This letter proposes a distributed strategy to achieve both persistent monitoring and target detection in a rectangular and obstacle-free environment. Each robot has to repeatedly follow a smooth trajectory and avoid collisions with other robots. To achieve this goal, we rely on the time-inverted Kuramoto dynamics and the use of Lissajous curves. We analyze the resiliency of the system to perturbations or temporary failures, and we validate our approach through both simulations and experiments on real robotic platforms. In the letter, we adopt Model Predictive Contouring Control as a low level controller to minimize the tracking error while accounting for the robots' dynamical constraints and the control inputs saturation. The results obtained in the experiments are in accordance with the simulations.

Different authors have addressed a number of problems in the area of distributed control proposing convincing solutions to specific problems such as static coverage, dynamic coverage/exploration, rendezvous, flocking, formation control. However, a major limitation of problem-specific approaches is a fundamental lack of flexibility when the group meets unexpected conditions and has to change its goal on the fly. In this paper, we show that a large class of distributed control problems can be cast into a general framework based on the adoption of the Lloyd methodology. The adoption of a unified framework enables efficient solutions for the specific problems guaranteeing at the same time important safety and functional properties and a large degree of flexibility in the execution of group tasks. The paper sets the theoretical basis for this development and proves the efficacy of the proposed solutions through extensive simulations and experimental results.