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.

翻译：我们展示了一种算法,连续指示两个机器人在以三个圆形形状的轨道上不发生碰撞而移动。我们显示,与这一问题相关的配置空间的地形复杂性是3。 地形复杂性是一种同质变异性,可以被认为是描述机器人在任何初始配置与任何未发生碰撞的最后配置之间移动所需的最起码的连续指示数量。 所呈现的算法是最佳的,因为它需要精确的3个连续指示。