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Evacuation of robots from a disk has attained a lot of attention recently. We visit the problem from the perspective of fault-tolerance. We consider two robots trying to evacuate from a disk via a single hidden exit on the perimeter of the disk. The robots communicate wirelessly. The robots are susceptible to crash faults after which they stop moving and communicating. We design the algorithms for tolerating one fault. The objective is to minimize the worst-case time required to evacuate both the robots from the disk. When the non-faulty robot chauffeurs the crashed robot, it takes α ≥ 1 amount of time to travel unit distance. With this, we also provide a lower bound for the evacuation time. Further, we evaluate the worst-case of the algorithms for different values of α and the crash time.

The design of distributed gathering and convergence algorithms for tiny robots has recently received much attention. In particular, it has been shown that convergence problems can even be solved for very weak, oblivious robots: robots which cannot maintain state from one round to the next. The oblivious robot model is hence attractive from a self-stabilization perspective, where state is subject to adversarial manipulation. However, to the best of our knowledge, all existing robot convergence protocols rely on the assumption that robots, despite being "weak", can measure distances. We in this paper initiate the study of convergence protocols for even simpler robots, called monoculus robots: robots which cannot measure distances. In particular, we introduce two natural models which relax the assumptions on the robots' cognitive capabilities: (1) a Locality Detection (L D) model in which a robot can only detect whether another robot is closer than a given constant distance or not, (2) an Orthogonal Line Agreement (O L A ) model in which robots only agree on a pair of orthogonal lines (say North-South and West-East, but without knowing which is which). The problem turns out to be non-trivial, and simple median and angle bisection strategies can easily increase the distances among robots (e.g., the area of the enclosing convex hull) over time. Our main contribution are deterministic self-stabilizing convergence algorithms for these two models, together with a complexity analysis. We also show that in some sense, the assumptions made in our models are minimal: by relaxing the assumptions on the monoculus robots further, we run into impossibility results.

This paper considers the area convergence problem, which requires a group of robots to gather in a small area not defined a priori. While it is known that robots can gather at a point if they can precisely measure distances, we, in this paper, show that without any agreement on the coordinate system, it is impossible for robots to converge to an area if they cannot measure distances or angles. We denote these robots without the ability to measure distances or angles as monoculus robots. We present a counterexample showing that monoculus robots fail in area convergence even with the capability of measuring angles. However, monoculus robots with a weak notion of distance or minimal agreement on the coordinate system are sufficient to achieve area convergence. In particular, we present area convergence algorithms in asynchronous model for such monoculus robots with one of the two following simple additional capabilities: (1) locality detection ($\mathcal{L}\mathcal{D}$), a notion of distance or (2) orthogonal line agreement ($\mathcal{O}\mathcal{L}\mathcal{A}$), a notion of direction. We discuss extensions corresponding to multiple dimensions and the termination. Additionally, we validate our findings using simulation and show the robustness of our algorithms in the presence of errors in observation or movement.