arXiv subjects

Dario Izzo

Publications and source records attributed to Dario Izzo.

At least 73 records · Page 4Linked to original sources

arXiv2021

Revisiting high-order Taylor methods for astrodynamics and celestial mechanics

We present heyoka, a new, modern and general-purpose implementation of Taylor's integration method for the numerical solution of ordinary differential equations. Detailed numerical tests focused on difficult high-precision gravitational problems in astrodynamics and celestial mechanics show how our general-purpose integrator is competitive with and often superior to state-of-the-art specialised symplectic and non-symplectic integrators in both speed and accuracy. In particular, we show how Taylor methods are capable of satisfying Brouwer's law for the conservation of energy in long-term integrations of planetary systems over billions of dynamical timescales. We also show how close encounters are modelled accurately during simulations of the formation of the Kirkwood gaps and of Apophis' 2029 close encounter with the Earth (where heyoka surpasses the speed and accuracy of domain-specific methods). heyoka can be used from both C++ and Python, and it is publicly available as an open-source project.

astro-ph.EP↗

arXiv2021

Shadow Neural Radiance Fields for Multi-view Satellite Photogrammetry

We present a new generic method for shadow-aware multi-view satellite photogrammetry of Earth Observation scenes. Our proposed method, the Shadow Neural Radiance Field (S-NeRF) follows recent advances in implicit volumetric representation learning. For each scene, we train S-NeRF using very high spatial resolution optical images taken from known viewing angles. The learning requires no labels or shape priors: it is self-supervised by an image reconstruction loss. To accommodate for changing light source conditions both from a directional light source (the Sun) and a diffuse light source (the sky), we extend the NeRF approach in two ways. First, direct illumination from the Sun is modeled via a local light source visibility field. Second, indirect illumination from a diffuse light source is learned as a non-local color field as a function of the position of the Sun. Quantitatively, the combination of these factors reduces the altitude and color errors in shaded areas, compared to NeRF. The S-NeRF methodology not only performs novel view synthesis and full 3D shape estimation, it also enables shadow detection, albedo synthesis, and transient object filtering, without any explicit shape supervision.

cs.CV↗

arXiv2020

Learning Dynamic-Objective Policies from a Class of Optimal Trajectories

Optimal state-feedback controllers, capable of changing between different objective functions, are advantageous to systems in which unexpected situations may arise. However, synthesising such controllers, even for a single objective, is a demanding process. In this paper, we present a novel and straightforward approach to synthesising these policies through a combination of trajectory optimisation, homotopy continuation, and imitation learning. We use numerical continuation to efficiently generate optimal demonstrations across several objectives and boundary conditions, and use these to train our policies. Additionally, we demonstrate the ability of our policies to effectively learn families of optimal state-feedback controllers, which can be used to change objective functions online. We illustrate this approach across two trajectory optimisation problems, an inverted pendulum swingup and a spacecraft orbit transfer, and show that the synthesised policies, when evaluated in simulation, produce trajectories that are near-optimal. These results indicate the benefit of trajectory optimisation and homotopy continuation to the synthesis of controllers in dynamic-objective contexts.

eess.SY↗

arXiv2020

Spacecraft Collision Avoidance Challenge: design and results of a machine learning competition

Spacecraft collision avoidance procedures have become an essential part of satellite operations. Complex and constantly updated estimates of the collision risk between orbiting objects inform the various operators who can then plan risk mitigation measures. Such measures could be aided by the development of suitable machine learning models predicting, for example, the evolution of the collision risk in time. In an attempt to study this opportunity, the European Space Agency released, in October 2019, a large curated dataset containing information about close approach events, in the form of Conjunction Data Messages (CDMs), collected from 2015 to 2019. This dataset was used in the Spacecraft Collision Avoidance Challenge, a machine learning competition where participants had to build models to predict the final collision risk between orbiting objects. This paper describes the design and results of the competition and discusses the challenges and lessons learned when applying machine learning methods to this problem domain.

cs.LG↗

arXiv2020

Safe Crossover of Neural Networks Through Neuron Alignment

One of the main and largely unexplored challenges in evolving the weights of neural networks using genetic algorithms is to find a sensible crossover operation between parent networks. Indeed, naive crossover leads to functionally damaged offspring that do not retain information from the parents. This is because neural networks are invariant to permutations of neurons, giving rise to multiple ways of representing the same solution. This is often referred to as the competing conventions problem. In this paper, we propose a two-step safe crossover(SC) operator. First, the neurons of the parents are functionally aligned by computing how well they correlate, and only then are the parents recombined. We compare two ways of measuring relationships between neurons: Pairwise Correlation (PwC) and Canonical Correlation Analysis (CCA). We test our safe crossover operators (SC-PwC and SC-CCA) on MNIST and CIFAR-10 by performing arithmetic crossover on the weights of feed-forward neural network pairs. We show that it effectively transmits information from parents to offspring and significantly improves upon naive crossover. Our method is computationally fast,can serve as a way to explore the fitness landscape more efficiently and makes safe crossover a potentially promising operator in future neuroevolution research and applications.

