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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, utilizing consolidated tools in optimal control theory. The planned actions are derived on the ground and transferred onboard where controllers have the task of tracking the uploaded guidance profile. Here we argue that end-to-end neural guidance and control architectures (here called G&CNets) allow transferring onboard the burden of acting upon these optimality principles. In this way, the sensor information is transformed in real time into optimal plans thus increasing the mission autonomy and robustness. We discuss the main results obtained in training such neural architectures in simulation for interplanetary transfers, landings and close proximity operations, highlighting the successful learning of optimality principles by the neural model. We then suggest drone racing as an ideal gym environment to test these architectures on real robotic platforms, thus increasing confidence in their utilization on future space exploration missions. Drone racing shares with spacecraft missions both limited onboard computational capabilities and similar control structures induced from the optimality principle sought, but it also entails different levels of uncertainties and unmodelled effects. Furthermore, the success of G&CNets on extremely resource-restricted drones illustrates their potential to bring real-time optimal control within reach of a wider variety of robotic systems, both in space and on Earth.

Reaching fast and autonomous flight requires computationally efficient and robust algorithms. To this end, we train Guidance & Control Networks to approximate optimal control policies ranging from energy-optimal to time-optimal flight. We show that the policies become more difficult to learn the closer we get to the time-optimal 'bang-bang' control profile. We also assess the importance of knowing the maximum angular rotor velocity of the quadcopter and show that over- or underestimating this limit leads to less robust flight. We propose an algorithm to identify the current maximum angular rotor velocity onboard and a network that adapts its policy based on the identified limit. Finally, we extend previous work on Guidance & Control Networks by learning to take consecutive waypoints into account. We fly a 4x3m track in similar lap times as the differential-flatness-based minimum snap benchmark controller while benefiting from the flexibility that Guidance & Control Networks offer.

Developing optimal controllers for aggressive high-speed quadcopter flight poses significant challenges in robotics. Recent trends in the field involve utilizing neural network controllers trained through supervised or reinforcement learning. However, the sim-to-real transfer introduces a reality gap, requiring the use of robust inner loop controllers during real flights, which limits the network's control authority and flight performance. In this paper, we investigate for the first time, an end-to-end neural network controller, addressing the reality gap issue without being restricted by an inner-loop controller. The networks, referred to as G\&CNets, are trained to learn an energy-optimal policy mapping the quadcopter's state to rpm commands using an optimal trajectory dataset. In hover-to-hover flights, we identified the unmodeled moments as a significant contributor to the reality gap. To mitigate this, we propose an adaptive control strategy that works by learning from optimal trajectories of a system affected by constant external pitch, roll and yaw moments. In real test flights, this model mismatch is estimated onboard and fed to the network to obtain the optimal rpm command. We demonstrate the effectiveness of our method by performing energy-optimal hover-to-hover flights with and without moment feedback. Finally, we compare the adaptive controller to a state-of-the-art differential-flatness-based controller in a consecutive waypoint flight and demonstrate the advantages of our method in terms of energy optimality and robustness., 11 pages, 16 figures

Interpretable regression models are important for many application domains, as they allow experts to understand relations between variables from sparse data. Symbolic regression addresses this issue by searching the space of all possible free form equations that can be constructed from elementary algebraic functions. While explicit mathematical functions can be rediscovered this way, the determination of unknown numerical constants during search has been an often neglected issue. We propose a new multi-objective memetic algorithm that exploits a differentiable Cartesian Genetic Programming encoding to learn constants during evolutionary loops. We show that this approach is competitive or outperforms machine learned black box regression models or hand-engineered fits for two applications from space: the Mars express thermal power estimation and the determination of the age of stars by gyrochronology.

Numerical simulations are at the center of predicting the space debris environment of the upcoming decades. In light of debris generating events, such as continued anti-satellite weapon tests and planned mega-constellations, accurate predictions of the space debris environment are critical to ensure the long-term sustainability of critical satellite orbits. Given the computational complexity of accurate long-term trajectory propagation for a large number of particles, numerical models usually rely on Monte-Carlo approaches for stochastic conjunction assessment. On the other hand, deterministic methods bear the promise of higher accuracy and can serve to validate stochastic approaches. However, they pose a substantial challenge to computational feasibility. In this work, we present the architecture and proof of concept results for a numerical simulation capable of modeling the long term debris evolution over decades with a deterministic conjunction tracking model. For the simulation, we developed an efficient propagator in modern C++ accounting for Earth's gravitational anomalies, solar radiation pressure, and atmospheric drag. We utilized AutoPAS, a sophisticated particle container, which automatically selects the most efficient data structures and algorithms. We present results from a simulation of 16 024 particles in low-Earth orbit over 20 years. Overall, conjunctions are tracked for predicted collisions and close encounters to allow a detailed study of both. We analyze the runtime and computational cost of the simulation in detail. In summary, the obtained results show that modern computational tools finally enable deterministic conjunction tracking and can serve to validate prior results and build higher-fidelity numerical simulations of the long-term debris environment.

