Local Frame Research Articles

Navigating stellar wobbles for imaging with the solar gravitational lens

The solar gravitational lens (SGL) offers unique capabilities for direct high-resolution imaging of faint, distant objects, such as exoplanets. For that purpose, in the near future, a spacecraft carrying a meter-class telescope with a solar coronagraph would be placed in the focal region of the SGL. That region begins at $\ensuremath{\sim}547$ astronomical units from the Sun and occupies the immediate vicinity of the target-specific primary optical axis---the line that connects the center of the target and that of the Sun. Clearly, this axis is not at rest. It undergoes complex motion as the exoplanet orbits its host star, as that star moves with respect to the Sun, and even as the Sun itself moves with respect to the Solar System's barycenter due to the gravitational pull of planets in our Solar System. Although less prominent, other motions exist. An image of an extended object is projected by the SGL into an image plane and moves within that plane, responding to the motion of the optical axis. To sample the image, a telescope must always be on the move, following the projection, with precise knowledge of its own position with respect to the image. We consider the dominant motions that determine the position of the focal line as a function of time. We evaluate the needed navigational capability for the telescope to conduct a multiyear exoplanet imaging mission in the focal region for the SGL. We show that even in a rather conservative case, when an Earth-like exoplanet is in our immediate stellar neighborhood at $\ensuremath{\sim}10$ light years, the motion of the image is characterized by a small total acceleration that is driven primarily by the orbital motion of the exoplanet (its effect on the projected image estimated to be at the level of $\ensuremath{\sim}6\text{ }\text{ }\ensuremath{\mu}{\mathrm{m}/\mathrm{s}}^{2}$, decreasing inversely with distance to a target) and by the reflex motion of our Sun (target independent, contributing at $\ensuremath{\sim}0.2\text{ }\text{ }\ensuremath{\mu}{\mathrm{m}/\mathrm{s}}^{2}$). We discuss how the amplified light of the host star allows us to establish a local reference frame that significantly relaxes navigational requirements for the imaging operations. We conclude that the required navigation in the SGL's focal region, although complex, can be accurately modeled, and a $\ensuremath{\sim}10$-year prospective imaging mission is achievable with the already available propulsion technology.

Learning Atomic Multipoles: Prediction of the Electrostatic Potential with Equivariant Graph Neural Networks.

The accurate description of electrostatic interactions remains a challenging problem for classical potential-energy functions. The commonly used fixed partial-charge approximation fails to reproduce the electrostatic potential at short range due to its insensitivity to conformational changes and anisotropic effects. At the same time, possibly more accurate machine-learned (ML) potentials struggle with the long-range behavior due to their inherent locality ansatz. Employing a multipole expansion offers in principle an exact treatment of the electrostatic potential such that the long-range and short-range electrostatic interactions can be treated simultaneously with high accuracy. However, such an expansion requires the calculation of the electron density using computationally expensive quantum-mechanical (QM) methods. Here, we introduce an equivariant graph neural network (GNN) to address this issue. The proposed model predicts atomic multipoles up to the quadrupole, circumventing the need for expensive QM computations. By using an equivariant architecture, the model enforces the correct symmetry by design without relying on local reference frames. The GNN reproduces the electrostatic potential of various systems with high fidelity. Possible uses for such an approach include the separate treatment of long-range interactions in ML potentials, the analysis of electrostatic potential surfaces, and static multipoles in polarizable force fields.

Cosmic-ray Transport in Magnetohydrodynamic Turbulence

Abstract This paper studies cosmic-ray (CR) transport in magnetohydrodynamic (MHD) turbulence. CR transport is strongly dependent on the properties of the magnetic turbulence. We perform test particle simulations to study the interactions of CR with both total MHD turbulence and decomposed MHD modes. The spatial diffusion coefficients and the pitch angle scattering diffusion coefficients are calculated from the test particle trajectories in turbulence. Our results confirm that the fast modes dominate the CR propagation, whereas Alfvén and slow modes are much less efficient and have shown similar pitch-angle scattering rates. We investigate the cross field transport on large and small scales. On large/global scales, normal diffusion is observed and the diffusion coefficient is suppressed by M A ζ compared to the parallel diffusion coefficients, with ζ closer to 4 in Alfvén modes than that in total turbulence, as theoretically expected. For the CR transport on scales smaller than the turbulence injection scale, both the local and global magnetic reference frames are adopted. Superdiffusion is observed on such small scales in all the cases. Particularly, CR transport in Alfvén modes show clear Richardson diffusion in the local reference frame. The diffusion transitions smoothly from the Richardson’s one with index 1.5 to normal diffusion as the particle mean free path decreases from λ ∥ ≫ L to λ ∥ ≪ L, where L is the injection/coherence length of turbulence. Our results have broad applications to CRs in various astrophysical environments.

