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.
@cite_8 extended this result to active target tracking with a single robot. A major contribution was to show that robot trajectories that are nearby in space can be pruned away (under certain conditions), leading to further computational savings. This was based on a linear system assumption. In this paper, we build on these works and make progress towards generalizing the solution for state-dependent observation systems.
@cite_8
1982284258
This paper presents a general approach for the simultaneous tracking of multiple moving targets using a generic active stereo setup. The problem is formulated on the plane, where cameras are modeled as “line scan cameras,” and targets are described as points with unconstrained motion. We propose to control the active system parameters in such a manner that the images of the targets in the two views are related by a homography. This homography is specified during the design stage and, thus, can be used to implicitly encode the desired tracking behavior. Such formulation leads to an elegant geometric framework that enables a systematic and thorough analysis of the problem at hand. The benefits of the approach are illustrated by applying the framework to two distinct stereo configurations. In the first case, we assume two pan-tilt-zoom cameras, with rotation and zoom control, which are arbitrarily placed in the working environment. It is proved that such a stereo setup can track up to N = 3 free-moving targets, while assuring that the image location of each target is the same for both views. The second example considers a robot head with neck pan motion and independent eye rotation. For this case, it is shown that it is not possible to track more than N = 2 targets because of the lack of zoom. The theoretical framework is used to derive the control equations, and the implementation of the tracking behavior is described in detail. The correctness of the results is confirmed through simulations and real tracking experiments.