cs.NE↗

arXiv2020

Satellite Pose Estimation Challenge: Dataset, Competition Design and Results

Reliable pose estimation of uncooperative satellites is a key technology for enabling future on-orbit servicing and debris removal missions. The Kelvins Satellite Pose Estimation Challenge aims at evaluating and comparing monocular vision-based approaches and pushing the state-of-the-art on this problem. This work is based on the Satellite Pose Estimation Dataset, the first publicly available machine learning set of synthetic and real spacecraft imageries. The choice of dataset reflects one of the unique challenges associated with spaceborne computer vision tasks, namely the lack of spaceborne images to train and validate the developed algorithms. This work briefly reviews the basic properties and the collection process of the dataset which was made publicly available. The competition design, including the definition of performance metrics and the adopted testbed, is also discussed. The main contribution of this paper is the analysis of the submissions of the 48 competitors, which compares the performance of different approaches and uncovers what factors make the satellite pose estimation problem especially challenging.

cs.CV↗

arXiv2020

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

We consider the Earth-Venus mass-optimal interplanetary transfer of a low-thrust spacecraft and show how the optimal guidance can be represented by deep networks in a large portion of the state space and to a high degree of accuracy. Imitation (supervised) learning of optimal examples is used as a network training paradigm. The resulting models are suitable for an on-board, real-time, implementation of the optimal guidance and control system of the spacecraft and are called G&CNETs. A new general methodology called Backward Generation of Optimal Examples is introduced and shown to be able to efficiently create all the optimal state action pairs necessary to train G&CNETs without solving optimal control problems. With respect to previous works, we are able to produce datasets containing a few orders of magnitude more optimal trajectories and obtain network performances compatible with real missions requirements. Several schemes able to train representations of either the optimal policy (thrust profile) or the value function (optimal mass) are proposed and tested. We find that both policy learning and value function learning successfully and accurately learn the optimal thrust and that a spacecraft employing the learned thrust is able to reach the target conditions orbit spending only 2 permil more propellant than in the corresponding mathematically optimal transfer. Moreover, the optimal propellant mass can be predicted (in case of value function learning) within an error well within 1%. All G&CNETs produced are tested during simulations of interplanetary transfers with respect to their ability to reach the target conditions optimally starting from nominal and off-nominal conditions.

cs.NE↗

arXiv2019

Aggressive Online Control of a Quadrotor via Deep Network Representations of Optimality Principles

Optimal control holds great potential to improve a variety of robotic applications. The application of optimal control on-board limited platforms has been severely hindered by the large computational requirements of current state of the art implementations. In this work, we make use of a deep neural network to directly map the robot states to control actions. The network is trained offline to imitate the optimal control computed by a time consuming direct nonlinear method. A mixture of time optimality and power optimality is considered with a continuation parameter used to select the predominance of each objective. We apply our networks (termed G\&CNets) to aggressive quadrotor control, first in simulation and then in the real world. We give insight into the factors that influence the `reality gap' between the quadrotor model used by the offline optimal control method and the real quadrotor. Furthermore, we explain how we set up the model and the control structure on-board of the real quadrotor to successfully close this gap and perform time-optimal maneuvers in the real world. Finally, G\&CNet's performance is compared to state-of-the-art differential-flatness-based optimal control methods. We show, in the experiments, that G\&CNets lead to significantly faster trajectory execution due to, in part, the less restrictive nature of the allowed state-to-input mappings.

cs.RO↗

arXiv2019

Super-Resolution of PROBA-V Images Using Convolutional Neural Networks

ESA's PROBA-V Earth observation satellite enables us to monitor our planet at a large scale, studying the interaction between vegetation and climate and provides guidance for important decisions on our common global future. However, the interval at which high resolution images are recorded spans over several days, in contrast to the availability of lower resolution images which is often daily. We collect an extensive dataset of both, high and low resolution images taken by PROBA-V instruments during monthly periods to investigate Multi Image Super-resolution, a technique to merge several low resolution images to one image of higher quality. We propose a convolutional neural network that is able to cope with changes in illumination, cloud coverage and landscape features which are challenges introduced by the fact that the different images are taken over successive satellite passages over the same region. Given a bicubic upscaling of low resolution images taken under optimal conditions, we find the Peak Signal to Noise Ratio of the reconstructed image of the network to be higher for a large majority of different scenes. This shows that applied machine learning has the potential to enhance large amounts of previously collected earth observation data during multiple satellite passes.

