NEAR-OPTIMAL HORIZONTAL TRAJECTORIES FOR AUTONOMOUS AIR VEHICLES

Minimum-time trajectories of unmanned aircraft in a horizontal plane a re studied. The boundary conditions comprise initial and final locatio ns and heading angles. The system model assumes instantaneously changi ng velocity. We view this model as a generalization of the constant-ve locity model. As the study of that model has shwon, the favorable traj ectories that meet these boundary conditions, which have an analytical solution and comply with the minimum principle (MP), are of a hang-le vel-bang type. Thus, we adopt such trajectories to the current problem and investigate their compliance with the MP. The interesting result of this study is that such trajectories do not satisfy the necessary c onditions of the MP inherently (as was the case in the constant veloci ty model), but under restrictive conditions, which are derived and ana lyzed. Analytic solutions are given together with some examples of the trajectories obtained. A numerical example of an optimal trajectory ( with no restrictions on the number of switching points) is examined wi th regard to the general conditions for compliance with the MP.