Trajectory Optimization For Lunar Soft Landing With Complex Constraints

Lunar exploration program has started a new era of human exploration in outer space,which is of great significance to the development of science and technology,economy,politics,and military.For one thing,the lunar soft landing from lunar orbit is one of the most important mission in the lunar exploration program.For another,the Vertical Takeoff Vertical Landing(VTVL)might be a most promising mobility method on the lunar surface in future.Therefore,the trajectory optimization for two typical lunar soft landing is studied in this paper.The trajectory optimization problem is essentially an optimal control problem(OCP)with various complex constraints,such as landing velocity,position,attitude,attitude angular rate,discontinuous thrust,multi-phase connections,lunar terrain,dynamic differential equation and so on.The optimal control problem is discretized and transcribed directly into a nonlinear programming problem(NLP)by Gauss pseudospectral method(GPM).The GPM can obtain higher precision solutions with less parameters,high computational efficiency,and strong stability.The NLP problem is solved by the SNOPT solver that is based on the sequential quadratic programming algorithm.The main research contents and contributions are as follows:(1)The background and significance of the lunar exploration and lunar soft landing mission are introduced in detail.Two typical main missions of the lunar soft landing are studied in this paper,including Apollo-like Landing mission from low lunar orbit and Vertical Takeoff Vertical Landing mission from lunar surface.The unified kinetic model of two landing missions is established.(2)The discontinuous adjustable thrust magnitude constraint is transformed into a nonlinear algebraic inequality constraint as a path constraint by using R-function method and single-variable-high-order-inequality method.The advanced initialization strategies,including the constraints enhancement and collocation points refinement,are developed to enhance both the convergence and computation efficiency.(3)The information fusion method is adopted to construct the complex lunar terrain model.The initialization strategy of trajectory patching is proposed to improve the convergence and computation efficiency of the lunar soft landing with the complex terrain constraints.(4)A variety of lunar soft landing scenarios with specific requirements and complex constraints are designed and described optimal control problems.A unified trajectory optimization framework based on GPM is proposed for solving these optimal control problems numerically.Abovementioned advanced initialization strategies are developed to improve the performance of optimization framework.The simulation results demonstrate the adaptability and flexibility of the framework.