cs.CV↗

arXiv2019

Neural Network Architecture Search with Differentiable Cartesian Genetic Programming for Regression

The ability to design complex neural network architectures which enable effective training by stochastic gradient descent has been the key for many achievements in the field of deep learning. However, developing such architectures remains a challenging and resourceintensive process full of trial-and-error iterations. All in all, the relation between the network topology and its ability to model the data remains poorly understood. We propose to encode neural networks with a differentiable variant of Cartesian Genetic Programming (dCGPANN) and present a memetic algorithm for architecture design: local searches with gradient descent learn the network parameters while evolutionary operators act on the dCGPANN genes shaping the network architecture towards faster learning. Studying a particular instance of such a learning scheme, we are able to improve the starting feed forward topology by learning how to rewire and prune links, adapt activation functions and introduce skip connections for chosen regression tasks. The evolved network architectures require less space for network parameters and reach, given the same amount of time, a significantly lower error on average.

cs.NE↗

arXiv2019

Interplanetary Transfers via Deep Representations of the Optimal Policy and/or of the Value Function

A number of applications to interplanetary trajectories have been recently proposed based on deep networks. These approaches often rely on the availability of a large number of optimal trajectories to learn from. In this paper we introduce a new method to quickly create millions of optimal spacecraft trajectories from a single nominal trajectory. Apart from the generation of the nominal trajectory, no additional optimal control problems need to be solved as all the trajectories, by construction, satisfy Pontryagin's minimum principle and the relevant transversality conditions. We then consider deep feed forward neural networks and benchmark three learning methods on the created dataset: policy imitation, value function learning and value function gradient learning. Our results are shown for the case of the interplanetary trajectory optimization problem of reaching Venus orbit, with the nominal trajectory starting from the Earth. We find that both policy imitation and value function gradient learning are able to learn the optimal state feedback, while in the case of value function learning the optimal policy is not captured, only the final value of the optimal propellant mass is.

cs.NE↗

arXiv2019

Learning the optimal state-feedback via supervised imitation learning

Imitation learning is a control design paradigm that seeks to learn a control policy reproducing demonstrations from expert agents. By substituting expert demonstrations for optimal behaviours, the same paradigm leads to the design of control policies closely approximating the optimal state-feedback. This approach requires training a machine learning algorithm (in our case deep neural networks) directly on state-control pairs originating from optimal trajectories. We have shown in previous work that, when restricted to low-dimensional state and control spaces, this approach is very successful in several deterministic, non-linear problems in continuous-time. In this work, we refine our previous studies using as a test case a simple quadcopter model with quadratic and time-optimal objective functions. We describe in detail the best learning pipeline we have developed, that is able to approximate via deep neural networks the state-feedback map to a very high accuracy. We introduce the use of the softplus activation function in the hidden units of neural networks showing that it results in a smoother control profile whilst retaining the benefits of rectifiers. We show how to evaluate the optimality of the trained state-feedback, and find that already with two layers the objective function reached and its optimal value differ by less than one percent. We later consider also an additional metric linked to the system asymptotic behaviour - time taken to converge to the policy's fixed point. With respect to these metrics, we show that improvements in the mean absolute error do not necessarily correspond to better policies.

cs.LG↗

arXiv2019

On the stability analysis of deep neural network representations of an optimal state-feedback

Recent work have shown how the optimal state-feedback, obtained as the solution to the Hamilton-Jacobi-Bellman equations, can be approximated for several nonlinear, deterministic systems by deep neural networks. When imitation (supervised) learning is used to train the neural network on optimal state-action pairs, for instance as derived by applying Pontryagin's theory of optimal processes, the resulting model is referred here as the guidance and control network. In this work, we analyze the stability of nonlinear and deterministic systems controlled by such networks. We then propose a method utilising differential algebraic techniques and high-order Taylor maps to gain information on the stability of the neurocontrolled state trajectories. We exemplify the proposed methods in the case of the two-dimensional dynamics of a quadcopter controlled to reach the origin and we study how different architectures of the guidance and control network affect the stability of the target equilibrium point and the stability margins to time delay. Moreover, we show how to study the robustness to initial conditions of a nominal trajectory, using a Taylor representation of the neurocontrolled neighbouring trajectories.

cs.NE↗

arXiv2019

Deep Networks as Approximators of Optimal Transfers Solutions in Multitarget Missions

