# Cooperative Standoff Tracking of Moving Targets Using Modified Lyapunov Vector Field Guidance
## 1 Introduction  
Fixed-wing unmanned aerial vehicles (UAVs) have been widely used in area surveillance, convoy protection, coordinate combat, and forest firefighting. One of the main applications is cooperative standoff \"targets\" tracking, usually a vehicle on the ground, static or moving. To render the problem feasible, there is a need to divide it into three subproblems. The first subproblem is to generate the optimal flyable path for a single UAV where UAVs should follow in order to achieve stable standoff tracking of static targets. In the standoff tracking approach, UAVs should stably keep an appropriate distance from the target. The next component is concerned with standoff tracking of moving targets, mainly the states (location and velocity) estimation of the target, which could help modify the guidance law for a moving target. However, it is usually ignored in many researches. The last subproblem is the coordination of a team of UAVs, mainly keeping a fixed intervehicle phase. The three subproblems are interrelated and they should be solved simultaneously. Tremendous research efforts have been made in order to generate the optimal path for a single UAV. The guidance laws are usually based on several approaches: Helmsman behavior control [1], model prediction control [2, 3], reference point control [4, 5], and vector field guidance. As a classic guidance law, Lyapunov vector field guidance (LVFG) has been improved up to now. It is in a decoupled structure in which the rate of heading and speed change are separately controlled for standoff distance and phase angle keeping. [PERSON] et al. [6] introduced the Lyapunov vector field into the loitering algorithm for standoff tracking. [PERSON] et al. [7] extended single UAV tracking to cooperative tracking. To shortenthe convergence time, [PERSON] et al. [8] combined the tangent with the Lyapunov vector field guidance and [PERSON] et al. [9] used the tangent vector field in conjunction with the sliding mode control that is modified by introducing additional adaptive terms. Besides integrating control methods into vector field, [PERSON] et al. [10] added a new non-dimensional parameter \(c\) into original algorithm, adjusting the convergence time to standoff circle by changing \(c\) and in this way, arrival position and time are controlled. Aiming to limit the UAV turn rate within the capability imposed by the angle limits, [PERSON] et al. [11] transformed \(c\) to a simple function of \(R\), orbit radius. [PERSON] et al. [12] analyzed the criteria guidance term \(c\) should fulfill, proposed a series of guidance functions satisfying the conditions, and an offline parameter search algorithm was designed for selecting the optimal function, while flexibility is limited. The methods mentioned above mainly concern themselves with converging to the standoff distance at the highest speed and keeping it steady, but they cannot address the fast convergence and stable tracking simultaneously. When tracking a ground moving target, the UAVs need to modify the guidance laws using the state of the target. The access to the location and velocity of the target is of vital importance to standoff tracking. In the past research of guidance laws in standoff tracking, some researchers [5; 7; 13; 14] simplify the problem by assuming that the state of the target is available. They assumed that the state of the target can be obtained via direct communication with a cooperative ground vehicle, or continuous data for the target state are used in experiments. It is obviously not realistic when tracking an uncooperative target. Other researchers take tighter experimental conditions into consideration. In [PERSON]'s research [2], the state-vector fusion based on the extend Kalman filter (EKF) was utilized to estimate the state of the moving target for two UAVs. [PERSON] et al. [15] took unknown wind and target motions into one variable and proposed an adaptive estimator for a more accurate estimation of the unknown factor.