Frames-of-Reference-Based Learning: Overcoming Perceptual Aliasing in Multistep Decision-Making Tasks

Perceptual aliasing challenges reinforcement learning agents. They struggle to learn stable policies by failing to identify and disambiguate perceptually identical states in the environment that require different actions to reach a goal. As the agent often has only a local frame of reference, it cannot represent the global environment. Frame-of-reference-based learning is a feature of vertebrate intelligence that allows multiple simultaneous representations of an environment at different levels of abstraction. This enables the resolution of patterns that are made up of patterns that are made up of features. The evolutionary computation technique of learning classifier systems has shown promise in learning nested patterns in single-step domains. This work uses the frame-of-reference concept within a learning classifier system to learn stable policies in non-Markov multistep domains. Considering aliased states at a constituent level enables the system to place them appropriately in holistic-level policies. Instead of enumerating a huge search space, evolution computation empowers the novel system to evolve fitter rules and policies. The experimental results show that the novel system effectively solves complex aliasing patterns in non-Markov environments that have been challenging to artificial agents. For example, the novel system utilizes only 6.5, 3.71, and 3.22 steps to resolve Maze10, Littman57, and Woods102, respectively.

Cooperative Fencing Control of Multiple Vehicles for a Moving Target With an Unknown Velocity

In this article, we investigate a moving-target-fencing problem for multiple vehicles using nearest neighbor rules where the target moves with an unknown constant velocity. Without a predefined stand-off distance or formation, two local cooperative controllers are proposed using only the relative position information from the target and its neighbors within its local frame of reference. The controllers consist of three functionalities. The repulsive term between a vehicle and its neighbors is used to avoid collision. The attractive term between a vehicle and the target drives the vehicle toward the target. The adaptive term amounts to estimate the target's velocity. Specifically, with the first controller, the vehicles follow the target's velocity in the average sense resulting in rotation about the target; with the second controller, each vehicle is able to follow the target's velocity resulting in a rigid formation. Furthermore, a decentralized estimator is applied to handle the case where only a portion of vehicles can access the target's position. Both controllers assure target fencing. The results are proved by rigorous theoretical analysis and verified by extensive numerical simulation.

Personalised gravitational loading of the cervical spine from biplanar X-rays for asymptomatic and clinical subjects in neutral standing position

BackgroundAs a leading cause of disability with a high societal and economic cost, it is crucial to better understand risk factors of neck pain and surgical complications. Getting subject-specific external loading is essential for quantifying muscle forces and joint loads but it requires exertion trials and load cells which are uncommon in clinical settings. MethodsThis paper presents a method to compute the gravitational loading at four levels of the cervical spine (C3C4, C4C5, C5C6, C6C7) in neutral standing position from biplanar radiographs exclusively. The resulting load was decomposed in local disc frames and its components were used to compare different populations: 118 asymptomatic subjects and 46 patients before and after surgery (anterior cervical discectomy and fusion or total disc replacement). Comparisons were performed at C6C7 and the upper level adjacent to surgery. FindingsSignificant changes in gravitational loading were observed with age in healthy subjects as well as in patients after surgery and have been associated with changes in posture. InterpretationThis approach quantifies the influence of postural changes on gravitational loading on the cervical spine. It represents a simple way to obtain necessary input for muscle force quantification models in clinical routine and to use them for patient evaluation. The study of the subsequent subject-specific spinal loading could help further the understanding of cervical spine biomechanics, degeneration mechanisms and complications following surgery.

The Motion Formalism for Flexible Multibody Systems

Abstract This paper describes a finite element approach to the analysis of flexible multibody systems. It is based on the motion formalism that (1) uses configuration and motion to describe the kinematics of flexible multibody systems, (2) recognizes that these are members of the special Euclidean group thereby coupling their displacement and rotation components, and (3) resolves all tensors components in local frames. The goal of this review paper is not to provide an in-depth derivation of all the elements found in typical multibody codes but rather to demonstrate how the motion formalism (1) provides a theoretical framework that unifies the formulation of all structural elements, (2) leads to governing equations of motion that are objective, intrinsic, and present a reduced order of nonlinearity, (3) improves the efficiency of the solution process, and (4) prevents the occurrence of singularities.

