An improved technique for matching the asymptotic solutions of non-linear differential equations is presented and successfully applied to the three-dimensional atmospheric skip trajectories. The classical method of matched asymptotic expansions (MAE) is generally applied to two-point-boundary value problems. When we apply the MAE method to initial value problems, due to error propagation, the resulting accuracy usually depends on the physical problems. In the proposed technique, the second-order solutions are obtained by first generating a set of equations for the small perturbations which are the discrepancies between the uniformly valid first-order solutions and the exact solutions. Then, the equations of the small perturbations are integrated separately near the outer and inner boundaries to obtain the perturbed outer and inner expansion solutions, respectively, for a secondorder matching. In addition, in this improved technique the end-point boundaries are artificially extended or constructed to strengthen the physical assumptions on the outer and inner expansions for the matching while in the evaluation of the constants of integration in the uniformly valid first-order solutions, the prescribed end-points are effectively enforced. In this paper, to show the applicability of the improved technique, we first apply it to the rectilinear restricted three-body problem. We men consider the threedimensional skip trajectory. Compared to the solutions obtained by numerical integration over a wide range of entry conditions, the second-order solutions obtained by this improved technique are very accurate. The trajectory elements at the lowest altitude and at exit as well as their accuracy are evaluated.

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In this paper, we propose a sliding-mode controller for a mini unmanned aerial vehicle (UAV) with propellers to follow the predetermined attitude trajectory. First the vehicle attitude dynamic model is established for angular displacements and for angular velocities, respectively. Next a sliding-mode controller with a switching surface is designed to eliminate uncertainties and disturbances. Then the attitude tracking control of a mini-UAV using the proposed control strategy is illustrated while flight. Finally, we employ the Lyapunov stability theory to fulfill the stability analysis of the proposed controller for the overall nonlinear control system. Extensive simulation results are gained to validate the effectiveness of the proposed sliding-mode controller.

This paper describes the dynamic modeling and analysis of a fixed-wing micro air vehicle (MAV). A nonlinear model for the MAV motion with six degrees of freedom is formulated first. Next, an extended version of the linear-time-invariant model for the MAV is derived by applying small perturbation theory and linearizing around an equilibrium flight condition. This ad hoc extended model for the MAV retains more terms that are generally neglected in mathematic models of conventional airplanes. To explore the stability and control characteristics, the aerodynamic derivatives required by dynamic modeling are evaluated using low-Reynolds-number wind tunnel testing data and some theoretical/empirical formulas. A fixed-wing MAV with a 15-cm wingspan successfully flown in 2002 is used as a baseline prototype for dynamic modeling and analysis. The longitudinal and lateral dynamic responses of the MAV under various conditions are demonstrated. The performance of the present extended MAV model is investigated by comparing the flight dynamics for different models. The simulation results show that the proposed extended model is consistent with the nonlinear dynamics model for a wider range of flight conditions. The present analysis may aid a better understanding of flight characteristics as well as design and analysis of MAV systems.

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