Autonomous Time-Optimal Many-Revolution Orbit Raising for Electric Propulsion GEO Satellites via Neural Networks

Abstract

I. Introduction Epropulsion (EP) Geostationary Earth orbit (GEO) satellites are more efficient because they cost a lower fuel consumption and thus increase the payload mass or reduce the launch mass, compared to conventional chemical propulsion GEO satellites. EP has been tested and applied a lot in many deep space missions, and its application to the Earth orbit satellites has been a growing interest [1,2]. The world-first all-electric GEO platform, Boeing 702SP, has already been launched in March 2015 by a Falcon 9 rocket. China also launched its first EP-GEO satellite in April 2017. The design of GEO satellites is rapidly changing from classic high-thrust propulsion more and more toward low-thrust propulsion. Low-thrust orbit raising brings in a many-revolution long-duration transfer that is a special characteristic of EP-GEO satellites.Autonomous orbit raising is necessary for future EP-GEO missions because the support from the ground is expensive when transfer time is very long, for instance, hundreds of days for low-thrust orbit raising from low Earth orbit (LEO) to GEO. Recently, neural networks (NNs) have attracted the interest of many researchers and have had applications in various fields in recent years, including astrodynamics [3]. For landing problems and short-duration orbit transfers, NNs are trained to learn the optimal state-control pairs [4-6] and image-control relations [7]. Their results show that NNs have excellent performance in learning the optimal control of short-duration problems. In this Note, NNs are trained to learn the optimal control of many-revolution long-duration problems, that is, time-optimal low-thrust orbit raising problems.Optimization of time-optimal low-thrust orbit raising problems is necessary before training neural networks.The many-revolution long-duration characteristic makes it extremely difficult for numerical optimization methods to converge. Some methods based on Edelbaum's approach [8] have been proposed under the assumption of quasi-

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]).…”

“…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]). The time consuming creation of optimal examples, likely prevented these works to produce large enough datasets and thus train networks able to go well beyond the simple cases considered there and able to approximate the optimal guidance in a larger portion of interplanetary space with acceptable accuracies.…”

“…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.…”