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This Review discusses the main results obtained in training end-to-end neural architectures for guidance and control of interplanetary transfers, planetary landings, and close-proximity operations, highlighting the successful learning of optimality principles by the underlying neural models. Spacecraft and drones aimed at exploring our solar system are designed to operate in conditions where the smart use of onboard resources is vital to the success or failure of the mission. Sensorimotor actions are thus often derived from high-level, quantifiable, optimality principles assigned to each task, using consolidated tools in optimal control theory. The planned actions are derived on the ground and transferred on board, where controllers have the task of tracking the uploaded guidance profile. Here, we review recent trends based on the use of end-to-end networks, called guidance and control networks (G&CNets), which allow spacecraft to depart from such an architecture and to embrace the onboard computation of optimal actions. In this way, the sensor information is transformed in real time into optimal plans, thus increasing mission autonomy and robustness. We then analyze drone racing as an ideal gym environment to test these architectures on real robotic platforms and thus increase confidence in their use in future space exploration missions. Drone racing not only shares with spacecraft missions both limited onboard computational capabilities and similar control structures induced from the optimality principle sought but also entails different levels of uncertainties and unmodeled effects and a very different dynamical timescale. [ABSTRACT FROM AUTHOR]

We present a novel approach for the detection of events in systems of ordinary differential equations. The new method combines the unique features of Taylor integrators with state-of-the-art polynomial root finding techniques to yield a novel algorithm, ensuring strong event detection guarantees at a modest computational overhead. Detailed tests and benchmarks focused on problems in astrodynamics and celestial mechanics (such as collisional N -body systems, spacecraft dynamics around irregular bodies accounting for eclipses, computation of Poincaré sections, etc.) show how our approach is superior in both performance and detection accuracy to strategies commonly employed in modern numerical integration works. The new algorithm is available in our open source Taylor integration package heyoka. [ABSTRACT FROM AUTHOR]

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 specialized 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 time-scales. 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. [ABSTRACT FROM AUTHOR]

Recent works have shown that the optimal state feedback for deterministic, nonlinear autonomous systems can be approximated by deep neural networks. In this article, we consider the stability of nonlinear systems controlled by such a network representation of the optimal feedback. First, we show that principal methods from stability theory readily applies. We then propose a novel method based on differential algebra techniques to study the robustness of a nominal trajectory with respect to perturbations of the initial conditions. It is, to the best of our knowledge, the first time that differential algebraic techniques are shown to allow for the high-order analysis of motion stability for a nonlinear system in general and for a neurocontrolled system in particular. We exemplify the proposed method in the 2-D case of the optimal control of a quadcopter and demonstrate it for different neural network architectures. [ABSTRACT FROM AUTHOR]

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 article 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 article briefly reviews the basic properties and the collection process of the dataset that 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 article 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. [ABSTRACT FROM AUTHOR]

Self-supervised learning is a reliable learning mechanism in which a robot uses an original, trusted sensor cue for training to recognize an additional, complementary sensor cue. We study for the first time in self-supervised learning how a robot’s learning behavior should be organized, so that the robot can keep performing its task in the case that the original cue becomes unavailable. We study this persistent form of self-supervised learning in the context of a flying robot that has to avoid obstacles based on distance estimates from the visual cue of stereo vision. Over time it will learn to also estimate distances based on monocular appearance cues. A strategy is introduced that has the robot switch from flight based on stereo to flight based on monocular vision, with stereo vision purely used as “training wheels” to avoid imminent collisions. This strategy is shown to be an effective approach to the “feedback-induced data bias” problem as also experienced in learning from demonstration. Both simulations and real-world experiments with a stereo vision equipped ARDrone2 show the feasibility of this approach, with the robot successfully using monocular vision to avoid obstacles in a 5 × 5 m room. The experiments show the potential of persistent self-supervised learning as a robust learning approach to enhance the capabilities of robots. Moreover, the abundant training data coming from the own sensors allow to gather large data sets necessary for deep learning approaches. [ABSTRACT FROM AUTHOR]

We analyse active space debris removal efforts from a strategic, game-theoretical perspective. Space debris is non-manoeuvrable, human-made objects orbiting Earth, which pose a significant threat to operational spacecraft. Active debris removal missions have been considered and investigated by different space agencies with the goal to protect valuable assets present in strategic orbital environments. An active debris removal mission is costly, but has a positive effect for all satellites in the same orbital band. This leads to a dilemma: each agency is faced with the choice between the individually costly action of debris removal, which has a positive impact on all players; or wait and hope that others jump in and do the 'dirty' work. The risk of the latter action is that, if everyone waits, the joint outcome will be catastrophic, leading to what in game theory is referred to as the 'tragedy of the commons'. We introduce and thoroughly analyse this dilemma using empirical game theory and a space debris simulator. We consider two- and three-player settings, investigate the strategic properties and equilibria of the game and find that the cost/benefit ratio of debris removal strongly affects the game dynamics. [ABSTRACT FROM AUTHOR]

