Abstract-- Accurate estimation of the relative attitude and angular velocity between two rigid bodies is fundamental in aerospace applications such as spacecraft rendezvous and docking. In these scenarios, a chaser vehicle must determine the orientation and angular velocity of a target object using onboard sensors. This work addresses the challenge of designing an Equivariant Filter (EqF) that can reliably estimate both the relative attitude and the target's angular velocity using noisy observations of two known, non-collinear vectors fixed in the target frame. T o derive the EqF, a symmetry for the system is proposed and an equivariant lift onto the symmetry group is calculated. Observability and convergence properties are analyzed. Simulations demonstrate the filter's performance, with Monte Carlo runs yielding statistically significant results. The impact of low-rate measurements is also examined and a strategy to mitigate this effect is proposed. I. INTRODUCTION In the past decade, there has been a growing interest in the development and validation of On-Orbit Servicing (OOS) and Active Debris Removal (ADR) technologies [1], [2], [3], driven by the ever-increasing number of satellites deployed each year. In OOS and ADR missions, the chaser or servicer spacecraft will need to approach the target spacecraft and synchronize its motion before performing the planned operations. As such, the chaser must estimate the relative attitude and angular velocity of the target, as well as the relative position and linear velocity.

Abstract-- The manifold extended Kalman filter (Manifold EKF) has found extensive application for attitude determination. Magnetometers employed as sensors for such attitude determination are easily prone to disturbances by their sensitivity to calibration and external magnetic fields. The TRIAD (Tri-Axial Attitude Determination) algorithm is well-known as a sub-optimal attitude estimator . In this article, we incorporate this sub-optimal feature of the TRIAD in mitigating the influence of the magnetometer reading in the pitch and roll axis determination in the Manifold EKF algorithm. We substantiate our results with experiments. Accurate orientation estimation is critical for a wide range of applications, such as in Unmanned Aerial V ehicles (UA Vs), mobile devices and robotics. Numerous studies have been dedicated to improving sensor orientation estimation.

The real-world application of small drones is mostly hampered by energy limitations. Neuromorphic computing promises extremely energy-efficient AI for autonomous flight, but is still challenging to train and deploy on real robots. In order to reap the maximal benefits from neuromorphic computing, it is desired to perform all autonomy functions end-to-end on a single neuromorphic chip, from low-level attitude control to high-level navigation. This research presents the first neuromorphic control system using a spiking neural network (SNN) to effectively map a drone's raw sensory input directly to motor commands. We apply this method to low-level attitude estimation and control for a quadrotor, deploying the SNN on a tiny Crazyflie. We propose a modular SNN, separately training and then merging estimation and control sub-networks. The SNN is trained with imitation learning, using a flight dataset of sensory-motor pairs. Post-training, the network is deployed on the Crazyflie, issuing control commands from sensor inputs at $500$Hz. Furthermore, for the training procedure we augmented training data by flying a controller with additional excitation and time-shifting the target data to enhance the predictive capabilities of the SNN. On the real drone the perception-to-control SNN tracks attitude commands with an average error of $3$ degrees, compared to $2.5$ degrees for the regular flight stack. We also show the benefits of the proposed learning modifications for reducing the average tracking error and reducing oscillations. Our work shows the feasibility of performing neuromorphic end-to-end control, laying the basis for highly energy-efficient and low-latency neuromorphic autopilots.

This paper introduces a Transformer-Enhanced Physics-Informed Neural Network (TE-PINN) designed for accurate quaternion-based orientation estimation in high-dynamic environments, particularly within the field of robotics. By integrating transformer networks with physics-informed learning, our approach innovatively captures temporal dependencies in sensor data while enforcing the fundamental physical laws governing rotational motion. TE-PINN leverages a multi-head attention mechanism to handle sequential data from inertial sensors, such as accelerometers and gyroscopes, ensuring temporal consistency. Simultaneously, the model embeds quaternion kinematics and rigid body dynamics into the learning process, aligning the network's predictions with mechanical principles like Euler's laws of motion. The physics-informed loss function incorporates the dynamics of angular velocity and external forces, enhancing the network's ability to generalize in complex scenarios. Our experimental evaluation demonstrates that TE-PINN consistently outperforms traditional methods such as Extended Kalman Filters (EKF) and LSTM-based estimators, particularly in scenarios characterized by high angular velocities and noisy sensor data. The results show a significant reduction in mean quaternion error and improved gyroscope bias estimation compared to the state-of-the-art. An ablation study further isolates the contributions of both the transformer architecture and the physics-informed constraints, highlighting the synergistic effect of both components in improving model performance. The proposed model achieves real-time performance on embedded systems typical of mobile robots, offering a scalable and efficient solution for orientation estimation in autonomous systems.

