We extend the motion-planning-through-gadgets framework to several new scenarios involving various numbers of robots/agents, and analyze the complexity of the resulting motion-planning problems. While past work considers just one robot or one robot per player, most of our models allow for one or more locations to spawn new robots in each time step, leading to arbitrarily many robots. In the 0-player context, where all motion is deterministically forced, we prove that deciding whether any robot ever reaches a specified location is undecidable, by representing a counter machine. In the 1-player context, where the player can choose how to move the robots, we prove equivalence to Petri nets, EXPSPACE-completeness for reaching a specified location, PSPACE-completeness for reconfiguration, and ACKERMANN-completeness for reconfiguration when robots can be destroyed in addition to spawned. Finally, we consider a variation on the standard 2-player context where, instead of one robot per player, we have one robot shared by the players, along with a ko rule to prevent immediately undoing the previous move. We prove this impartial 2-player game EXPTIME-complete.

翻译：我们扩展了“通过小装置进行运动规划”框架，涵盖了涉及不同数量机器人/智能体的多种新场景，并分析了由此产生的运动规划问题的复杂性。以往的研究仅考虑单个机器人或每个玩家一个机器人的情况，而我们的大多数模型允许在每一步从一处或多处位置生成新机器人，从而导致任意数量的机器人。在零玩家情境中，所有运动均被确定性强制，我们通过表示计数器机，证明了判断是否有机器人到达指定位置的问题是不可判定的。在单玩家情境中，玩家可选择如何移动机器人，我们证明了其与佩特里网的等价性，到达指定位置为EXPSPACE完全问题，重新配置为PSPACE完全问题，而在机器人既可生成也可销毁的情况下，重新配置为阿克曼完全问题。最后，我们考虑了标准双玩家情境的一种变体：每个玩家并非拥有独立的机器人，而是共享一个机器人，并引入“劫”规则以防止立即撤销上一步操作。我们证明这一无偏双玩家游戏为EXPTIME完全问题。