Optimal Mars Entry Trajectory Planning And Guidance Design Considering Uncertainties

Mars exploration mission has high request on safety,robustness and reliability,thus it is necessary to develop trajectory planning and guidance methods with consideration of uncertainties.In this paper,the robust and reliability-based trajectory design methods are developed with consideration of uncertainty.Two robust tracking guidance laws are also proposed and contribute to the complete solution for Mars entry trajectory design and control problem.The proposed theory and methods are also tested in a specific Mars entry mission.Main achievements are summarized as follows.The entry dynamic propagation models under aleatory and epistemic uncertainties are formulated.To tackle with various uncertainties in Mars entry mission,the aleatory and epistemic uncertainty models are respectively formulated according to the knowledge of uncertainty distributions.The effect of uncertainties on nonlinear entry dynamics are quantified via global sensitivity analysis and numerical propagation analysis.Besides,the uncertainty analysis method of reachable set is proposed for guiding entry mission design.The characteristics of Mars entry are then given based on the previous uncertainty analysis,including Mars atmosphere,entry constrains and mission design under uncertainties.The trajectory optimization method under aleatory uncertainty is proposed,considering the stochastic entry dynamics,robust objective function and reliability-based path constraints.Compared with the traditional trajectory optimization model,the formulated reliability-based model quantifies the aleatory uncertainty,probability of constraint satisfaction and statistics of objective values.Then the approximate polynomial chaos expansion of trajectory solution is obtained using generalized polynomial chaos theory.The stochastic trajectory optimization is thus transferred to an equivalent deterministic optimization.The sequence optimization strategy based on iteration is finally proposed,which uses the most probable point searching method combining with nonintrusive polynomial chaos method.Compared with the traditional deterministic optimization method,the proposed method can improve the reliability of constraint satisfaction,reduce deployment dispersion and achieve high computational efficiency and accuracy.The trajectory optimization method under epistemic uncertainty is proposed.The entry dynamics considering interval-based epistemic uncertainty is first formulated.The belief and plausibility from Dempster-Shafer evidence theory are then used to quantify the epistemic uncertainty.The robust objective function based on evidence level and path constaints based on extreme case are also developed.Additionally,the random set theory is used to analyze the epistemic uncertainty propagation in stochastic entry dynamics.Furthermore,the original averaging discretization method is modified and used to discretize the uncertainty space.The robust epistemic uncertainty optimization method,in which the outer-loop optimization searches the optimal control profile subject to the minimal objective value,and the inner loop searches the specific uncertainty values subject to the minimal and maximal values of the trajectory solution,is subsequently proposed.The simulation results show that the proposed method has high accuracy and exhibits a remarkable improvement in the computational efficiency compared to the traditional optimization method.The tracking guidance law based on optimal feedback and the receding horizon optimal controller for reference trajectory tracking are designed.To avoid losing robustness caused by linearization in traditional feedback guidance,the feedback gains are obtained via nonlinear dynamics using optimal control theory.Besides,to further reduce the loss of robustness caused by decoupling,a full-state based tracking guidance law which combines longitudinal and lateral guidances,is designed.The proposed law integrated with differential transformation and receding horizon optimal control not only eases the inconvenience caused by decoupling,but also shows high accuracy and strong robustness.This paper takes uncertainties into consideration when formulating entry dynamics and control models,and proposes a complete solution for trajectory planning and tracking problem under uncertainties.Using the proposed methods and algorithms,the robustness of Mars mission against uncertainties can be improved and the mission risk can be reduced.Furthermore,the proposed methods can also offer references for Earth reentry and other planetary exploration missions.