On-line Optimization Of Accurate Landing Trajectory Of Rocket Based On Convex Optimization

The trajectory planning of precise landing stage of the vertical recovery of rocket is a kind of optimal control problem with complex nonlinear state constraints and control constraints.This stage requires that the constraint conditions such as position accuracy,speed,etc.be met,and the attitude at the moment of landing must meet the strict constraints.Considering that the initial position,aerodynamic force and landing point of the precise landing stage of the rocket are greatly uncertain,the solution of the optimal trajectory is required to have good real-time performance.Most of the existing nonlinear planning methods cannot meet the real-time requirements.Therefore,this paper studies the trajectory optimization of the precise landing stage of the rocket based on the convex optimization method.The main research tasks are as follows:Firstly,to analyze the force of the rocket during the vertical return process,and derive the simplified equations of motion in the soft landing coordinate system;analyze the constraints during the vertical return process,determine the boundary of each constraint,and establish the mathematical description of the trajectory optimization in the precise landing stage of the rocket.Secondly,to introduce the basic theory and solution tools of convex optimization,and conduct the convex optimization on the trajectory optimization of the rocket landing stage,and transform the original multi constraint nonlinear problems into a series of convex optimization sub-problems by using lossless convex optimization,variable conversion and iterative linearization methods,respectively.Thirdly,to solve the trajectory optimization problem with the convex optimization solution tool,CVX,and design the algorithm of precise landing stage of rocket based on the idea of sequence convex optimization,obtain the optimal trajectory satisfying the constraint requirements through iterative optimization of convex optimization sub-problems,and verify the effectiveness and real-time performance of the algorithm through simulation.Finally,to further transform the convex optimization sub-problems into a quadratic programming problem,solve the trajectory optimization problem with the high-speed problem solver generated by the convex optimization solution tool CVXGEN,give the simulation results,and compare and analyze them with the results obtained through CVX,showing that the method has great advantages in terms of real-time performance.