The LISA DFACS: Model Predictive Control design for the test mass release phase

This paper presents a Model Predictive Control (MPC) design for the test mass release phase of the LISA space mission. LISA is a gravitational wave observatory consisting of a triangular constellation of three spacecraft. The gravitational waves are detected by measuring the relative distance between free falling test masses by means of a laser interferometer. Each test mass is a cubic body located inside an electrostatic suspension that is initially locked by a clamp mechanism. Once the plungers are retracted, the test masses are released with high initial offsets and velocities. To detect the gravitational waves, each test mass must be accurately positioned at the cage centre and its attitude must be aligned with the local cage frame. However, the low actuation authority of the electrostatic suspension along with the critical initial conditions, make the attitude and translation control a difficult task. MPC is a suitable technique for this application because it can systematically account for command saturations, state constraints and can provide optimal (or sub-optimal) control inputs by solving an optimization problem online. In this paper, an MPC controller is designed and validated by means of Monte Carlo simulations, achieving satisfactory results.

Parametric investigation of the assembled bolt-connected buckling-restrained brace and performance evaluation of its application into structural retrofit

In this paper, the hysteresis performance of an assembled bolt-connected buckling-restrained brace (AB-BRB) is experimentally discussed by a parametric study, and five changing factors are selected to analyze the corresponding influence in static behaviors. The deformation modes of core plates are compared, the critical points of hysteresis curves are analyzed, and six static indices for hysteresis responses are assessed. Afterwards, the seismic evaluations of AB-BRB applied into structural retrofit are conducted, based on an aged 3-span-3-story and 5-span-10-story reinforced concrete frame. The numerical model is established and verified for both local AB-BRB and integral frame structure, and the simulation details as well as selection strategies are suggested during the process. The nonlinear time history analyses, incremental dynamic analyses and seismic fragility analyses are all performed, and three dynamic indices, three limit states, three fractile probabilities, three comparing conditions and two intensity levels are well discussed for assessment, before and after retrofitting, respectively. In general, the influences of shell thickness are less than shell height, and a larger gap clearance may transfer the deformation pattern into end-wave modes. Less bolt number may affect the assembly operation and global buckling capacity, which proves the effectiveness of bolt design equation in a sense. Bolt number contributes greatly to the macro hysteresis trends, and less tightening bolts may weaken the retraining property, accompanied with the bolt-slippage occurrence under huge vertical thrusts transferred from core plates. The seismic indices for each ground motion are below limitations and are more uniform with less discreteness after retrofitting with AB-BRB. The structural capacity can be guaranteed safely, and the damage degree of the integrated system can be controlled with the application of AB-BRB, illustrating the apparent retrofitting superiority in performance enhancement and providing reference for the follow-up research of AB-BRB in the earthquake-prone areas.

Quantum superposition of spacetimes obeys Einstein's equivalence principle

We challenge the view that there is a basic conflict between the fundamental principles of Quantum Theory and General Relativity and, in particular, the fact that a superposition of massive bodies would lead to a violation of the Equivalence Principle. It has been argued that this violation implies that such a superposition must inevitably spontaneously collapse (like in the Diósi–Penrose model). We identify the origin of such an assertion in the impossibility of finding a local and classical reference frame in which Einstein's Equivalence Principle would hold. In contrast, we argue that the formulation of the Equivalence Principle can be generalized so that it holds for reference frames that are associated with quantum systems in a superposition of spacetimes. The core of this new formulation is the introduction of a quantum diffeomorphism to such Quantum Reference Frames. This procedure reconciles the principle of linear superposition in Quantum Theory with the principle of general covariance and the Equivalence Principle of General Relativity. Hence, it is not necessary to invoke a gravity-induced spontaneous state reduction when a massive body is prepared in a spatial superposition.

‘Neutral’ Representations of Pacific Islands in the IPCC Special Report of 1.5°C Global Warming

ABSTRACT Pacific Islands are facing some of the most immediate and direct impacts of climate change. The Intergovernmental Panel on Climate Change (IPCC) Special Report of 1.5°C Global Warming (SR15) outlines the possibility that some low-lying atolls will become uninhabitable by 2030 and submerged by 2100. I analyse how and where SR15 presents climate change impacts for Pacific Islands. In doing so, I seek to highlight to what extent the IPCC’s structures and pressures influence SR15’s marginalisation of or emphasis on Pacific perspectives and challenges. The main findings that emerge from this discourse analysis are, first, that climate change impacts for Pacific Islands are largely conceptualised as relating to the physical environment and the economy. Second, SR15 frames Pacific Islands as vulnerable; however, it appears to be reflecting a shift in the literature toward recognising Pacific adaptation and resilience. The third finding is that the IPCC explicitly defines and acknowledges Indigenous and local knowledge but frames this knowledge as alternative to scientific expertise. I interpret these findings in the context of the underrepresentation of Pacific authors, the availability of published knowledge for assessment and the IPCC’s claims of neutrality. Pacific leaders and communities continue to advocate for the 1.5°C threshold investigated in SR15 and are mobilising IPCC assessments.

