This paper investigates how a novel paradigm called group-control can be effectively used for motion planning for microrobot swarms in a global field. We prove that Small-Time Local Controllability (STLC) in robot positions is achievable through group-control, with the minimum number of groups required for STLC being $\log_2(n + 2) + 1$ for $n$ robots. We then discuss the trade-offs between control complexity, motion planning complexity, and motion efficiency. We show how motion planning can be simplified if appropriate primitives can be achieved through more complex control actions. We identify motion planning problems that balance the number of motion primitives with planning complexity. Various instantiations of these motion planning problems are explored, with simulations used to demonstrate the effectiveness of group-control.

翻译：本文研究了一种称为群控的新范式如何有效地用于全局场中微机器人集群的运动规划。我们证明了通过群控可以实现机器人位置的小时间局部可控性，对于n个机器人，实现STLC所需的最小群组数为$\log_2(n + 2) + 1$。随后我们探讨了控制复杂度、运动规划复杂度与运动效率之间的权衡关系。研究表明，若能通过更复杂的控制动作实现适当的运动基元，运动规划过程可得到显著简化。我们识别了能够平衡运动基元数量与规划复杂度的运动规划问题，并通过多种具体实例展开探讨，辅以仿真实验验证群控方法的有效性。