Robots with Lights: Overcoming Obstructed Visibility Without Colliding

Robots with lights is a model of autonomous mobile computational entities operating in the plane in Look-Compute-Move cycles: each agent has an externally visible light which can assume colors from a fixed set; the lights are persistent (i.e., the color is not erased at the end of a cycle), but otherwise the agents are oblivious. The investigation of computability in this model, initially suggested by Peleg, is under way, and several results have been recently established. In these investigations, however, an agent is assumed to be capable to see through another agent. In this paper we start the study of computing when visibility is obstructable, and investigate the most basic problem for this setting, Complete Visibility: The agents must reach within finite time a configuration where they can all see each other and terminate. We do not make any assumption on a-priori knowledge of the number of agents, on rigidity of movements nor on chirality. The local coordinate system of an agent may change at each activation. Also, by definition of lights, an agent can communicate and remember only a constant number of bits in each cycle. In spite of these weak conditions, we prove that Complete Visibility is always solvable, even in the asynchronous setting, without collisions and using a small constant number of colors. The proof is constructive. We also show how to extend our protocol for Complete Visibility so that, with the same number of colors, the agents solve the (non-uniform) Circle Formation problem with obstructed visibility

Mutual visibility by luminous robots without collisions

We consider the Mutual Visibility problem for anonymous dimensionless robots with obstructed visibility moving in a plane: starting from distinct locations, the robots must reach, without colliding, a configuration where no three of them are collinear. We study this problem in the luminous robots model, in which each robot has a visible light that can assume colors from a fixed set. Among other results, we prove that Mutual Visibility can be solved in SSynch with 2 colors and in ASynch with 3 colors. If an adversary can interrupt and stop a robot moving to its computed destination, Mutual Visibility is still solvable in SSynch with 3 colors and, if the robots agree on the direction of one axis, also in ASynch. As a byproduct, we provide the first obstructed-visibility solutions to two classical problems for oblivious robots: collision-less convergence to a point (also known as near-gathering) and circle formation

Synchronized Dancing of Oblivious Chameleons

It has been recently discovered that oblivious iguanid lizards can form a periodic sequence of tableaux vivants with some restrictions on the tableaux. By viewing each tableau as a dance step, a formable sequence can be seen as a dance choreography, performable by the lizards. Interestingly, a complete characterization exists of the dances performable by all families of oblivious iguanid lizards except for the family of chameleons. This gap in knowledge opens the main research question addressed here: what choreographies can be danced by oblivious chameleons? We provide a full answer to this question, investigating formable tableaux, danceable choreographies as well as number of skin colours. We show that, unlike other lizards, in their feasible dances chameleons can touch and repeat steps. Also, they can do this even if they are asynchronous