Relative Navigation and Terrain-based Path Planning using Flash LiDAR based Surfel Grid Map for Asteroid Exploration

Due to lack of spacecraft's global position and attitude information on small solar system bodies (SSSBs) like asteroids, only relative state measurements are available for navigation. Therefore, relative navigation with respect to a local reference frame is the basis for in-situ autonomous exploration on the asteroids. The relative navigation changes a local reference frame during the flight, which guarantees local accuracy of state estimation and mapping. We present the relative navigation framework using surfel grid map-based scan-to-map matching for localization and mapping on asteroid surface. We also propose a terrain-based path planning that makes use of inherent terrain surface properties of surfel grid maps. A thorough validation of our navigation approach and comparison to a global flash LiDAR-based navigation in different flight scenarios and in both MIL (model-in-the-loop) and real-time PIL (processor-in-the-loop) tests show the viability of this novel navigation framework.

R-PointHop: A Green, Accurate, and Unsupervised Point Cloud Registration Method.

Inspired by the recent PointHop classification method, an unsupervised 3D point cloud registration method, called R-PointHop, is proposed in this work. R-PointHop first determines a local reference frame (LRF) for every point using its nearest neighbors and finds local attributes. Next, R-PointHop obtains local-to-global hierarchical features by point downsampling, neighborhood expansion, attribute construction and dimensionality reduction steps. Thus, point correspondences are built in hierarchical feature space using the nearest neighbor rule. Afterwards, a subset of salient points with good correspondence is selected to estimate the 3D transformation. The use of the LRF allows for invariance of the hierarchical features of points with respect to rotation and translation, thus making R-PointHop more robust at building point correspondence, even when the rotation angles are large. Experiments are conducted on the 3DMatch, ModelNet40, and Stanford Bunny datasets, which demonstrate the effectiveness of R-PointHop for 3D point cloud registration. R-PointHop's model size and training time are an order of magnitude smaller than those of deep learning methods, and its registration errors are smaller, making it a green and accurate solution. Our codes are available on GitHub (https://github.com/pranavkdm/R-PointHop).

2-D Directed Formation Control Based on Bipolar Coordinates

This work proposes a novel 2-D formation control scheme for acyclic triangulated directed graphs (a class of minimally acyclic persistent graphs) based on bipolar coordinates with (almost) global convergence to the desired shape. Prescribed performance control is employed to devise a decentralized control law that avoids singularities and introduces robustness against external disturbances while ensuring predefined transient and steady-state performance for the closed-loop system. Furthermore, it is shown that the proposed formation control scheme can handle formation maneuvering, scaling, and orientation specifications simultaneously. Additionally, the proposed control law is implementable in agents' arbitrarily oriented local coordinate frames using only low-cost onboard vision sensors, which are favorable for practical applications. Finally, a formation maneuvering simulation study verifies the proposed approach.

Learning General and Distinctive 3D Local Deep Descriptors for Point Cloud Registration.

An effective 3D descriptor should be invariant to different geometric transformations, such as scale and rotation, robust to occlusions and clutter, and capable of generalising to different application domains. We present a simple yet effective method to learn general and distinctive 3D local descriptors that can be used to register point clouds that are captured in different domains. Point cloud patches are extracted, canonicalised with respect to their local reference frame, and encoded into scale and rotation-invariant compact descriptors by a deep neural network that is invariant to permutations of the input points. This design is what enables our descriptors to generalise across domains. We evaluate and compare our descriptors with alternative handcrafted and deep learning-based descriptors on several indoor and outdoor datasets that are reconstructed by using both RGBD sensors and laser scanners. Our descriptors outperform most recent descriptors by a large margin in terms of generalisation, and also become the state of the art in benchmarks where training and testing are performed in the same domain.

