An algorithm of decentralized encircling coverage and termination of a moving deformable region by mobile robotic sensor/actuator networks

The paper introduces the problems of encircling coverage and termination of a moving a deformable planar region by a mobile sensor/actuator network. We propose a decentralized randomized algorithm for self-deployment of a network of mobile robotic sensors/actuators for these problems. In the encircling coverage problem, the aim is to deploy sensors around a bounded connected region so that any point of a certain neighbourhood of the region is sensed by at least one mobile robotic sensor. In the termination problem, the aim is to terminate a moving region that may represent an oil spill or a hazardous chemical field. In this case, the moving robots are equipped with not only sensors but with actuators releasing neutralizing chemical so that the shape of the polluted region is controlled. The proposed algorithm is based only on information about the closest neighbours of each sensor. The moving region is of an arbitrary shape and not known to the sensors a priori. We give mathematically rigorous proofs of asymptotic optimality and convergence with probability 1 of the proposed randomized algorithm.