The term ``neuromorphic'' refers to systems that are closely resembling the architecture and/or the dynamics of biological neural networks. Typical examples are novel computer chips designed to mimic the architecture of a biological brain, or sensors that get inspiration from, e.g., the visual or olfactory systems in insects and mammals to acquire information about the environment. This approach is not without ambition as it promises to enable engineered devices able to reproduce the level of performance observed in biological organisms -- the main immediate advantage being the efficient use of scarce resources, which translates into low power requirements. The emphasis on low power and energy efficiency of neuromorphic devices is a perfect match for space applications. Spacecraft -- especially miniaturized ones -- have strict energy constraints as they need to operate in an environment which is scarce with resources and extremely hostile. In this work we present an overview of early attempts made to study a neuromorphic approach in a space context at the European Space Agency's (ESA) Advanced Concepts Team (ACT).

Asteroids and other small bodies in the solar system tend to have irregular shapes, owing to their low gravity. This irregularity does not only apply to the topology, but also to the underlying geology, potentially containing regions of different densities and materials. The topology can be derived from optical observations, while the mass density distribution of an object is only observable, to some extent, in its gravitational field. In a companion paper, we presented geodesyNets, a neural network approach to infer the mass density distribution of an object from measurements of its gravitational field. In the present work, we apply this approach to the asteroid Bennu using real data from the Osiris Rex mission. The mission measured the trajectories of not only the Osiris Rex spacecraft itself, but also of numerous pebble-sized rock particles which temporarily orbited Bennu. From these trajectory data, we obtain a representation of Bennu's mass density and validate it by propagating, in the resulting gravity field, multiple pebbles not used in the training process. The performance is comparable to that of a polyhedral gravity model of uniform density, but does not require a shape model. As little additional information is needed, we see this as a step towards autonomous on-board inversion of gravitational fields.

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.

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.

As organizers of the 9th edition of the Global Trajectory Optimization Competition we were tasked to design a challenging trajectory optimization problem to be solved during the duration of one month. We gave ourselves the goal to create a problem which was accessible enough for newcomers, deep enough for experts, unconventional in its objective function and which allowed for a real-time format of the competition. This document describes our design process from the initial idea up to the final form. We document some of our experiments conducted to learn about the solution landscape of an earlier simplified version of the problem and show how this exploration helped us in tuning the problem parameters to create a balanced and challenging task.

The eleventh issue of the Acta Futura Journal contains several contributions form the teams participating to the 9th edition of the Global Trajectory Competition, including the top teams and the organizers.

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.

The tenth issue of the Acta Futura Journal ison Space Architectures andpresents a selection of advanced concepts related to establishing an extra-terrestrial outpost.

Self-Supervised Learning (SSL) 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 SSL 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 SSL 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 stereo vision based flight to monocular flight, 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 AR drone 2.0 show the feasibility of this approach, with the robot successfully using monocular vision to avoid obstacles in a 5 x 5 room. The experiments show the potential of persistent SSL as a robust learning approach to enhance the capabilities of robots. Moreover, the abundant training data coming from the own sensors allows to gather large data sets necessary for deep learning approaches.

Paper given at Dynamics and Control of Systems and Structures in Space (DCSSS), 5th conference, Kings College, Cambridge, July 2002 An extension of the Hill-Clohessey-Wiltshire equations is presented. The equations refer to the relative motion of two satellites as seen by a Chief undergoing a circular Keplerian motion. Both the Earth oblateness and the air drag are included. The new set of equations is then used to study a simple 100m Leader-Follower formation in a near polar orbit at 600Km of altitude. As the system shows to be linear with time periodic coefficients, Floquet theory is used to determine the stability of the formation and the relative trajectory. Poincar exponents are also determined and discussed.

Autonomous navigation and robust obstacle avoidance are prerequisites for the successful operation of a planetary rover. Typical approaches to tackling this problem rely on complex and computationally expensive navigation strategies based upon the creation of 3D maps of the environment. In contrast, this research proposes a simple artificial neural network relying on infrared sensory input as the control structure. This paper presents a unified framework for designing such control structures for a simulated rover, taking advantage of code parallelisation and the latest advances in global optimisation research. In particular, it details a 3D physics-based simulation of a planetary rover and a tool set for performing the optimisation of ANN parameters within the island model. This paper also presents preliminary results showing that the aforementioned framework can parallelise the controller design process without any loss in performance over traditional methods, and will outline research directions, which aim to take full advantage of this technique's potential.