In the design of multitarget interplanetary missions, there are always many options available, making it often impractical to optimize in detail each transfer trajectory in a preliminary search phase. Fast and accurate estimation methods for optimal transfers are thus of great value. In this paper, deep feed-forward neural networks are employed to estimate solutions to three types of optimization problems: the transfer time of time-optimal low-thrust transfers, fuel consumption of fuel-optimal low-thrust transfers, and the total dv of minimum-dv J2-perturbed multi-impulse transfers. To generate the training data, low-thrust trajectories are optimized using the indirect method and J2-perturbed multi-impulse trajectories are optimized using J2 homotopy and particle swarm optimization. The hyper-parameters of our deep networks are searched by grid search, random search, and the tree-structured Parzen estimators approach. Results show that deep networks are capable of estimating the final mass or time of optimal transfers with extremely high accuracy; resulting into a mean relative error of less than 0.5% for low-thrust transfers and less than 4% for multi-impulse transfers. Our results are also compared with other off-the-shelf machine-learning algorithms and investigated with respect to their capability of predicting cases well outside of the training data.

math.OC↗

arXiv2018

A Survey on Artificial Intelligence Trends in Spacecraft Guidance Dynamics and Control

The rapid developments of Artificial Intelligence in the last decade are influencing Aerospace Engineering to a great extent and research in this context is proliferating. We share our observations on the recent developments in the area of Spacecraft Guidance Dynamics and Control, giving selected examples on success stories that have been motivated by mission designs. Our focus is on evolutionary optimisation, tree searches and machine learning, including deep learning and reinforcement learning as the key technologies and drivers for current and future research in the field. From a high-level perspective, we survey various scenarios for which these approaches have been successfully applied or are under strong scientific investigation. Whenever possible, we highlight the relations and synergies that can be obtained by combining different techniques and projects towards future domains for which newly emerging artificial intelligence techniques are expected to become game changers.

cs.NE↗

arXiv2018

Machine learning and evolutionary techniques in interplanetary trajectory design

After providing a brief historical overview on the synergies between artificial intelligence research, in the areas of evolutionary computations and machine learning, and the optimal design of interplanetary trajectories, we propose and study the use of deep artificial neural networks to represent, on-board, the optimal guidance profile of an interplanetary mission. The results, limited to the chosen test case of an Earth-Mars orbital transfer, extend the findings made previously for landing scenarios and quadcopter dynamics, opening a new research area in interplanetary trajectory planning.

cs.NE↗

arXiv2018

Target selection for a small low-thrust mission to near-Earth asteroids

The preliminary mission design of spacecraft missions to asteroids often involves, in the early phases, the selection of candidate target asteroids. The final result of such an analysis is a list of asteroids, ranked with respect to the necessary propellant to be used, that the spacecraft could potentially reach. In this paper we investigate the sensitivity of the produced asteroids rank to the employed trajectory model in the specific case of a small low-thrust propelled spacecraft beginning its journey from the Sun-Earth $L_2$ Lagrangian point and heading to a rendezvous with some near-Earth asteroid. We consider five increasingly complex trajectory models: impulsive, Lambert, nuclear electric propulsion, nuclear electric propulsion including the Earth's gravity, solar electric propulsion including the Earth's gravity and we study the final correlation between the obtained target rankings. We find that the use of a low-thrust trajectory model is of great importance for target selection, since the use of chemical propulsion surrogates leads to favouring less attractive options 19\% of times, a percentage that drops to 8\% already using a simple nuclear electric propulsion model that neglects the Earth's gravity effects and thrust dependence on the solar distance. We also find that for the study case considered, a small interplanetary CubeSat named M-ARGO, the inclusion of the Earth's gravity in the considered dynamics does not affect the target selection significantly.

astro-ph.EP↗

arXiv2017

Multi-rendezvous Spacecraft Trajectory Optimization with Beam P-ACO

The design of spacecraft trajectories for missions visiting multiple celestial bodies is here framed as a multi-objective bilevel optimization problem. A comparative study is performed to assess the performance of different Beam Search algorithms at tackling the combinatorial problem of finding the ideal sequence of bodies. Special focus is placed on the development of a new hybridization between Beam Search and the Population-based Ant Colony Optimization algorithm. An experimental evaluation shows all algorithms achieving exceptional performance on a hard benchmark problem. It is found that a properly tuned deterministic Beam Search always outperforms the remaining variants. Beam P-ACO, however, demonstrates lower parameter sensitivity, while offering superior worst-case performance. Being an anytime algorithm, it is then found to be the preferable choice for certain practical applications.

cs.NE↗