This article considers the problem of conflict-free distribution of point-sized agents on a circular periphery encompassing all agents. The two key elements of the proposed policy include the construction of a set of convex layers (nested convex polygons) using the initial positions of the agents, and a novel search space region for each of the agents. The search space for an agent on a convex layer is defined as the region enclosed between the lines passing through the agent's position and normal to its supporting edges. Guaranteeing collision-free paths, a goal assignment policy designates a unique goal position within the search space of an agent at the initial time itself, requiring no further computation thereafter. In contrast to the existing literature, this work presents a one-shot, collision-free solution to the circular distribution problem by utilizing only the initial positions of the agents. Illustrative examples and extensive Monte-Carlo studies considering various practical attributes demonstrate the effectiveness of the proposed method.

翻译：本文研究点状智能体在包含所有智能体的圆形外围上的无冲突分布问题。所提出策略的两个关键要素包括：利用智能体初始位置构建一组凸层（嵌套凸多边形），以及为每个智能体定义新颖的搜索空间区域。位于凸层上的智能体，其搜索空间定义为通过该智能体位置且垂直于其支撑边的两条直线所围成的区域。通过保证无碰撞路径，目标分配策略在初始时刻即为每个智能体在其搜索空间内指定唯一的目标位置，此后无需进一步计算。与现有文献相比，本研究仅利用智能体的初始位置，为圆形分布问题提供了一种单次计算、无碰撞的解决方案。通过示例性案例和考虑多种实际属性的广泛蒙特卡洛研究，验证了所提方法的有效性。