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Bioinspir Biomim. 2019 Nov 6;15(1):015001. doi: 10.1088/1748-3190/ab49a4.
We present a survey on the application of fluid approximations, in the form of mean-field models, to the design of control strategies in swarm robotics. Mean-field models that consist of ordinary differential equations, partial differential equations, and difference equations have been used in the swarm robotics literature, depending on whether the state of each agent and the time variable take values from a discrete or continuous set. These macroscopic models are independent of the number of agents in the swarm, and hence can be used to synthesize robot control strategies in a scalable manner, in contrast to individual-based microscopic models of swarms that represent finite numbers of discrete agents. Moreover, mean-field models are amenable to rigorous investigation using tools from dynamical systems theory, control theory, stochastic processes, and analysis of partial differential equations, enabling new insights and provable guarantees on the dynamics of collective behaviors. In this paper, we survey the applications of these models to problems in swarm robotics that include coverage, task allocation, self-assembly, consensus, and environmental mapping.
我们对基于流体近似的方法（以平均场模型的形式）在群体机器人控制策略设计中的应用进行了综述。在群体机器人文献中，根据每个个体的状态和时间变量取值是离散的还是连续的，使用了常微分方程、偏微分方程和差分方程的平均场模型。这些宏观模型与群体中的个体数量无关，因此可以以可扩展的方式综合机器人控制策略，与代表有限数量离散个体的基于个体的微观群体模型形成对比。此外，平均场模型可以使用动力系统理论、控制理论、随机过程和偏微分方程分析的工具进行严格研究，从而为集体行为的动态提供新的见解和可证明的保证。在本文中，我们调查了这些模型在包括覆盖、任务分配、自组装、一致性和环境映射等群体机器人问题中的应用。
