Maximum Information Bounds for Planning Active Sensing Trajectories

This paper considers the problem of planning trajectories for robots equipped with sensors whose task is to track an evolving target process in the world. We focus on processes which can be represented by a Gaussian random variable, which is known to reduce the general stochastic information acquisition problem to a deterministic problem, which is much simpler to solve. Previous work on solving the resulting deterministic problem focuses on computing a search tree by Forward Value Iteration and pruning uninformative nodes early on in the search via a domination criteria. In this work we formulate the Active Information Acquisition problem as a deterministic planning problem where algorithms like Dijkstra and A* can produce optimal solutions. To use A* effectively in long planning horizons we derive a consistent and admissible heuristic as a function of the sensor model which can be used in information acquisition tasks such as actively mapping static and moving targets in an environment with obstacles. We validate the results in several simulations indicating that the resulting heuristic informed algorithm can recover optimal solutions faster than existing search-based methods.