Maximizing visibility in collaborative trajectory planning

In this paper we address the issue of coordinating the trajectories of two collaborating robots in environments with obstacles so that visibility between them is maximized in the presence of competing constraints. Specifically, we examine the problem of allowing one robot (the “photographer”) to follow another robot (“the subject”) through a planar environment while maintaining visual contact to the maximum degree consistent with an efficient traversal. This problem has numerous applications, for instance in scenarios where communication between robots requires line-of-sight. We formalize this problem in the context of centralized kinodynamic planning and we present solutions based on the asymptotically optimal sampling-based RRT* planner. We discuss connections to the traditional formulation of pursuit-evasion games where the analysis typically ends the moment the evader manages to escape the pursuer's visibility region. We also illustrate types of environments and other conditions under which allowing the pair of robots to break the line-of-sight is a better option than always requiring the presence of visual contact.