Particle Computation: Designing Worlds to Control Robot Swarms with only Global Signals
This addresses the challenge of efficiently planning motions for large swarms of simple robots, such as in micro- and nanorobotics, with incremental advancements in complexity analysis and hardware design.
The paper tackles the problem of controlling robot swarms with global signals, proving that finding optimal control sequences is PSPACE-complete, and demonstrates practical applications by designing obstacles to form permutations, build an absolute encoder, and construct universal logic gates for evaluating any logical expression.
Micro- and nanorobots are often controlled by global input signals, such as an electromagnetic or gravitational field. These fields move each robot maximally until it hits a stationary obstacle or another stationary robot. This paper investigates 2D motion-planning complexity for large swarms of simple mobile robots (such as bacteria, sensors, or smart building material). In previous work we proved it is NP-hard to decide whether a given initial configuration can be transformed into a desired target configuration; in this paper we prove a stronger result: the problem of finding an optimal control sequence is PSPACE-complete. On the positive side, we show we can build useful systems by designing obstacles. We present a reconfigurable hardware platform and demonstrate how to form arbitrary permutations and build a compact absolute encoder. We then take the same platform and use dual-rail logic to build a universal logic gate that concurrently evaluates AND, NAND, NOR and OR operations. Using many of these gates and appropriate interconnects we can evaluate any logical expression.