Lyapunov stability of track guidance algorithm for unmanned aerial vehicle

This paper presents a track guidance algorithm verified with Lyapunov stability theory. In order to minimize the track error between a pre-assigned flight path and the position of an UAV, its heading or yaw rate is guided to keep a certain distance ahead on the flight path. The proposed guidance algorithm is a spatial version of the first order dynamics for a time-dependent system. An invariant tracking performance is guaranteed in a spatial domain so that a constant flight trajectory pattern is obtained regardless of a speed of the vehicle. Crucial design parameters are a spatial constant and a gain K_p. The spatial constant determines a shape of the convergence to an assigned flight path and the gain K_p affects convergence stability of an UAV trajectory. Hence, Lyapunov stability theory and LaSalle´s invariance principle are applied to show that the guidance algorithm is asymptotically stable and to decide the available boundaries of the spatial constant and the gain K_p. Reference flight trajectories are designed based on a two-dimensional vehicle model, and the proposed algorithm is verified by numerical simulations using six degree of freedom rigid body UAV dynamics with MATLAB/Simulink Aerosim Blockset.