Assessment of Machine Learning Techniques for Time-Optimal Landing Trajectories
Creators: name:  P. SOLANO LOPEZ 
name:   R. GUTIERREZ RAMON 
name:   H. URRUTXUA CEREIJO 
name:   A. BAREA VILAR 
Publisher: name: Proceedings of  the 9th European Conference for Aerospace Sciences. Lille, France, 27 June - 1 July, 2022
Year: 2022
Subjects: FLIGHT DYNAMICS
GNC
AVIONICS
OPTIMIZATION

description: The advent of Machine Learning (ML) and its applications at space engineering has allowed to rethink complex problems associated with mission planning and the Attitude Determination and Control System (ADCS). It is more and more common to find such techniques as helping tools for the guidance, navigation and control of aerospace vehicles as well as mechanisms to deal with unknown physics in traditional trajectory determination and optimization problematics. As an example, it has been proven that, using ML, orbital trajectories can be learnt from existent or artificial data, making possible to predict the future states of a Spacecraft without the need of a mathematical approximated model (e.g., data driven prediction). Also, another interesting research area of these mathematical tools is the treatment of optimal control problems for rendezvous, landing in partially known environments and such kind of applications. Neural Networks (NN) can be constructed in such a way they learn these optimal solutions to then perform parametrical continuation or they provide unknown initial/final states of the problem. Finally, another point of interest is the parametrical identification for uncomplete models, e.g., asteroid shape determination, perturbation of unknown orbits, etc. In this contribution, we focus on the optimal control problematic. Specifically, the problem at hand entails the determination of a time-optimal landing trajectory such that a particular point of an asteroid surface is reached with null touchdown velocity. This can be modelled as an optimal control problem with the thrust orientation as the control variable. Its resolution involves the determination of the so called costate variables, whose rates of change are defined by the desired optimality conditions. In turn, the initial values of the costate variables must be tuned so as to comply with the desired boundary conditions. This can prove a difficult task, since these costates are mathematical entities without a clear physical transcription and the behaviour of the trajectory can be especially sensitive to small changes of the initial values of the costates. This work proposes a NN-based approach to obtain an initial guess of said initial values of the costate variables. First, given a range of initial states and costates of the lander, a set of optimal trajectories is generated. These trajectories have to reach the surface of a predefined ellipsoidal body with null velocity. It must be noted that not every state-costate combination generates a feasible trajectory (e.g., some combinations generate trajectories that escape the gravitational influence of the body, while others can result in a collision with it). The feasible state-costate combinations along with their associated landing point are used to train a NN. In particular, the initial state and the landing point are the network features and the costates represent its output. Then, the resulting NN is used as an initial guess for the initial costates corresponding to landing trajectories under the influence of polyhedral gravitational models. The high-fidelity polyhedral models corresponding to the asteroids Castalia and Bennu are used to assess the performance of different NN architectures and hyperparameter values. It is shown that the proposed approach represents a viable strategy to accelerate the resolution of the aforementioned optimal control problems.