Research On Trajectory Planning Method Based On Convex Optimization For Hypersonic Glide Vehicle

Trajectory planning online is one of the key basic technologies for the future development of hypersonic glide vehicle guidance methods.Convex optimization provides a feasible technique for trajectory planning online because of its good theoretical properties and high solving efficiency.As for the hypersonic glide vehicle trajectory planning problem in glide phase,the trajectory planning method based on convex optimization is studied,focusing on the poor convergence of sequential convex programming method,the commands discontinuity if control variable is expanded,the contradiction between precision and efficiency for uniform mesh discretization,and the low solution efficiency of robust trajectory planning.The main research work of this dissertation is given as follows:1)The sequential convex programming method based on the adaptive trust-region constraint is proposed.Firstly,the entry trajectory planning model with the energy as independent variable and the bank angle as original control is built.The convexification method for the original problem is studied,by which the new control variables are defined and the additional two-dimensional control constraint is proved to be the lossless convexification theoretically.Secondly,an adaptive trust-region constraint is proposed for handling the poor convergence of the sequential convex programming method.Compared with the fixed trust-region constraint,the trust-region radius can be adjusted in the proposed adaptive trust-region constraint according to the change of the performance index.Using the adaptive trust-region constraint,the search space of convex subproblems is reduced gradually,which can ensure the convergence of the sequential convex programming method in solving highly nonlinear optimal control problems;Finally,the convergence of the sequential convex programming method is discussed theoretically.The simulation analysis shows that the proposed method effectively improves the convergence of the sequential convex programming method to solve entry trajectory planning problem,and its converged solution is feasible for the original problem.2)The sequential convex programming method for trajectory planning problem with two control variables is studied.Firstly,the new control variables are defined,and the relationship between the new control variables and the original control variables(i.e.,the angle of attack and the bank angle)is built.Meanwhile,the additional three-dimensional control constraint is introduced.Secondly,the entry trajectory planning model with the energy as independent variable is built.The convexification method for the original problem is studied,and the additional three-dimensional control constraint is proved to be the lossless convexification theoretically.Finally,in order to handle the discontinuity of two original commands,a new command updating method based on low-pass filtering is proposed.The simulation analysis shows that the proposed sequential convex programming method can converge to the feasible solution for the original problem.At the same time,the trajectory planning problem with two original control variables can give full play to the maneuvering ability of the hypersonic glide vehicle.3)The sequential convex programming method based on adaptive mesh update is studied.Firstly,the entry trajectory planning model with the time as independent variable and the change rate of bank angle as original control variable is built.The convexification method for the original problem is studied.Secondly,as for the contradiction between precision and efficiency for the fixed uniform mesh discretization,an adaptive mesh update method based on nonlinear error is proposed.The quantitative result of the nonlinear error at each mesh point is obtained to assess whether to add,delete or retain the mesh point.Based on the update method,the adaptive adjustment of mesh points number and distribution is achieved;Finally,a new convergence condition is defined,which can be used to measure the convergence progress of the sequential convex programming method,and reduce the iterations number while ensuring the solution precision.Compared with the sequential convex programming method based on fixed uniform mesh,the proposed method can effectively improve the computation efficiency of the original problem while ensuring the solution precision,and the computation time is reduced by 23.28%.Therefore,the proposed method balances the contradiction between precision and efficiency.4)The sequential convex programming method for entry robust trajectory planning problem is studied.Firstly,based on the generalized polynomial chaos expansion theory,the stochastic dynamic differential equations considering the uncertainty factors are transformed into the high-dimensional deterministic differential equations about the polynomial chaos expansion coefficients,and the uncertainty analysis method for the entry dynamic model is proposed.Secondly,the robust trajectory planning model considering the uncertainty factors is established,and the convexification and discretization methods for the original problem are studied.The original robust trajectory planning problem is transformed into a convex programming problem.Finally,the initialization method of polynomial chaos expansion coefficients is given,and the sequential convex programming method to solve the original robust trajectory planning problem is proposed.The simulation analysis shows that the proposed uncertainty analysis method can describe accurately the propagation properties of uncertainty factors under entry dynamic model.By robust trajectory planning,the open-loop robustness of the terminal state variables and path constraints is improved.Meanwhile,the computation time for robust trajectory planning problem is reduced by the proposed method.In this dissertation,the convex optimization theory is applied to solve the trajectory planning problem of hypersonic glide vehicle,which extends the application of convex optimization theory and explores a new solution method for highly nonlinear optimal control problem.The work of this dissertation lays the foundation for the research of trajectory planning online and guidance method of hypersonic glide vehicle,and has great theoretical significance and potential engineering application value.