Trajectory Planning And Control Method For Autonomous Asteroid Landing

In terms of the characteristics of the coupling dynamics,multiple constraints,strong non-convexity and uncertainties for the asteroid landing mission,considering the requirements for pin-point landing,autonomous control,onboard real-time calculation and robustness,this paper studies trajectory planning and control method for autonomous asteroid powered landing.The paper is organized as follows:First,by analyzing the characteristics of the asteroid landing mission and dividing the asteroid landing phases,the model of the asteroid's gravitational field and the vehicle dynamics,as well as the constraints on keeping the flight safety of the vehicle,tracking the landing site and the control ability restriction are given.Then the optimal control problem of asteroid landing trajectory planning is established with comprehensively considering the performance of fuel consumption and flight time.The Hp Pseudospectral method is used to solve the optimal control problem,and the simulation results under different cost functions and mesh refinement tolerances are given.The results show that the asteroid landing trajectory planning optimal control problem can be solved and all the constraints can be meet.The iteration number of solving by Hp Pseudospectral method is small but the calculation time varies greatly under different cost functions.The number of nodes and the calculation time will increase sharply when the mesh refinement tolerance becomes smaller,which indicates the calculation speed of Hp Pseudospectral method is time-consuming and unstable.Therefore,Hp Pseudospectral method is not suitable for solving the problem in terms of the application of autonomous control and onboard real-time calculation.Considering the requirement of onboard real-time calculation,the convex programming with good convergence and global optimality is used to study the asteroid landing trajectory planning problem.First,the convexification of dynamics and nonconvex state constraints based on modified Rodrigues parameters is proposed for the fixed-time asteroid landing trajectory planning optimal control problem.Then the method of convexifying the nonconvex control constraint under coupled dynamics is given and proved.On account of the problem of artificial infeasibility and unbounded solution that may appear in the process of convexification,the successive convexification method using virtual control and state trust region constraints with low initial reference sensitivity is adopted to generate the optimal trajectory.The simulation results show that the successive convexification method is feasible to solve the asteroid landing trajectory planning problem,and has faster more stable calculation speed compared to Hp Pseudospectral method.Besides,simulation results for landing on different asteroid with or without considering asteroid gravity show that the gravity of asteroid whose volume and mass are small is similar to disturbance and has little effect on the trajectory.In addition,by comparing the simulation results with the asteroid landing trajectory planning problem based on quaternion,it is found that using modified Rodriguez parameters to establish the vehicle dynamics can not only reduce the number of optimization parameters,but also reduce the iteration numbers and improve the calculating speed in the solving process.Furthermore,the convex programming is used to study the asteroid landing trajectory planning optimal control problem with segmented state constraints.First,two time dilation coefficients are introduced to normalize the system state equation,so that the segmented state constrained optimization problem can be transformed into a fixed normalized time optimization problem.Then the convexification and discretization of the time normalization problem are given,especially for cost function considering both flight time and fuel consumption.Considering the non-convexity of the system state equation is enhanced after normalizing the original problem,the successive convexification method with full-variable trust region constraints is used to generate the optimal trajectory,and the effectiveness of virtual control and trust region as well as the convergence of the successive convexification are analyzed.The simulation verifies the feasibility of solving the segmented state constraint optimization problem under the convex programming framework,and the trajectory planning algorithm suitable for giving the tracking trajectory of the controller.Then the effect of fuel consumption penalty factor and the size of constraint ellipsoid in the state constraint on the flight time is analyzed.Finally,in order to satisfy the requirement of autonomous asteroid landing,the control method for the onboard controller is required to have characteristics of fast calculation speed,high reliability and strong robustness.Therefore,the model predictive control with online rolling optimization,feedback correction and good tracking effect on the reference trajectory is used to realize the closed-loop control for asteroid landing.First,the predictive equation,the optimization solution and the feedback mechanism in the model predictive control are described mathematically,and the asteroid autonomous landing trajectory tracking control method based on model prediction is given.Then the joint algorithm composed of the convex planning algorithm for asteroid landing trajectory under segmented state constraints and the fixed-time asteroid landing trajectory convex programming algorithm is used to give the tracking trajectory,the simulation verifies that the control method has good control and tracking effects.Through the simulation by imposing disturbance on the current state in each rolling optimization process and the simulation under asteroid rotation period observation error show that the model predictive control for asteroid landing has good anti-interference and certain ability to overcome system uncertainty.