Three-Dimensional Anisotropy and Scaling Properties of Solar Wind Turbulence at Kinetic Scales in the Inner Heliosphere: Parker Solar Probe Observations

Abstract We utilize the data from the Parker Solar Probe mission at its first perihelion to investigate the three-dimensional (3D) anisotropies and scalings of solar wind turbulence for the total, perpendicular, and parallel magnetic-field fluctuations at kinetic scales in the inner heliosphere. By calculating the five-point second-order structure functions, we find that the three characteristic lengths of turbulence eddies for the total and the perpendicular magnetic-field fluctuations in the local reference frame ( L ˆ ⊥ , l ˆ ⊥ , l ˆ ∣ ∣ ) defined with respect to the local mean magnetic field B local feature as l ∣∣ > L ⊥ > l ⊥ in both the transition range and the ion-to-electron scales, but l ∣∣ > L ⊥ ≈ l ⊥ for the parallel magnetic-field fluctuations. For the total magnetic-field fluctuations, the wave-vector anisotropy scalings are characterized by l ∣ ∣ ∝ l ⊥ 0.78 and L ⊥ ∝ l ⊥ 1.02 in the transition range, and they feature as l ∣ ∣ ∝ l ⊥ 0.44 and L ⊥ ∝ l ⊥ 0.73 in the ion-to-electron scales. Still, we need more complete kinetic-scale turbulence models to explain all these observational results.

Analysis of Polar Region Navigation Algorithm of Laser Gyro Single-axis Rotation Modulation Inertial Navigation

In the polar regions, the local geographic frame will become invalid due to the convergence of meridians and other reasons. In response to this problem, the inertial navigation algorithm was reorganized in the transversal frame, and the error equation was also analyzed. The simulation experiment and actual experiment are carried out to verify the effectiveness of the inertial navigation algorithm in the transversal frame based on the single-axis rotation modulation inertial navigation system. Experimental results show that the transversal INS mechanization based on single-axis rotation modulation can solve the computational problems caused by the convergence of meridians in polar regions, achieving high-precision navigation.

A Novel 3-D Local DAISY-Style Descriptor to Reduce the Effect of Point Displacement Error in Point Cloud Registration

Three-dimensional (3-D) point clouds are widely considered for applications in different fields. Various methods have been proposed to generate point cloud data: LIDAR and image matching from static and mobile platforms, including, e.g., terrestrial laser scanning. With multiple point clouds from stationary platforms, point cloud registration is a crucial and fundamental issue. A standard approach is a point-based registration, which relies on pairs of corresponding points in two-point clouds. Therefore, a necessary step in point-based registration is the construction of 3-D local descriptors. One of the (many) challenges that will specifically affect the performance of local descriptors with local spatial information is the point displacement error. This error is caused by the difference in the distributions of points surrounding a (potentially) corresponding center point in the two-point clouds. It can occur for various reasons such as 1) distortions caused by the sensors recording the data, 2) moving objects, 3) varying density of point cloud, 4) change of viewing angle, and 5) different of the sensors. The purpose of this article is to develop a new 3-D local descriptor reducing the effect of this type of error in point cloud coarse registration. The approach includes an improved local reference frame and a new geometric arrangement in point cloud space for the 3-D local descriptor. Inspired by the 2-D DAISY descriptor, a geometric arrangement is created to reduce the effect of the point displacement error. in addition, directional histograms are considered as features. Investigations are performed for point clouds from challenging environments, which are publicly available. The results of this study show the high performance of the proposed approach for point cloud registration, especially in more challenging and noisy environments.

Instant Orientation Correction Strategy: Holonomic System-Based Decentralized Control for Nonholonomic Agents

This study proposes an instant orientation correction strategy to perform an orientation alignment-based formation control applicable to nonholonomic agents. Generally, an orientation alignment-based formation control cannot be applied to nonholonomic agents with orientation constraints because it is originally a protocol for holonomic agents. Therefore, we improved the orientation alignment-based formation control using an instant orientation correction strategy that modifies the local frame of the nonholonomic agents. To examine the effect of the proposed method, simulations and experiments using representative parameters were conducted for unicycle-modeled nonholonomic agents. As a result, nonholonomic agents could execute a holonomic system-based control law by applying the proposed correction strategy. The simulation confirmed the change in the convergence time and the cumulative error of the angular velocity according to the number of agents and the updated step size of the local desired position. As the updated step size increased, the cumulative error of the angular velocity tended to increase (0.3 rad/s~0.4rad/s). Also, the convergence time was not dramatically affected by the update step size and the number of the agents (~400 converge step).

Accurate Ground-Truth Depth Image Generation Via Overfit Training of Point Cloud Registration Using Local Frame Sets

Accurate Ground-Truth Depth Image Generation Via Overfit Training of Point Cloud Registration Using Local Frame Sets