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Dynamic perimeter surveillance with a team of robots

In this paper, we propose a motion planning method to escort a set of agents from one place to a goal in an environment with obstacles. The agents are distributed in a finite area, with a time-varying perimeter, in which we put multiple robots to patrol around it with a desired velocity. Our proposal is composed of two parts. The first one generates a plan to move and deform the perimeter smoothly, and as a result, we obtain a twice differentiable boundary function. The second part uses the boundary function to compute a trajectory for each robot, we obtain each resultant trajectory by first solving a differential equation. After receiving the boundary function, the robots do not need to communicate among themselves until they finish their trajectories. We validate our proposal with simulations and experiments with actual robots.