As satellites become smaller, the ability to maintain stable pointing decreases as external forces acting on the satellite come into play. At the same time, reaction wheels used in the attitude determination and control system (ADCS) introduce high frequency jitter which can disrupt pointing stability. For space domain awareness (SDA) tasks that track objects tens of thousands of kilometres away, the pointing accuracy offered by current nanosats, typically in the range of 10 to 100 arcseconds, is not sufficient. In this work, we develop a novel payload that utilises a neuromorphic event sensor (for high frequency and highly accurate relative attitude estimation) paired in a closed loop with a piezoelectric stage (for active attitude corrections) to provide highly stable sensor-specific pointing. Event sensors are especially suited for space applications due to their desirable characteristics of low power consumption, asynchronous operation, and high dynamic range. We use the event sensor to first estimate a reference background star field from which instantaneous relative attitude is estimated at high frequency. The piezoelectric stage works in a closed control loop with the event sensor to perform attitude corrections based on the discrepancy between the current and desired attitude. Results in a controlled setting show that we can achieve a pointing accuracy in the range of 1-5 arcseconds using our novel payload at an operating frequency of up to 50Hz using a prototype built from commercial-off-the-shelf components. Further details can be found at https://ylatif.github.io/ultrafinestabilisation

This paper presents a novel end-to-end deep learning framework for real-time inertial attitude estimation using 6DoF IMU measurements. Inertial Measurement Units are widely used in various applications, including engineering and medical sciences. However, traditional filters used for attitude estimation suffer from poor generalization over different motion patterns and environmental disturbances. To address this problem, we propose two deep learning models that incorporate accelerometer and gyroscope readings as inputs. These models are designed to be generalized to different motion patterns, sampling rates, and environmental disturbances. Our models consist of convolutional neural network layers combined with Bi-Directional Long-Short Term Memory followed by a Fully Forward Neural Network to estimate the quaternion. We evaluate the proposed method on seven publicly available datasets, totaling more than 120 hours and 200 kilometers of IMU measurements. Our results show that the proposed method outperforms state-of-the-art methods in terms of accuracy and robustness. Additionally, our framework demonstrates superior generalization over various motion characteristics and sensor sampling rates. Overall, this paper provides a comprehensive and reliable solution for real-time inertial attitude estimation using 6DoF IMUs, which has significant implications for a wide range of applications.

Inertial-based navigation refers to the navigation methods or systems that have inertial information or sensors as the core part and integrate a spectrum of other kinds of sensors for enhanced performance. Through a series of papers, the authors attempt to explore information blending of inertial-based navigation by a polynomial optimization method. The basic idea is to model rigid motions as finite-order polynomials and then attacks the involved navigation problems by optimally solving their coefficients, taking into considerations the constraints posed by inertial sensors and others. In the current paper, a continuous-time attitude estimation approach is proposed, which transforms the attitude estimation into a constant parameter determination problem by the polynomial optimization. Specifically, the continuous attitude is first approximated by a Chebyshev polynomial, of which the unknown Chebyshev coefficients are determined by minimizing the weighted residuals of initial conditions, dynamics and measurements. We apply the derived estimator to the attitude estimation with the magnetic and inertial sensors. Simulation and field tests show that the estimator has much better stability and faster convergence than the traditional extended Kalman filter does, especially in the challenging large initial state error scenarios.

Compelling evidence has been given for the high energy efficiency and update rates of neuromorphic processors, with performance beyond what standard Von Neumann architectures can achieve. Such promising features could be advantageous in critical embedded systems, especially in robotics. To date, the constraints inherent in robots (e.g., size and weight, battery autonomy, available sensors, computing resources, processing time, etc.), and particularly in aerial vehicles, severely hamper the performance of fully-autonomous on-board control, including sensor processing and state estimation. In this work, we propose a spiking neural network (SNN) capable of estimating the pitch and roll angles of a quadrotor in highly dynamic movements from 6-degree of freedom Inertial Measurement Unit (IMU) data. With only 150 neurons and a limited training dataset obtained using a quadrotor in a real world setup, the network shows competitive results as compared to state-of-the-art, non-neuromorphic attitude estimators. The proposed architecture was successfully tested on the Loihi neuromorphic processor on-board a quadrotor to estimate the attitude when flying. Our results show the robustness of neuromorphic attitude estimation and pave the way towards energy-efficient, fully autonomous control of quadrotors with dedicated neuromorphic computing systems.

In disaster-stricken environments, it's vital to assess the damage quickly, analyse the stability of the environment, and allocate resources to the most vulnerable areas where victims might be present. These missions are difficult and dangerous to be conducted directly by humans. Using the complementary capabilities of both the ground and aerial robots, we investigate a collaborative approach of aerial and ground robots to address this problem. With an increased field of view, faster speed, and compact size, the aerial robot explores the area and creates a 3D feature-based map graph of the environment while providing a live video stream to the ground control station. Once the aerial robot finishes the exploration run, the ground control station processes the map and sends it to the ground robot. The ground robot, with its higher operation time, static stability, payload delivery and tele-conference capabilities, can then autonomously navigate to identified high-vulnerability locations. We have conducted experiments using a quadcopter and a hexapod robot in an indoor modelled environment with obstacles and uneven ground. Additionally, we have developed a low-cost drone add-on with value-added capabilities, such as victim detection, that can be attached to an off-the-shelf drone. The system was assessed for cost-effectiveness, energy efficiency, and scalability.

This paper presents a lightweight, efficient calibration neural network model for denoising low-cost microelectromechanical system (MEMS) gyroscope and estimating the attitude of a robot in real-time. The key idea is extracting local and global features from the time window of inertial measurement units (IMU) measurements to regress the output compensation components for the gyroscope dynamically. Following a carefully deduced mathematical calibration model, LGC-Net leverages the depthwise separable convolution to capture the sectional features and reduce the network model parameters. The Large kernel attention is designed to learn the long-range dependencies and feature representation better. The proposed algorithm is evaluated in the EuRoC and TUM-VI datasets and achieves state-of-the-art on the (unseen) test sequences with a more lightweight model structure. The estimated orientation with our LGC-Net is comparable with the top-ranked visual-inertial odometry systems, although it does not adopt vision sensors. We make our method open-source at: https://github.com/huazai665/LGC-Net