Distributed Multi-agent Deployment for Full Visibility of 1.5D and 2.5D Polyhedral Terrains

Abstract

This paper presents deployment strategies to achieve full visibility of 1.5D and 2.5D polyhedral environments for a team of mobile robots. Agents may only communicate if they are within line-of-sight. In 1.5D polyhedral terrains we achieve this by algorithmically determining a set of locations that the robots can occupy in a distributed fashion. We characterize the time of completion of the resulting algorithm, which is dependent on the number of peaks and the initial condition. In 2.5D polyhedral terrains we achieve full visibility by asynchronously deploying groups of agents who utilize graph coloring and may start from differential initial conditions. We characterize the total number of agents needed for deployment as a function of the environment properties and allow the algorithm to activate additional agents if necessary. We provide lower and upper bounds for the time of completion as a function of the number of vertices in a planar graph representing the environment. We illustrate our results in simulation and an implementation on a multi-agent robotics platform.