Optimal path planning and resource allocation for active target localization

This paper addresses optimal path planning and resource allocation for active multi-target localization. For each target, we solve a local Dynamic Program (DP) that plans optimal trajectories in the joint state-space of robot positions and target location uncertainties, captured by a cumulative error covariance matrix. The transitions in the space of robot positions are governed by the robot dynamics, while the transitions in the space of target uncertainties are regulated by a Kalman filter (KF) that fuses new information about the target locations with the current beliefs. The fused target uncertainties enter the objective function of the local DP using the trace of the associated covariance matrix. Using the optimal sensing policies local to each target, we construct a global DP to determine how far along the single target optimal trajectories the sensor should travel before transitioning to the next target. The integrated system jointly optimizes the collective target localization uncertainty and the total distance traveled by the sensing agent. The proposed control scheme is more computationally efficient than methods that use only the sensor configuration to compute future uncertainty and more exact than methods that abstract away the filtered sensing uncertainty.