دانلود رایگان مقاله بهینه سازی مسیر با استراتژی پالایش مش تطبیقی بر اساس هامیلتونی

Abstract

In this study, the problem of fuel-optimal lunar soft landing trajectory optimization using variablethrust propulsion is considered. First, the lunar soft landing trajectory optimization problem with threedimensional kinematics and dynamics model, boundary conditions, and path constraints strictly described is formulated. Then, the formulated trajectory optimization problem is solved by the simultaneous dynamic optimization approach. With bounds imposed on the magnitude of engine thrust, the optimal control solutions typically have a “bang-bang” thrust profile. The general simultaneous dynamic optimization approach has difficulty handling breakpoints in the control profiles. A novel adaptive mesh refinement strategy based on a constant Hamiltonian profile is proposed to address the difficulty of locating breakpoints in the thrust profile. Two cases are simulated. The engine of the first case is throttleable between zero and full thrust. The engine of the second case is throttleable between 10% and 60% of full thrust, and at full thrust. Union property of R-function method is utilized to express the thrust profile of the second case in the trajectory optimization problem. Simulation results show that the enhanced simultaneous dynamic optimization approach with adaptive mesh refinement strategy can effectively capture the breakpoints in the optimal thrust profile and obtain more refined lunar soft landing optimal solutions, compared with the results obtained by the general simultaneous dynamic optimization approach.

6. Conclusion

In this study, an enhanced simultaneous dynamic optimization framework to determine the fuel-optimal trajectory of lunar soft landing with variable-thrust propulsion is presented. The thrust profile with piecewise property is formulated in the trajectory optimization problem by utilizing the Union property of R-function method. The optimal thrust profile in this study has a “bang-bang profile, which results in the existence of breakpoints in the optimal thrust profile. A novel adaptive mesh refinement strategy is proposed to capture the breakpoints in the thrust profile. The proposed mesh refinement strategy can add finite elements to the collocation point mesh based on a constant Hamiltonian profile, which is adaptive and efficient rather than add a large number of finite elements equally to the mesh. Compared with the general simultaneous dynamic optimization approach, the proposed enhanced simultaneous dynamic optimization approach with adaptive mesh refinement strategy can effectively capture the breakpoints of optimal thrust profile, and obtain more refined lunar soft landing optimal trajectory. The adaptive mesh refinement strategy is quite time-consuming. Thus, several additional heuristics could be considered to accelerate the adaptive mesh refinement strategy in the future. A clear trend in the field of aerospace guidance and control, called “computational guidance and control” (CG&C), has recently emerged. The traits of CG&C are critical for system autonomy and support of autonomous operations. Optimized solutions based on model or data are desired or even necessary in CG&C. Consequently, the success of CG&C likely demands more up-front investment in formulating, modeling, and analyzing the problem. The enhanced simultaneous dynamic optimization framework for lunar soft landing is beneficial to the up-front investment of CG&C, which may eventually benefit the future autonomous lunar descent missions.