标题： 无碰撞圆环楔形运动规划 显示英文标题

标题： Collision free motion planning on a wedge of circles

摘要： 我们展示了一个具有连续指令的算法，用于两个机器人在形状为三个圆组成的楔形轨道上无碰撞移动。 我们证明了与该问题相关的配置空间的拓扑复杂度为3。 拓扑复杂度是一个同伦不变量，可以看作是在没有任何碰撞的情况下，描述从任何初始配置到任何最终配置的机器人运动所需的最少连续指令数量。 所提出的算法是最佳的，因为它恰好需要3个连续指令。 显示英文摘要

摘要： We exhibit an algorithm with continuous instructions for two robots moving without collisions on a track shaped as a wedge of three circles. We show that the topological complexity of the configuration space associated with this problem is 3. The topological complexity is a homotopy invariant that can be thought of as the minimum number of continuous instructions required to describe the movement of the robots between any initial configuration to any final one without collisions. The algorithm presented is optimal in the sense that it requires exactly 3 continuous instructions.