On the Complexity of Randolph’s Robot Game

We introduce a type of movement constraints for a swarm of robots in a grid environment, which is inspired by Alex Randolph’s board game Ricochet Robot and new to the field of robot motion planning. This type of movement may be used to model robots with very limited abilities for self localization: We assume that once a robot starts to drive in a certain direction, it does not stop its movement until it hits an obstacle wall or another robot. We give some lower bounds on the number of robots needed to reach every cell. Especially, it is easy to see that three robots are necessary and sufficient to reach every cell in a simple rectangular environment. Further, we consider the question, whether a certain cell can be reached is in arbitrary environments. A Java applet for simulating robot swarms moving with these constraints can be found in http://www.geometrylab.de/RacingRobots/