We present for the first time an explicit, complete and closed-form solution to the threedimensional problem of two fixed centres, based onWeierstrass elliptic and related functions. With respect to previous treatments of the problem, our solution is exact, valid for all initial conditions and physical parameters of the system (including unbounded orbits and repulsive forces), and expressed via a unique set of formulae.Various properties of the three-dimensional problem of two fixed centres are investigated and analysed, with a particular emphasis on quasi-periodic and periodic orbits, regions of motion and equilibrium points. [ABSTRACT FROM AUTHOR]

Tragopogon pratensis is a small herbaceous plant that uses wind as the dispersal vector for its seeds. The seeds are attached to parachutes that increase the aerodynamic drag force and increase the total distance travelled. Our hypothesis is that evolution has carefully tuned the air permeability of the seeds to operate in the most convenient fluid dynamic regime. To achieve final permeability, the primary and secondary fibres of the pappus have evolved with complex weaving; this maximises the drag force (i.e., the drag coefficient), and the pappus operates in an “optimal” state. We used computational fluid dynamics (CFD) simulations to compute the seed drag coefficient and compare it with data obtained from drop experiments. The permeability of the parachute was estimated from microscope images. Our simulations reveal three flow regimes in which the parachute can operate according to its permeability. These flow regimes impact the stability of the parachute and its drag coefficient. From the permeability measurements and drop experiments, we show how the seeds operate very close to the optimal case. The porosity of the textile appears to be an appropriate solution to achieve a lightweight structure that allows a low terminal velocity, a stable flight and a very efficient parachute for the velocity at which it operates. [ABSTRACT FROM AUTHOR]

Two bioinspired landing strategies are studied. Both strategies enforce a constant ventral optic flow with constantly decreasing time-to-contact or exponentially decreasing time-to-contact. Until now these strategies have only been studied assuming the visual quantities to be known, i.e., without sensor noise and delay. In this study, the control laws executing the aforementioned landing strategies are studied both theoretically and empirically, taking into account the actual extraction of the visual cues from images. [ABSTRACT FROM AUTHOR]

The orbital boundary value problem, also known as Lambert problem, is revisited. Building upon Lancaster and Blanchard approach, new relations are revealed and a new variable representing all problem classes, under L-similarity, is used to express the time of flight equation. In the new variable, the time of flight curves have two oblique asymptotes and they mostly appear to be conveniently approximated by piecewise continuous lines. We use and invert such a simple approximation to provide an efficient initial guess to an Householder iterative method that is then able to converge, for the single revolution case, in only two iterations. The resulting algorithm is compared, for single and multiple revolutions, to Gooding's procedure revealing to be numerically as accurate, while having a significantly smaller computational complexity. [ABSTRACT FROM AUTHOR]

We propose and study a decentralized formation flying control architecture based on the evolutionary robotic technique. We develop our control architecture for the MIT SPHERES robotic platform on board the International Space Station and we show how it is able to achieve micrometre and microradians precision at the path planning level. Our controllers are homogeneous across satellites and do not make use of labels (i.e. all satellites can be exchanged at any time). The evolutionary process is able to produce homogeneous controllers able to plan, with high precision, for the acquisition and maintenance of any triangular formation. [ABSTRACT FROM AUTHOR]

A multi-objective problem is addressed consisting of finding optimal low-thrust gravity-assist trajectories for interplanetary and orbital transfers. For this, recently developed pruning techniques for incremental search space reduction - which will be extended for the current situation - in combination with subdivision techniques for the approximation of the entire solution set, the so-called Pareto set, are used. Subdivision techniques are particularly promising for the numerical treatment of these multi-objective design problems since they are characterized (amongst others) by highly disconnected feasible domains, which can easily be handled by these set oriented methods. The complexity of the novel pruning techniques is analysed, and finally the usefulness of the novel approach is demonstrated by showing some numerical results for two realistic cases. [ABSTRACT FROM AUTHOR]

We investigate upon the change of an asteroid orbit caused by an impact. We find that, given the assumption of two dimensional motion, the asteroid displacement may be described by an analytic and explicit expression that is the vectorial sum of a radial component and a component along the asteroid velocity. The new formulation bridges the gap between the study of short-term effects, using numerical methods and the analytic study of secular changes of the asteroid orbit. The relation of the method to the established formulations is described and the known results are derived as limiting cases.The application of the new method for the performance evaluation of an asteroid deflection demonstration mission is illustrated. In such a mission the measurement of the change of the asteroid orbit by an impact will be conducted by radio-ranging to a spacecraft orbiting the deflected asteroid. Hence the measurement will primarily be sensitive to the deflection projected onto the Earth-asteroid line of sight. We discuss how the new formulation of the deflection can conveniently be employed for the estimation of the measurement accuracy and the optimal planning of a deflection demonstration mission. [ABSTRACT FROM PUBLISHER]

Roger Walker and colleagues consider the potential for sending nanospacecraft into deep space. [ABSTRACT FROM AUTHOR]