Fast and accurate estimation of fuel-optimal trajectories to Near-Earth Asteroids

This paper proposes an improved method for the preliminary evaluation of minimum-propellant trajectories to Near-Earth Asteroids (NEAs). The method applies to missions from Earth to asteroids with small eccentricity and inclination. A planar and a plane-change problem can be distinguished. In the planar problem, the solution assumes that multiple burn arcs are performed in correspondence of the apsides of the target asteroid in order to change the initial spacecraft orbit (i.e., Earth’s orbit) into the target one. The number of arcs is established once the time of flight is given (1 burn at each apsis per revolution, 1 revolution per year can be assumed). The length and propellant consumption of each arc to attain the required changes of semi-major axis and eccentricity are computed by a procedure based on Edelbaum’s approximation, which is well-suited to the problem at hand, as eccentricity changes are expected to be small for feasible missions. No numerical integration is required, but only the numerical solution of a three-unknown algebraic system is needed, making the procedure extremely fast. Plane change is taken into account assuming a constant out-of-plane thrust angle during each burn. A previous simple formulation used an averaged thrust effect over one revolution and neglected the fact that plane changes are more effective at the nodes. Several improvements are here introduced, which greatly increase the method accuracy. The influences of the eccentricity change, the angle between the asteroid line of nodes and line of apsides, and the expected length of the arc are considered: In fact, when the eccentricity is small, the thrust arc can be performed at the nodes where the inclination is efficiently changed, with little penalty in the planar maneuver. An efficient plane change is also performed when the angle between the asteroid line of nodes and line of apsides is small and/or the length of the arc is large, because, in this case, the node is comprised in the apsidal burn. A simple corrective formula accounts for this effect. The new method shows remarkable accuracy. The results comparison with solutions obtained with an indirect optimization method for a set of more than 60 NEAs shows a 0.95 correlation coefficient in the propellant masses. The estimation error is below 10% for 75% of the targets, below 15% for 95% of the targets, and always below 20%

Asteroid Flyby Cycler Trajectory Design Using Deep Neural Networks

Asteroid exploration has been attracting more attention in recent years. Nevertheless, we have just visited tens of asteroids while we have discovered more than one million bodies. As our current observation and knowledge should be biased, it is essential to explore multiple asteroids directly to better understand the remains of planetary building materials. One of the mission design solutions is utilizing asteroid flyby cycler trajectories with multiple Earth gravity assists. An asteroid flyby cycler trajectory design problem is a subclass of global trajectory optimization problems with multiple flybys, involving a trajectory optimization problem for a given flyby sequence and a combinatorial optimization problem to decide the sequence of the flybys. As the number of flyby bodies grows, the computation time of this optimization problem expands maliciously. This paper presents a new method to design asteroid flyby cycler trajectories utilizing a surrogate model constructed by deep neural networks approximating trajectory optimization results. Since one of the bottlenecks of machine learning approaches is the computation time to generate massive trajectory databases, we propose an efficient database generation strategy by introducing pseudo-asteroids satisfying the Karush-Kuhn-Tucker conditions. The numerical result applied to JAXA's DESTINY+ mission shows that the proposed method is practically applicable to space mission design and can significantly reduce the computational time for searching asteroid flyby sequences

Artificial neural networks for multiple NEA rendezvous missions with continuous thrust

The interest for near-Earth asteroids for scientific studies and, in particular, for potentially hazardous asteroids requires the space community to perform multiple-asteroid missions with close-up observations. To this end, multiple near-Earth asteroid rendezvous missions can help reduce the cost of the mission. Given the enormous number of asteroids, this work proposes a method based on artificial neural networks (ANNs) to quickly estimate the transfer time and cost between asteroids using low-thrust propulsion. The neural network output is used in a sequence search algorithm based on a tree-search method to identify feasible sequences of asteroids to rendezvous. The rendezvous sequences are optimized by solving an optimal control problem for each leg to verify the feasibility of the transfer. The effectiveness of the presented methodology is assessed through sequences of asteroids of interest optimized using two low-thrust propulsion systems, namely solar electric propulsion and solar sailing. The results show that ANNs are able to estimate the duration and cost of low-thrust transfers with high accuracy in a modest computational time

Artificial neural networks for multi-target low-thrust missions

Multi-target missions are an attractive solution to visit multiple bodies in a single mission, increasing the scientific return and reducing the cost, compared to multiple missions to individual targets. Designing multi-target missions represents a challenging task since it requires multiple options to be estimated, given the large number of objects which can be considered as potential targets. Low-thrust propulsion systems are preferred to rendezvous multiple targets in a mission as they allow to utilise less propellant mass than high-thrust systems to perform the same trajectory. However, low-thrust trajectories are computationally expensive to compute. This PhD thesis proposes to use artificial neural networks (ANN), as a fast and accurate estimation method for optimal low-thrust transfers. An artificial neural network and a sequence search (SS) algorithm can be designed to find solutions to three kinds of multi-target global optimisation problems: (i) multiple active debris removal missions (MADR), (ii) multiple near-Earth asteroid rendezvous (MNR) missions, with the option of returning a sample to Earth, and (iii) multi-objective optimisation of low-thrust propulsion systems for multi-target missions. MADR missions allows for the disposal of inactive satellites and larger objects, preventing the build-up of space junk and allowing to replace ageing agents in a constellation. Similarly, MNR missions allow to reduce the cost of each NEA observation and increase the possibility of visiting multiple asteroids of interest in a single mission. The trained ANN is employed within a SS algorithm, based on a tree-search method and breadth-first criterion, to identify multiple rendezvous sequences and select those with lowest time of flight and/or required propellant mass. To compute the full trajectory and control history, the sequences are subsequently recalculated by using an optimal control solver based on a pseudospectral method. Also, to optimise the propulsion system for a given mission, a multi-objective optimisation using a genetic algorithm is performed, where ANNs are employed to quickly estimate the cost and duration of multi-target transfers. The results show that neural networks can estimate the duration and cost of low-thrust transfers with high accuracy, for all the three applications. Employing machine learning within a sequence search algorithm to preliminary design multitarget missions allows to significantly reduce the computational time required with respect to other most commonly used methods in the literature, while maintaining a high accuracy. Given the combinatorial nature of the problem, the benefits in terms of computational time introduced by the ANN increase exponentially with a linear increase of the number of bodies in the database

Artificial Neural Network for Preliminary Multiple NEA Rendezvous Mission Using Low Thrust

No abstract available

Simple Δv approximation for optimization of debris-to-debris transfers

In this paper, a simple analytical method is developed to accurately approximate the transfer costs between two objects of the removal sequence. The accuracy of these estimations is verified by comparison with existing optimized solutions.Rendezvous transfers between two given orbits are dealt with using an accurate dynamic model that takes J2 perturbation into account. The state-of-the-art solution winner of the ninth Global Trajectory Optimization Competition (GTOC9) by the Jet Propulsion Laboratory (JPL) is used as benchmark to verify the accuracy of the method presented in this paper