Trajectory Optimization For Powered Landing Of Vertical Takeoff And Vertical Landing Launch Vehicles

Reducing the cost of aerospace launch is one of the major challenges faced by the aerospace industry.Reusing launch vehicles is an important way to reduce launch costs.In recent years,the first stage of vertical takeoff and vertical landing(VTVL)launch vehicle produced by SpaceX,a private US aerospace company,has been successfully recovered and reused.VTVL is proven to be a feasible technology for rocket recovery.Trajectory design,navigation,guidance,and control are among the critical aspects of VTVL recovery.Traj ectory optimization is one of the key methods of trajectory design,navigation,guidance,and control technology.Focusing on the powered landing process of VTVL launch vehicles,this study conducts a series of investigations on trajectory optimization with complex constraints,convergence and real-time problems of trajectory optimization.A trajectory optimization technical framework based on overall expression,simultaneous solving,and online computation is established.The content of this study can be divided into two parts:trajectory design and computational guidance.The main contributions are as follows:1.Simultaneous computing framework for optimal trajectory design of VTVL launch vehicles with complex constraints.This framework employs simultaneous approaches to fully discretize formulated optimal trajectory design problems.The simultaneous approach is based on orthogonal collocation on finite elements(OCFE).The primal-dual interior point method is used to solve the nonlinear programming(NLP)problem obtained by the simultaneous approach.The three-degree-of-freedom optimal trajectory design problem for the entire flight process of a VTVL launch vehicle is solved using the simultaneous computing framework.Additionally,a heuristic initialization strategy is designed to enhance the convergence of solving the trajectory optimization problem.The six-degree-of-freedom optimal trajectory design problem for the powered landing of a VTVL launch vehicle is also solved using the simultaneous computing framework.Moreover,an adaptive mesh refinement algorithm based on discretization error estimation of non-collocation points and a Hamiltonian is proposed to further improve the accuracy and optimality of the solution to the trajectory optimization problem.The algorithm can accurately catch breakpoints of the thrust magnitude.2.Receding-horizon trajectory optimization based computational guidance framework for the powered landing of VTVL launch vehicles.This framework is proposed to overcome a series of uncertainties in the powered landing process.First,a basic receding-horizon trajectory optimization based computational guidance framework considering computational delay is established.To reduce the effect of the computational delay of trajectory optimization,a predictor-corrector algorithm based on NLP sensitivity is presented.In the predictor algorithm,the real state of the VTVL launch vehicle at the current sampling time is utilized to predict its state at next sampling time.The optimal trajectory from the predicted state at the next sampling time to a specified landing site is computed in the current sampling period.In the corrector algorithm,the trajectory from the real state of the VTVL launch vehicle at the current sampling time to the specified landing site can be generated by online correcting the optimal trajectory from the predicted state at the current sampling time to the specified landing site based on NLP sensitivity.Simulation experiments demonstrate the effectiveness of the proposed predictor-corrector receding-horizon trajectory optimization based computational guidance framework.3.Fast trajectory optimization for the powered landing of VTVL launch vehicles.The basic receding-horizon trajectory optimization based computational guidance framework and predictor-corrector receding-horizon trajectory optimization based computational guidance framework both need to complete trajectory optimization during the sampling period.The simulation results illustrate that shortening the sampling period can improve guidance performance,which presents the real-time requirements for solving the trajectory optimization problem.Thus,the fast trajectory optimization algorithm associated with simultaneous approaches and convexification methods for the powered landing is proposed in this study.Lossless convexification is applied to the non-convex thrust constraints.Then,the OCFE based simultaneous approach and successive convexification algorithm are utilized to transform solving the original trajectory optimization problem into solving a sequence of second order cone programming problems.Virtual control and trust region strategies are introduced to enhance the convergence of successive convexification.Furthermore,an initialization strategy is designed for the successive convexification algorithm.The algorithm fully employs the theoretical basis of the high discretization accuracy and good numerical stability of the simultaneous approach as well as the fast solving and definite convergence of convex optimization problems.4.Extension of powered landing trajectory optimization methods in deep space exploration.The simultaneous computing framework is used to solve the optimal trajectory design problem of VTVL maneuvers on the moon.A homotopy based backtracking strategy is designed to enhance the convergence of solving the trajectory optimization problem.Moreover,the proposed adaptive mesh refinement algorithm is used to improve the accuracy and optimality of the solution and accurately catch breakpoints of the thrust magnitude.An NLP sensitivity and modified K-means clustering method based online trajectory optimization algorithm for multi-point powered landing is proposed to address the online trajectory optimization problem for multi-point powered landing on Mars.In the proposed algorithm,the NLP sensitivity is considered in estimating the fuel consumption of the probe as it moves toward each candidate landing site,and the modified K-means clustering method is applied to cluster the candidate landing sites and improve the estimation accuracy of fuel consumption.An optimal trajectory to the selected landing site can be quickly generated based on an estimated trajectory after the best landing site has been selected.