Randolphs Robot Game is NP-hard!

We introduce a new type of movement constraints for a swarm of robots in a grid environment inspired by Alex Randolphs board game Ricochet Robots. 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. (This property can be used to model robots with very limited abilities for self-localization.) We show that the question whether a given cell can be reached is NP-hard for arbitrary environments. A Java applet for simulating robot swarms moving with these constraints can be found in http://www.geometrylab.de/RacingRobots/.