In this paper a UAV guidance law for tracking circular paths based on proportional navigation is developed. It is shown that when gradient information is available, the UAV can perform a gradient descent search operation in a given area of interest by suitably selecting its heading direction. The guidance law is further extended to cooperating multiple UAVs. Using repulsive potential functions, it is shown that the UAVs can locate multiple maxima/minima in the search region. A complete Lyapunov stability analysis of the guidance law in the horizontal plane is performed to prove asymptotic stability for all initial conditions. Numerical simulations are presented to show the circular path tracking and gradient search capability of the guidance law.
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