This paper introduces a novel distributed algorithm for deploying multi-robot systems, consisting of mobile robots with onboard sensing and wireless communication of limited ranges, to approach the desired sensory coverage while maintaining communication connection over targeted 2D environments. A virtual potential energy is defined for each mobile robot according to the difference between the actual and desired configurations in the neighborhood of the robot, which generates the actuating force to move the robot towards the desired local coverage. The Rayleigh's dissipation function is adopted to provide the necessary damping mechanism which maintains the stability of the deployment motion for each robot. The equation of deployment motion for each mobile robot is then derived from the Hamilton's principle using the method of the variational calculus, which defines the movement of the robot to approach the desired local configuration. The formulation of the variational calculus also provides a convenience way to incorporate the nonholonomic constraint arising in wheeled robots. Since the equation of deployment motion for each robot depends on only the robot's own kinematic state and its detectable positional relationship with nearby objects, the proposed algorithm decentralizes the multi-robot deployment problem into the motion control of individual robots. Simulation results show the feasibility of the proposed approach in guiding the deployment of multi-robot systems.
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