A dynamic path-planning algorithm is proposed for UAV tracking. Based on tangent lines between two dynamic UAV turning and objective circles, analytical optimal path is derived with UAV operational constraints given a target position and the current UAV dynamic state. In this paper, we first illustrate that path planning for UAV tracking a ground target can be formulated as an optimal control problem consisting of a system dynamic, a set of boundary conditions, control constraints and a cost criterion. Then we derive close form solution to initiate dynamic tangent lines between UAV turning limit circle and an objective circle, which is a desired orbit pattern over a target. Basic tracking strategies are illustrated to find the optimal path for UAV tracking. Particle filter method is applied as a target is moving on a defined road network. Obstacle avoidance strategies are also addressed. With the help of computer simulations, we showed that the algorithm provides an efficient and effective tracking performance in various scenarios, including a target moving according to waypoints (time-based and/or speed-based) or a random kinematics model.
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