Topologically distinct trajectory predictions for probabilistic pursuit

We address the integrated planning and control problem that enables a single follower robot (the ``photographer'') to maintain a moving target (the ``subject'') in its field of view for as long as possible. We propose a real-time pursuit algorithm that seamlessly handles the often neglected, yet unavoidable, scenario in which the target escapes the follower's field of view; a scenario that simple, reactive controllers are ill-equipped to handle. Our algorithm aims to minimize the expected time until visual contact is re-established, which enables the photographer to track the subject for as long as possible, even in the presence of loss of visibility. At the core of our pursuit algorithm is an efficient method for sampling plausible trajectories from different homotopy classes. We do this by generating topologically distinct shortest paths by using the Voronoi diagram. We use these paths to make informed, model-based predictions of the likely future locations of the target, given a history of observations. Given these predictions, our algorithm produces pursuit trajectories that approximately minimize the expected time to recover visual contact. We show that constraining the predictive pursuit problem to the space of homotopy classes condenses the expanse of possibilities that our algorithm must consider, which enables target tracking in large occupancy grids, as opposed to many POMDP methods that are constrained to small environments. We benchmark the tracking behavior of our algorithm against the baseline of human subjects who performed the same set of pursuit tasks in simulation, as well as against two other pursuit algorithms that only take into account paths from a single homotopy class. We show that considering homotopy alternatives in 2D pursuit improves the tracking performance and that our algorithm does at least as well as humans in most pursuit scenarios.