Collaborative Evacuation of Mobile Robots

Distributed evacuation of mobile robots has recently raised the interest of researchers. Czyzowicz et al. [1] introduced the evacuation problem minimizing the time required for the last searcher to reach the target. They showed the optimal evacuation time for two robots in the wireless model while achieved an upper and lower bound for two robots in the face-to-face model. This has been further improved in subsequent papers. The objective is to plan the path of robots such that the worst-case evacuation time can be minimized. In a variation with faulty robots not able to detect the exit, Czyzowicz et al. [2] focused on minimizing the evacuation time for the latest non-faulty robot. They presented a lower and upper bound for three robots where at most one is susceptible to crash fault with wireless communication. Please refer [3] for detailed related works. Model and Problems. The two robots, initially located at the center of a unit disk, have to evacuate the disk through the two exits situated on the perimeter of the disk at unknown locations. The distance d between the two exits along the perimeter is given. The robots communicate either in the wireless model (sending messages over a long distance) or the face-to-face model (exchange of information is possible by meeting). The objective is to minimize the worst-case evacuation time in both the wireless and face-to-face communication model for two robots with two exits (labeled or unlabeled). The second problem considers a robot can become faulty at any point of time during evacuation. Instead of abandoning the crashed robot, the non-faulty robot chauffeurs it to the exit. It takes α ≥ 1 amount of time to chauffeur for unit distance. The objective is to minimize the worst-case evacuation time even in the presence of one faulty robot with a single exit on the disk. Results. Given two exits located on the perimeter of a unit disk, there are two variations considered. An exit can be labeled or unlabeled. A robot at a labeled exit can exactly determine the location of the other exit, while a robot at an unlabeled exit, can only determine two potential locations for the other exit at a distance d along the perimeter. We propose an algorithm where the robots move towards the perimeter of the disk starting from the center at an angle ζ < d with each other. Both robots move in the opposite direction, i.e., one moves clockwise and the other moves counter-clockwise along the perimeter. Once a robot finds an exit, it sends a message and evacuates. The other robot determines the location of exit by arrival time of the message as it knows the path of the other robot. We analyze the worst-case time with respect to ζ [4]. In the face-to-face model, the robots exchange information by meeting. In this case, we consider the robots starting with an initial angle of ζ = d to reach the perimeter and search in opposite directions. Note that, meeting of the robots depends on the time (distance traveled) at which one finds the exit. We use the linear detour strategy for the path of robots and also determine the length of detours. Additionally, we present lower bounds for evacuation by discretizing the locations of exits based on the value of d [5]. In the chauffeuring model, we consider at most one robot is faulty, and carrying the crashed robot increases the time required by a factor of α. The non-faulty robot determines the crashed robot's position from message exchange. Both robots follow a predetermined path unless they find an exit or get crashed. We present lower bounds based on the time a robot crashes. A trivial strategy is to move both robots together, and after one crashes, the other searches the exit while chauffeuring. We present two algorithms, where the robots move in the same direction (say, clockwise) starting at an angle ζ or in opposite directions starting from the same point on the perimeter. More details are in [3]. A generalization with more robots can be considered with multiple faulty robots.