| Vertical takeoff and vertical landing reusable rockets,which are becoming practical in recent years,are useful tools to send payloads to orbits with reduced cost and enhanced efficiency.During the development of this new type of launch vehicle,many advanced technologies have been motivated,including guidance and control methods.Meanwhile,with the development of computing equipments and technologies,online trajectory optimization technology is widely believed to be an effective approach for solving aerospace guidance problems.With the above background,this thesis studies online trajectory optimization and optimal guidance methods for reusable rockets,while the basic tool of the study is the convex optimization algorithm which enjoys superior convergence properties.The main tasks of the study are the convexification of trajectory optimization problems,and the design of optimization and guidance algorithms with superior efficiency and accuracy.The main contents of the thesis are as follows.The flight characteristics of the rocket are analyzed,and the bases of modeling the trajectory optimization problems are proposed based on the force bearing properties and the change patterns of the state profiles during the flight.Two different optimization models are built according to different application requirements.The nonconvex properties of the models are analyzed based on the convex optimization theory.The continuous optimal control problems are discretized by the pseudospectral method.For the nonconvex thrust constraint,the lossless convexification method is studied.Firstly,the slack variable is introduced to transform the nonconvex constraint into a second order cone constraint and a linear constraint.Secondly,using the high-fidelity model considering the aerodynamic forces,and based on the Pontryagin’s principle,the constraint transformation is proved to be lossless with the assumption that the state path constraints are inactive during the flight.Thirdly,when the state path constraints are set to be active,the losslessness of the transformation is analyzed by using the numerical optimality conditions and numerical experiments.The applicability of the lossless convexification method has been extended by the above study.For the nonlinear dynamics which cannot be convexified losslessly,an iterative-constant-profile convexification method is proposed.Then,a homotopic iterative convex programming algorithm is designed,which is capable of solving the rocket landing trajectory optimization problem efficiently and accurately.The algorithm starts with a losslessly convexified problem without considering the drag force.Then during the iteration,the drag profile is approximated by the last updated solution,so the system dynamics is convexified.Besides,the drag force is introduced into the problem homotopicly to guarantee the feasibility of the optimization.This algorithm is initial-trajectory-free,the convergence is fast and the solution is accurate.Thus,the algorithm has the potential to be implemented online and onboard.Aiming at convexifying the high-fidelity nonlinear dynamics and path constraints efficiently and accurately,a pesudospectal-improved successive convexification(PiSC)algorithm is designed based on the successive linearization technique.The advantages of convex optimization method and pseudospectral method are combined in this algorithm,and a novel dynamic trust-region update method is proposed to improve the convergence performance.Then,the convergence proof of the algorithm is studied.Compared with other classical successive convexification algorithms,this algorithm is superior in convergence speed,solution accuracy,and the ability of handling complex constraints.The algorithm also has the potential to be implemented online.At last,the PiSC algorithm is embedded into the model predictive control(MPC)framework to solve the optimal rocket landing guidance problem,and a parallel feasibility-guaranteed model predictive guidance(PFGMPG)algorithm is proposed.The characteristic of the algorithm is that the recursive feasibility is guaranteed by executing a relaxed and a standard PiSC algorithm in parallel.Thus,based on the advantages of convex optimization method and modern multi-core processor,the update frequency of the MPC-based guidance algorithm is increased,so the implicit closed-loop feedback is formed.Based on the proofs of recursive feasibility and guidance error boundedness,as well as the simulation results,the algorithm is verified to be capable of providing optimal and robust guidance commands to the rocket under disturbances and uncertainties.In summary,a sophisticated research is performed regarding to online trajectory optimization and optimal guidance methods for the reusable rocket landing problem.The existing methods are improved,and several new ideas are proposed.Novel and engineering promising methods are obtained through the study. |
