用密度矩阵建模机器人集群，让大规模群集计算更高效。
Density Matrix-based Dynamics for Quantum Robotic Swarms
- 将集群视为混合量子态，用密度矩阵表示，不随集群规模增大而膨胀。
- 1000个机器人的仿真验证了方法在大规模场景下的可行性。
- 能从全局信息中提取局部行为，适合分布式控制场景。
在机器人集群中，位置和距目标距离等参数可用概率振幅描述。近期研究提出以块矩阵形式表示集群，但其规模随集群增大急剧增长，难以用于大规模集群。为此，本文提出一种新方法：将机器人集群和网络视为混合量子态，通过密度矩阵进行数学表征。该方法的规模仅取决于机器人的自由度，而非集群规模，因此可有效扩展至大规模集群。此外，该模型能从密度矩阵中提取个体机器人信息，实现与整体行为一致的去中心化控制。我们在包含最多1000个机器人的多种仿真中验证了该方法的有效性，并为未来研究提供了方向。
原文摘要 · Abstract (English)
In a robotic swarm, parameters such as position and proximity to the target can be described in terms of probability amplitudes. This idea led to recent studies on a quantum approach to the definition of the swarm, including a block-matrix representation. However, the size of such matrix-based representation increases drastically with the swarm size, making them impractical for large swarms. Hence, in this work, we propose a new approach for modeling robotic swarms and robotic networks by considering them as mixed quantum states that can be represented mathematically via density matrices. The size of such an approach only depends on the available degrees of freedom of the robot, and not its swarm size and thus scales well to large swarms. Moreover, it also enables the extraction of local information of the robots from the global swarm information contained in the density matrices, facilitating decentralized behavior that aligns with the collective swarm behavior. Our approach is validated on several simulations including large-scale swarms of up to 1000 robots. Finally, we provide some directions for future research that could potentially widen the impact of our approach.
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