This paper addresses an Optimal Transport (OT)-based efficient multi-robot exploration problem, considering the energy constraints of a multi-robot system. The efficiency in this problem implies how a team of robots (agents) covers a given domain, reflecting a priority of areas of interest represented by a density distribution, rather than simply following a preset of uniform patterns. To achieve an efficient multi-robot exploration, the optimal transport theory that quantifies a distance between two density distributions is employed as a tool, which also serves as a means of performance measure. The energy constraints for the multi-robot system is then incorporated into the OT-based multi-robot exploration scheme. The proposed scheme is decoupled from robot dynamics, broadening the applicability of the multi-robot exploration plan to heterogeneous robot platforms. Not only the centralized but also decentralized algorithms are provided to cope with more realistic scenarios such as communication range limits between agents. To measure the exploration efficiency, the upper bound of the performance is developed for both the centralized and decentralized cases based on the optimal transport theory, which is computationally tractable as well as efficient. The proposed multi-robot exploration scheme is also applicable to a time-varying distribution, where the spatio-temporal evolution of the given reference distribution is desired. To validate the proposed method, multiple simulation results are provided.

中文翻译：

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基于最优传输理论的能量约束多机器人高效探索

考虑到多机器人系统的能量限制，本文解决了基于最优传输 (OT) 的高效多机器人探索问题。这个问题的效率意味着一组机器人（代理）如何覆盖给定的域，反映由密度分布表示的感兴趣区域的优先级，而不是简单地遵循预设的统一模式。为了实现高效的多机器人探索，量化两个密度分布之间距离的最优传输理论被用作工具，它也用作性能测量的手段。然后将多机器人系统的能量约束纳入基于 OT 的多机器人探索方案。所提出的方案与机器人动力学分离，扩大多机器人探索计划对异构机器人平台的适用性。不仅提供了集中式算法，还提供了分散式算法来应对更现实的场景，例如代理之间的通信范围限制。为了衡量勘探效率，基于最优传输理论为集中式和分散式情况开发了性能上限，这在计算上易于处理且高效。所提出的多机器人探索方案也适用于时变分布，其中需要给定参考分布的时空演化。为了验证所提出的方法，提供了多个仿真结果。不仅提供了集中式算法，还提供了分散式算法来应对更现实的场景，例如代理之间的通信范围限制。为了衡量勘探效率，基于最优传输理论为集中式和分散式情况开发了性能上限，这在计算上易于处理且高效。所提出的多机器人探索方案也适用于时变分布，其中需要给定参考分布的时空演化。为了验证所提出的方法，提供了多个仿真结果。不仅提供了集中式算法，还提供了分散式算法来应对更现实的场景，例如代理之间的通信范围限制。为了衡量勘探效率，基于最优传输理论为集中式和分散式情况开发了性能上限，这在计算上易于处理且高效。所提出的多机器人探索方案也适用于时变分布，其中需要给定参考分布的时空演化。为了验证所提出的方法，提供了多个仿真结果。性能的上限是基于最优传输理论为集中式和分散式情况开发的，该理论在计算上易于处理且高效。所提出的多机器人探索方案也适用于时变分布，其中需要给定参考分布的时空演化。为了验证所提出的方法，提供了多个仿真结果。性能的上限是基于最优传输理论为集中式和分散式情况开发的，该理论在计算上易于处理且高效。所提出的多机器人探索方案也适用于时变分布，其中需要给定参考分布的时空演化。为了验证所提出的方法，提供了多个仿真结果。