On-Board Convex Optimization for Powered Descent Landing of EAGLE

Abstract

Future space exploration missions require new solutions in Guidance, Navigation and Control for autonomous high precision landing. The German Aerospace Centre, DLR, is currently developing the environment for autonomous GNC Landing experiments, EAGLE, acting as a demonstrator for vertical take-off and landing. The goal of this thesis is to develop a prototype real-time applicable guidance function based on optimal control theory for the powered descent landing, which can be implemented and tested on the on-board computer of EAGLE. Based on the principle of loss less convexification developed by Açikmese and Ploen [1], the powered descent landing fuel-optimal control problem is converted into a second order cone problem. A discretization and transcription method is designed in order to solve the resulting non-linear program by means of the embedded conic solver ECOS and the developed algorithm is verified by the comparison of simulation results for an example pinpoint landing on Mars from [1]. After the implementation into C-code and a Simulink-Environment, the developed method is adapted by a preceding heuristic estimation for the fuel-optimal flight time given Initial and final conditions, which is used as input for the developed trajectory optimization algorithm. This results in a prototype, sub-optimal trajectory optimization and guidance function applicable on on-board systems. The guidance function is tested with EAGLE-specific parameters in two extensive simulation of 41503 sets, respectively, with different initial and final conditions. For all the sets, the resulting trajectory and fuel consumption calculated by the guidance function are compared to the actual fuel-optimal solution, which is obtained via a search algorithm scanning through different flight times in a given range around the estimated flight time. We find that the developed guidance function overestimates the optimal flight time in all cases, related to a fuel consumption which is 20% higher than the optimal case in 80% of the sets. Furthermore, the typical computation time of the guidance function on the on-board computer of EAGLE can be expected to be less than 0:8 seconds, proving the on-board feasibility of the proposed algorithm. The developed prototype guidance function sets a base for further work on on-board optimization applications and is currently subject to improvement regarding optimality and robustness.