Trajectory Optimization for Target Localization Using Small Unmanned Aerial Vehicles

Abstract

Small unmanned aerial vehicles (UAVs) equipped with navigation and video capabilities can be used to perform target localization. Combining UAV state estimates with image data leads to bearing measurements of the target that can be processed to determine its position. This 3-D bearings-only estimation problem is nonlinear and traditional filtering methods are prone to biases, noisy estimates, and filter instabilities. The performance of the target localization is highly dependent on the vehicle trajectory, motivating the development of optimal UAV trajectories. This work presents methods for designing trajectories that increase the amount of information provided by the measurements and shows that these trajectories lead to enhanced estimation performance.The Fisher Information Matrix (FIM) is used to quantify the information provided by the measurements. Several objective functions based on the FIM are considered and the A-optimality criterion is shown to be the best suited for trajectory optimization in the 3-D bearings-only target localization problem. The resulting trajectories produce spirals, which increase the angular separation between measurements and reduce the range to the target, supporting geometric intuition. The problem of simultaneous target estimation and vehicle trajectory optimization is explored and the resulting algorithms produce vehicle trajectories that increase the information provided by the measurements, enhancing the target estimation performance by increasing accuracy, reducing uncertainty and improving filter convergence.

Vision-based target tracking with a small UAV: Optimization-based control strategies

“…Ponda et al consider the problem of optimizing trajectories for a single UAV equipped with a bearings-only sensor to estimate and track both fixed and moving targets [14]. By performing a constrained optimization that minimizes the trace of the Cramer-Rao Lower Bound at each discrete time step, they show that the UAV tends to spiral towards the target in order to increase the angular separation between measurements while simultaneously reducing its distance to the target.…”

“…While the existing literature offers methods for target tracking using continuous-time feedback control laws [6][7][8][9][10][11][12] or optimization based methods [13][14][15], these individual works make assumptions that simplify the UAV dynamics, target motion, and/or sensor visibility constraints, thereby hindering the feasibility of a real world implementation with actual hardware. This paper has detailed the design of two optimization-based control policies for vision-based target tracking, where strict trajectories must be flown by an underactuated UAV to maintain visibility and proximity to an unpredictable ground target.…”

Aircraft trajectory tracking with large sideslip angles for sense and avoid intruder state estimation

“…However, their application needs persistent excitation of the filter which estimates the intruder distance and flying direction (see [2] for example). Several other sources point out that lateral acceleration of the observer is required to provide intruder observability ( [3], [4], [5]). …”

Performance comparison of SISO and MIMO low level controllers in a special trajectory tracking application

“…This needs persistent excitation of the estimator (see [1] for example). Several other sources point out that lateral acceleration of the observer is required to provide intruder observability ( [2], [3], [4]). …”