Non-Myopic Target Tracking Strategies for State-Dependent Noise

TL;DR

This paper develops a non-myopic, closed-loop control strategy for robot target tracking that accounts for state-dependent measurement noise, optimizing the sequence of actions to reduce uncertainty more effectively than greedy methods.

Contribution

It introduces a novel control policy planning approach that considers multiple future steps and exploits Kalman Filter properties to reduce computational complexity while maintaining optimality guarantees.

Findings

Policy tree significantly reduces computation compared to naive enumeration.

The approach effectively minimizes maximum uncertainty in simulations.

Relaxed guarantees further improve computational efficiency.

Abstract

We study the problem of devising a closed-loop strategy to control the position of a robot that is tracking a possibly moving target. The robot is capable of obtaining noisy measurements of the target's position. The key idea in active target tracking is to choose control laws that drive the robot to measurement locations that will reduce the uncertainty in the target's position. The challenge is that measurement uncertainty often is a function of the (unknown) relative positions of the target and the robot. Consequently, a closed-loop control policy is desired which can map the current estimate of the target's position to an optimal control law for the robot. Our main contribution is to devise a closed-loop control policy for target tracking that plans for a sequence of control actions, instead of acting greedily. We consider scenarios where the noise in measurement is a function of the state of the target. We seek to minimize the maximum uncertainty (trace of the posterior covariance matrix) over all possible measurements. We exploit the structural properties of a Kalman Filter to build a policy tree that is orders of magnitude smaller than naive enumeration while still preserving optimality guarantees. We show how to obtain even more computational savings by relaxing the optimality guarantees. The resulting algorithms are evaluated through simulations.