Closing the Gap Between SGP4 and High-Precision Propagation via Differentiable Programming

The Simplified General Perturbations 4 (SGP4) orbital propagation method is widely used for predicting the positions and velocities of Earth-orbiting objects rapidly and reliably. Despite continuous refinement, SGP models still lack the precision of numerical propagators, which offer significantly smaller errors. This study presents dSGP4, a novel differentiable version of SGP4 implemented using PyTorch. By making SGP4 differentiable, dSGP4 facilitates various space-related applications, including spacecraft orbit determination, state conversion, covariance transformation, state transition matrix computation, and covariance propagation. Additionally, dSGP4's PyTorch implementation allows for embarrassingly parallel orbital propagation across batches of Two-Line Element Sets (TLEs), leveraging the computational power of CPUs, GPUs, and advanced hardware for distributed prediction of satellite positions at future times. Furthermore, dSGP4's differentiability enables integration with modern machine learning techniques. Thus, we propose a novel orbital propagation paradigm, ML-dSGP4, where neural networks are integrated into the orbital propagator. Through stochastic gradient descent, this combined model's inputs, outputs, and parameters can be iteratively refined, surpassing SGP4's precision. Neural networks act as identity operators by default, adhering to SGP4's behavior. However, dSGP4's differentiability allows fine-tuning with ephemeris data, enhancing precision while maintaining computational speed. This empowers satellite operators and researchers to train the model using specific ephemeris or high-precision numerical propagation data, significantly advancing orbital prediction capabilities.

End-to-end Reinforcement Learning for Time-Optimal Quadcopter Flight

Aggressive time-optimal control of quadcopters poses a significant challenge in the field of robotics. The state-of-the-art approach leverages reinforcement learning (RL) to train optimal neural policies. However, a critical hurdle is the sim-to-real gap, often addressed by employing a robust inner loop controller -an abstraction that, in theory, constrains the optimality of the trained controller, necessitating margins to counter potential disturbances. In contrast, our novel approach introduces high-speed quadcopter control using end-to-end RL (E2E) that gives direct motor commands. To bridge the reality gap, we incorporate a learned residual model and an adaptive method that can compensate for modeling errors in thrust and moments. We compare our E2E approach against a state-of-the-art network that commands thrust and body rates to an INDI inner loop controller, both in simulated and real-world flight. E2E showcases a significant 1.39-second advantage in simulation and a 0.17-second edge in real-world testing, highlighting end-to-end reinforcement learning's potential. The performance drop observed from simulation to reality shows potential for further improvement, including refining strategies to address the reality gap or exploring offline reinforcement learning with real flight data.

Tracking Particles Ejected From Active Asteroid Bennu With Event-Based Vision

Early detection and tracking of ejecta in the vicinity of small solar system bodies is crucial to guarantee spacecraft safety and support scientific observation. During the visit of active asteroid Bennu, the OSIRIS-REx spacecraft relied on the analysis of images captured by onboard navigation cameras to detect particle ejection events, which ultimately became one of the mission's scientific highlights. To increase the scientific return of similar time-constrained missions, this work proposes an event-based solution that is dedicated to the detection and tracking of centimetre-sized particles. Unlike a standard frame-based camera, the pixels of an event-based camera independently trigger events indicating whether the scene brightness has increased or decreased at that time and location in the sensor plane. As a result of the sparse and asynchronous spatiotemporal output, event cameras combine very high dynamic range and temporal resolution with low-power consumption, which could complement existing onboard imaging techniques. This paper motivates the use of a scientific event camera by reconstructing the particle ejection episodes reported by the OSIRIS-REx mission in a photorealistic scene generator and in turn, simulating event-based observations. The resulting streams of spatiotemporal data support future work on event-based multi-object tracking.

Small Celestial Body Exploration with CubeSat Swarms

This work presents a large-scale simulation study investigating the deployment and operation of distributed swarms of CubeSats for interplanetary missions to small celestial bodies. Utilizing Taylor numerical integration and advanced collision detection techniques, we explore the potential of large CubeSat swarms in capturing gravity signals and reconstructing the internal mass distribution of a small celestial body while minimizing risks and Delta V budget. Our results offer insight into the applicability of this approach for future deep space exploration missions.

On the Generation of a Synthetic Event-Based Vision Dataset for Navigation and Landing

An event-based camera outputs an event whenever a change in scene brightness of a preset magnitude is detected at a particular pixel location in the sensor plane. The resulting sparse and asynchronous output coupled with the high dynamic range and temporal resolution of this novel camera motivate the study of event-based cameras for navigation and landing applications. However, the lack of real-world and synthetic datasets to support this line of research has limited its consideration for onboard use. This paper presents a methodology and a software pipeline for generating event-based vision datasets from optimal landing trajectories during the approach of a target body. We construct sequences of photorealistic images of the lunar surface with the Planet and Asteroid Natural Scene Generation Utility at different viewpoints along a set of optimal descent trajectories obtained by varying the boundary conditions. The generated image sequences are then converted into event streams by means of an event-based camera emulator. We demonstrate that the pipeline can generate realistic event-based representations of surface features by constructing a dataset of 500 trajectories, complete with event streams and motion field ground truth data. We anticipate that novel event-based vision datasets can be generated using this pipeline to support various spacecraft pose reconstruction problems given events as input, and we hope that the proposed methodology would attract the attention of researchers working at the intersection of neuromorphic vision and guidance navigation and control.

Investigation of the Robustness of Neural Density Fields

Recent advances in modeling density distributions, so-called neural density fields, can accurately describe the density distribution of celestial bodies without, e.g., requiring a shape model - properties of great advantage when designing trajectories close to these bodies. Previous work introduced this approach, but several open questions remained. This work investigates neural density fields and their relative errors in the context of robustness to external factors like noise or constraints during training, like the maximal available gravity signal strength due to a certain distance exemplified for 433 Eros and 67P/Churyumov-Gerasimenko. It is found that both models trained on a polyhedral and mascon ground truth perform similarly, indicating that the ground truth is not the accuracy bottleneck. The impact of solar radiation pressure on a typical probe affects training neglectable, with the relative error being of the same magnitude as without noise. However, limiting the precision of measurement data by applying Gaussian noise hurts the obtainable precision. Further, pretraining is shown as practical in order to speed up network training. Hence, this work demonstrates that training neural networks for the gravity inversion problem is appropriate as long as the gravity signal is distinguishable from noise. Code and results are available at https://github.com/gomezzz/geodesyNets

Optimality Principles in Spacecraft Neural Guidance and Control

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.

Guidance & Control Networks for Time-Optimal Quadcopter Flight

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.

An Adaptive Control Strategy for Neural Network based Optimal Quadcopter Controllers

Developing optimal controllers for aggressive high-speed quadcopter flight is a major challenge in the field of robotics. Recent work has shown that neural networks trained with supervised learning can achieve real-time optimal control in some specific scenarios. In these methods, the networks (termed G&CNets) are trained to learn the optimal state feedback from a dataset of optimal trajectories. An important problem with these methods is the reality gap encountered in the sim-to-real transfer. In this work, we trained G&CNets for energy-optimal end-to-end control on the Bebop drone and identified the unmodeled pitch moment as the main 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.