Extremal Control and Modified Explicit Guidance for Autonomous Unmanned Aerial Vehicles

This study aims to develop and integrate guidance and control functions for applications. The utility of integrated nonlinear optimal control and explicit guidance functions replaces linear PID control laws. This approach leverages UAV flight autonomy, thereby paving the way for creating an autonomous control technology with real-time target-relative guidance and re-targeting capabilities. A 360° roll maneuver combines extremal control and modified explicit guidance. The roll maneuver accurately reaches the desired position and velocity vectors through the proposed integration. Satisfying the first-order necessary optimality conditions demonstrates that the roll maneuver has extremal trajectories. To the best of the authors' knowledge, this is the first time analyzing and testing the Weierstrass condition and the first and second-order conditions of optimality for UAVs. Second-order conditions show that the 360° roll maneuver with explicit rotational attitude guidance does not have an optimal trajectory and yields an extremal trajectory.