Performance and Lyapunov Stability of a Nonlinear Path Following Guidance Method

TLDR: In this paper, the adaptive nature of the guidance method makes its stability independent of vehicle velocity, and the stability analysis is also extended to show robust stability in the presence of saturated lateral acceleration, which is an inherent limitation of flight vehicles.

Abstract: Performance and stability are demonstrated for a nonlinear path-following guidance method for unmanned air vehicles. The method was adapted from a pure pursuit-based path following, which has been widely used in ground based robot applications. The method is known to approximate a proportional-derivative controller when following a straight line path, but it is shown that there is also an element of anticipatory control that enables tight tracking when following curved paths. Ground speed is incorporated into the computation of commanded lateral acceleration, which adds an adaptive capability to accommodate vehicle speed changes due to external disturbances such as wind. Asymptotic Lyapunov stability of the nonlinear guidance method is demonstrated when the unmanned air vehicle is following circular paths. The adaptive nature of the guidance method makes its stability independent of vehicle velocity. The stability analysis is also extended to show robust stability of the guidance law in the presence of saturated lateral acceleration, which is an inherent limitation of flight vehicles. Flight tests of the algorithm, using two small unmanned air vehicles, showed that each aircraft was controlled to within 1.6 m root mean square when following circular paths. The method was used to perform a rendezvous of the two aircraft, bringing them into very close proximity, within 12 m of along track separation and 1.4 m root mean square relative position errors.