Flight Trajectory Optimization Based On Path-shaping And Multi-resolution Mesh Refinement

Flight trajectory optimization is a high-dimensional optimal control problem with characteristics of multi-constraint and nonlinearity. When it was solved numerically, those characteristics always result in the “curse of dimensionality”, which leads to a formidable amount of computation and unreliable solutions. Regard this as cutting point, this dissertation studies subjects of the mesh refinement techniques and trajectory optimization methods based on trajectory-shaping. The proposed methods are used to solve the trajectory optimization problems for the missiles and aircrafts, and design the multi-event noise abatement route for major hub airports in this paper. The main results achieved in this dissertation are summarized as follows:Two multi-resolution mesh refinement techniques in trajectory optimization are presented. In the Lasso-based mesh adaptive refinement approach, higher resolution nodes and associated radial basis function set are created firstly. Sequentially, the control variables are approximated using the resulting radial basis function set. Finally, the coefficients of the formulated approximation function are estimated based on statistical variable selection method-Lasso. The higher resolution nodes associated with radial basis functions with non-zero coefficient are selected as new nodes. In the energy-based mesh refinement approach, the energy of nodes in the discrete optimal control curve is calculated, and nodes with relatively high energy as well as their associated support region are determined firstly. Sequentially, a higher resolution mesh is created and the new nodes located within given support regions are selected. The stability and generality of the formulated trajectory optimization algorithm is demonstrated by several typical examples.A dimensionality reduction-optimization strategy based on trajectory-shaping is presented. According to the boundary conditions, the unknown trajectory is shaped using the B-spline with limited shape variables. Concepts of inverse dynamic and parametric transform are introduced to reduce the original problem to a lower dimensional optimal control problem. It is resulted that lower dimensional problem tends to have a better solution when it is solved by direct optimization method numerically. The validation of the proposed method over conventional direct optimization method is demonstrated by the simulation results.The intelligent optimization algorithms can be used to search the global optimal trajectories in trajectory optimization problems, but its convergence and optimality is influenced by the numbers of optimization variables. In view of this, a novel spatial trajectory shaping and optimization strategy based on rational Bezier curves is proposed. According to the boundary conditions, the unknown spatial trajectory is shaped using the rational Bezier curves with limited shaping variables. And the flight-path angle, the heading angle as well as their rate, the normal acceleration and the performance index are determined by the inverse dynamic technique and dynamic equations of missile. Consequently, the optimal spatial trajectory can be obtained through optimizing the shaping variables. In order to handle the constraints, the continuous trajectory is discretized into a series of data-points and a penalty function is formulated using the value of constraints violation at the data-points. A data-points selection strategy based on the value of constraints violation is introduced to improve the calculation efficiency and guarantee the feasibility of the optimized trajectory. Finally, the original constrained parametric optimization formulation is transformed to an unconstrained one and subsequently solved by the genetic algorithm and pattern search method. The resulting optimal trajectory is perfectly smooth and flyable. The validity and practicality of the proposed method are demonstrated by comparison simulation.The trajectory-shaping method is used to design the multi-event noise abatement route for major hub airports. The routes of aircraft-streams are modeled by rational Bezier curves, and the optimal routes are obtained by optimizing shaping variables under the index of minimal noise influence and flying range. The proposed method not only can be used to optimize single route in isolation, but also be suitable to multiple routes optimized simultaneously. When it was used in optimizing multiple routes simultaneously, the calculation efficiency and optimality of the solutions will be improved dramatically. In order to calculate the noise and handle the constraints, the continuous routes are discretized into a series of data points and approximated by piecewise linear curves. A data-points selection strategy is introduced to improve the calculation accuracy and guarantee the feasibility of the optimized routes. The original constrained parameter optimization problem is finally transformed to an unconstrained one and subsequently solved by the genetic algorithm and pattern search methods. The feasibility of the proposed method is demonstrated in the design of the route for Airport Schiphol in the Netherland.