Optimization, Stability Analysis and Trajectory Tracking of Fixed-Wing Aircraft Perching Maneuvers

Abstract

This paper presents aircraft perching as an optimization problem, analyzes the stability of optimal perching maneuvers, and formulates the problem into a trajectory tracking problem. Aircraft perching problem is formulated into a trajectory optimization problem to reduce the spatial bounds of the maneuver. By choosing level-flight trim state as initial condition and near-zero velocity state as final velocity, trajectory length is defined as cost function to be minimized, and perching trajectories are generated. Contraction theory, which can analyze stability around non-equilibrium points, is used to carry out the stability analysis of optimal perching trajectories. By selecting an identity matrix for positive-definite transformation matrix, generalized Jacobian and the corresponding eigenvalues are computed along the optimal perching trajectory. It is found that the trajectories are not stable and result in divergence in case of state perturbations. To address the divergence issues and avoid deviation from the desired landing point, the aircraft perching problem is formulated into a trajectory tracking problem. Sliding mode control technique is used to design the controller and optimal perching trajectories are chosen as reference trajectories to be tracked. Sliding functions to track the optimal trajectory with respect to spatial location from the landing point are formulated and a control law is derived. The controller design is validated by perturbing the initial conditions and performing simulations. Successful tracking results are obtained, justifying the selection of sliding functions and derivation of control law.