Mars Entry Trajectory Design,Optimization,and Guidance Methods

China has released details of a series of ambitious plans for space exploration in the coming years.They include the first Mars mission probe set to be launched around2020.The probe is expected to orbit the red planet,land and deploy a rover all in one mission.This work was supported by the National Basic Research Program of China: Research on navigation,guidance,and control problem for planetary precision landing(No.2012CB720000).In the context of the first Mars landing exploration mission,this dissertation is focused on the entry guidance problem for Mars Entry,Descent,and Landing(EDL).The main research contents are summarized as follows:Based on Newtonian mechanics,the dynamic modeling problem for an entry vehicle is first addressed.The dynamic models derived in this work include six-degree-of-freedom equations of motion(EOM)and several trajectory guidance design models.The wellknown entry terminal point controller(ETPC)and the MSL attitude control scheme are also introduced in detail for trajectory guidance and attitude control of an entry vehicle.This part of research contents lays the foundation of Mathematics for the guidance design,simulations,and evaluations in this dissertation.For Mars entry terminal altitude(ETA)optimization design and the trajectory-designparameter analysis,the optimization theory,models,and algorithms are developed.For the ETA-optimization problem,an ETA-optimization-design model is first presented and then a rapid bank-angle profile optimization algorithm based on indirect methods is developed to deal with the corresponding initial values guess difficulty.Based on this bankangle profile optimization scheme,a rapid trajectory-design-parameter analysis scheme is proposed.In this part,the involved parameters are the entry flight-path angle(EFPA)and bank-angle control margin,which are usually considered to have relatively high effects on the trajectory performance.With this method,rapid local convergence is be ensured and then,numerical convergence,rapidity,and stability are improved.Numerical results show that the optimal bank-angle profile is Bang-Bang control type;the peak aerodynamic-load and peak heat-rate both increase with the optimal ETA;there are great differences in optimal ETAs with different EFPAs and bank-angle control margins.Considering the path-constraints on the aerodynamic-load,heat rate,and dynamic pressure,an indirect Mars ETA-optimization scheme is developed.Based on the proceeding ETA optimization model,an ETA-optimization-design model including the pathconstraints is presented.To address the path-constraint handling problem,a method based on exact penalty method(EPM)and smoothing technology is developed to avoid the structure guess for the optimal solution and solving the multi-point boundary value problem(MPBVP)in traditional methods.Combined with the initial value guess technology in the proceeding path-unconstrained ETA-optimization scheme,the performance index is reconstructed.By doing so,the initial value guess difficulty in this path-constrained ETAoptimization problem is overcome.Then,the convergence analysis is conducted to reveal the effects of the related parameters on computational accuracy.The developed algorithm does not need to derive and solve the corresponding MPBVP and can overcome the initial value guess difficulty and the path-constraint handling problem in one optimization scheme.Numerical results show that the path-constraints can low the optimal ETA to some extent;to satisfy the path-constraints,a minimum allowable bank-angle profile may be required in the early entry phase;the optimal bank-angle profile is also Bang-Bang type;Under the path-constraints,the number of bank-angle-profile discontinuous jump relies on the EFPA and for some shallow EFPAs,the number is two.To address the aerodynamic-load-constrained entry guidance problem,a numerical predictor-corrector(NPC)guidance design model and a novel constrained numerical predictor-corrector(CNPC)guidance algorithm are presented.Based on the three degreeof-freedom EOM,the longitudinal NPC design model is first built.Then,without further assumptions or simplifications on the NPC design model,the novel CNPC algorithm is developed.The performance of the proposed CNPC algorithm is analyzed by considering extreme deviations and disturbances.In accordance with unconstrained numerical predictor-corrector(UNPC)guidance algorithms,the proposed CNPC algorithm is based on the single-parameter iteration strategy.Therefore,the algorithm complexity is not increased in the development of the proposed CNPC algorithm.The numerical simulations show that this CNPC algorithm not only ensures the range-control robustness,but also satisfies the aerodynamic-load constraint effectively.Using the proceeding research results and according to the mission requirements,two guidance schemes for the mission are developed,optimized,and analyzed.Considering the high reliability of the parachute-deployment constraints,two entry guidance schemes are presented and the landing accuracy is identified.Using extreme-condition analysis methods,the entry corridor and the nominal parachute-deployment conditions are analyzed and identified.According to the constraints on the parachute-deployment altitude,dynamic-pressure,and Mach number,the perturbation entry guidance scheme based on ETPC is first discussed and optimized.In this part,the reference trajectory optimization and the trade selection of the trajectory-design-parameter are presented.Then,the development of the computation entry guidance scheme based on NPC is presented.In this scheme,the selections of the reference bank-angle profile,guidance period,and EFPA are discussed.Finally,the two entry guidance schemes are simulated and compared,according the performance indexes of parachute-deployment constraints,fuel consumption of attitude RCS,parachute-deployment footprints,and so on.