also prove that the actual swarm density converges to the target one in probability. Finally, simulation and comparison studies illustrate the effectiveness and advantages of the proposed algorithm over the existing results.

中文翻译：

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使用鲁棒模型预测平均场控制进行大规模机器人群的密度调节


本文研究了具有同质代理的大规模机器人群的密度调节问题。提出了一种新颖的鲁棒模型预测平均场控制方法，以显着提高控制性能和算法随种群规模的可扩展性。为此，首先采用自上而下的控制原理，将物理空间划分为有限的不相交箱，并将这些箱上的实际密度分布（ADD）视为宏观状态。然后通过在平均场模型中包含随机扰动来建立 ADD 的系统动力学，该模型描述了每个智能体在箱上的概率密度分布的演化过程。接下来，开发了一种基于优化的模型预测控制方法，以有效克服干扰项引起的性能下降。此外，严格制定了保证算法可行性的条件。我们还证明了实际群体密度在概率上收敛于目标群体密度。最后，仿真和比较研究说明了所提出算法相对于现有结果的有效性和优势。