A central problem in swarm robotics is to design a controller that will allow the member robots of the swarm to collectively perform a given task. Of particular interest in massively distributed applications are reactive controllers with severely limited computational and sensory abilities. In this article, we give the results of the first computational complexity analysis of the reactive swarm design problem. Our core results are derived relative to a generalization of what is arguably the simplest possible type of reactive controller, the so-called computation-free controller proposed by Gauci et al., which operates in grid-based environments in a noncontinuous manner. We show that the design of a generalized computation-free swarm for an arbitrary given task in an arbitrary given environment is not polynomial-time solvable either in general or by the most desirable types of approximation algorithms (including evolutionary algorithms with high probabilities of producing correct solutions) but is solvable in effectively polynomial time relative to several types of restrictions on swarms, environments, and tasks. All of our results hold for the design of several more complex types of generalized computation-free swarms. Moreover, all of our intractability and inapproximability results hold for the design of any type of reactive swarm (including those based on the popular feed-forward neural network and Brooks-style subsumption controllers) operating in grid-based environments in a noncontinuous manner whose member robots satisfy two simple conditions. As such, our results give the first theoretical survey of the types of efficient exact and approximate solution algorithms that are and are not possible for designing several types of reactive swarms.

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设计反应性机器人群的可行算法选项

群体机器人的一个核心问题是设计一个控制器，允许群体中的成员机器人共同执行给定的任务。对大规模分布式应用程序特别感兴趣的是计算和感知能力严重受限的反应式控制器。在本文中，我们给出了反应群设计问题的第一次计算复杂度分析的结果。我们的核心结果是相对于可以说是最简单的反应控制器类型的概括而得出的，这种控制器是 Gauci 等人提出的所谓的无计算控制器，它以非连续方式在基于网格的环境中运行。我们表明，在任意给定环境中为任意给定任务设计广义无计算群不是一般的多项式时间可解的，也不是通过最理想的近似算法类型（包括具有高概率产生正确解），但相对于对群、环境和任务的几种类型的限制，可以在有效的多项式时间内求解。我们所有的结果都适用于几种更复杂类型的广义无计算群的设计。而且，我们所有的难处理性和不可近似性结果都适用于任何类型的反应群的设计（包括那些基于流行的前馈神经网络和布鲁克斯风格的包含控制器）在基于网格的环境中以非连续方式运行，其成员机器人满足两个简单的条件。因此，我们的结果首次对有效的精确和近似解算法类型进行了理论调查，这些算法对于设计几种类型的反应群是不可能的。