Swarms of Bouncing Robots

We study models of mobile robots with limited capabilities that are deployed either on a cycle or an infinite line or on a segment. Robots start moving at the same time and when two robots collide their speeds and movement directions are instantaneously updated. Each of them has a collision detector and a clock to measure the times of its collisions. They do not have any knowledge on the total number of robots and do not have a common sense of direction. Besides, they neither have visibility nor control over their movements. We investigate the feasibility of the localization task in the cycle and the segment by bouncing robots: every robot should figure out the starting position and initial velocity of all the other robots. We consider two different scenarios when robots have common masses and speeds and robots of arbitrary masses and speeds. We give complete characterizations of all feasible configurations for the cycle in both scenarios. We study the survivability of bouncing robots. We say a robot survives if it never returns to its starting position. Non-surviving robots disappear from the environment. We provide sufficient and necessary conditions to have surviving robots in the cycle and in the segment. Finally we investigate communication protocols for bouncing robots that only communicate at the time of their collisions. We establish necessary and sufficient conditions for bouncing robots to perform gossiping, broadcasting and convergecast.