Optimization, Stability Analysis, and Trajectory Tracking of Perching Maneuvers

Abstract

This paper presents optimization of conventional fixed-wing aircraft perching, stability analysis of optimal perching maneuvers, and tracking formulation of the perching trajectory. Perching maneuvers are optimized to minimize undershoot or altitude gain during the climbing phase, where gravity is used to decelerate the aircraft. A single-phase formulation minimizing the trajectory length of the maneuver is proposed to simplify the optimization formulation and solution procedure. Compared with the existing two-phase approach, where the maneuver is optimized separately in its dive and climb phases, this single-phase formulation is shown to provide lower undershoot perching solutions. Stability analysis of the optimal perching trajectories is performed using contraction theory. It is shown that the perching solutions are in general unstable and will diverge during the terminal phase in the presence of state perturbations. To address this instability and avoid deviation from the desired landing point, a trajectory tracking problem is formulated. A controller based on a sliding-mode technique is proposed with optimal perching solutions as the reference trajectories. Sliding functions used to track the optimal trajectory with respect to spatial location from the landing point are formulated and a stable control law is derived. The resulting controller is validated by simulating the perching maneuver under perturbed initial conditions.