Neural Networks in Time-Optimal Low-Thrust Interplanetary Transfers

Abstract

In this paper, neural networks are trained to learn the optimal time, the initial costates, and the optimal control law of time-optimal low-thrust interplanetary trajectories. The aim is to overcome the difficult selection of first guess costates in indirect optimization, which limits their implementation in global optimization and prevents on-board applications. After generating a dataset, three networks that predict the optimal time, the initial costate, and the optimal control law are trained. A performance assessment shows that neural networks are able to predict the optimal time and initial costate accurately, especially a 100% success rate is achieved when neural networks are used to initialize the shooting function of indirtect methods. Moreover, learning the state-control pairs shows that neural networks can be utilized in real-time, on-board optimal control. INDEX TERMS Indirect methods, low-thrust trajectory optimization, initial costates, neural networks.

Real-Time Optimal Guidance and Control for Interplanetary Transfers Using Deep Networks

“…The works from Sanchez and Izzo [4,5] introduced the idea to use imitation learning (also known as behavioural cloning, and essentially based on the classical supervised learning scheme) to teach a deep artificial neural network to produce on-board, and in real time, the optimal guidance and tested it on several spacecraft landing scenarios. The results, triggering a number of other studies [6,7,8,9,10,11]) suggest that future space systems might use an artificial neural network in place of their on-board guidance and control systems, and hence these networks are called G&CNETs. An early study on the stability of a G&CNET controlled system [10] shows how it is also possible to provide control guarantees to the resulting neurocontrolled system, a fact of great relevance for such a mission critical component.…”

“…While not directly using the term G&CNET, a first study on deep networks for the real time optimal control of interplanetary transfers appeared recently [7], but only considering two dimensional dynamics and a simple solar sailing transfer with continuous controls. In following works from Li et al [8,9] neural networks are also trained to approximate the co-states, the optimal thrust and the value function of optimal interplanetary transfers, but only succeeding for time optimal cases (resulting in continuous thrust profiles) and in close neighbourhoods of nominal transfers (e.g. small perturbations of the order of 0.1 m/s on the initial velocity and 100m on the initial position were considered [9]).…”

“…Overall, in the context of this work, we are able to compute and release 4,000,000 mass optimal transfers containing multiple bang-off phases. For comparison, the datasets used in [8] contain roughly 12,000 trajectories, while the datasets used in [7,9] contain 1,000 trajectories (and all considering smooth thrust profiles). After the dataset creation, four different training methodologies are studied: one based on policy learning (i.e.…”

Neural representation of a time optimal, constant acceleration rendezvous

“…As a consequence, the solution to many Two Points Boundary Value Problems (TPBVPs) needs to be computed. Even in the optimistic case of good co-states guesses being available [3,12] and homotopy methods employed, these numerical procedures are time consuming and limit the amount of reference trajectories one can learn from [3,6]. A similar conclusion can be made also when direct methods are used to generate optimal examples.…”

“…D neural models for optimal spacecraft guidance and control have been recently proposed [1][2][3][4][5][6] and studied as a possible alternative to more classical architectures. Previously, researchers had proposed the use of "neurocontrollers" [7] as part of the guidance and control system, but mostly using a neural model to track some precomputed reference guidance signal.…”