Relative Position Error Research Articles

Attitude-Orbit Coupled Control of Gravitational Wave Detection Spacecraft with Communication Delays

In order to meet the position and attitude requirements of spacecrafts and test masses for gravitational-wave detection missions, the attitude-orbit coordination control of multiple spacecrafts and test masses is studied. A distributed coordination control law for spacecraft formation based on dual quaternion is proposed. By describing the relationship between spacecrafts and test masses in the desired states, the coordination control problem is converted into a consistent-tracking control problem in which each spacecraft or test mass tracks its desired states. An accurate attitude-orbit relative dynamics model of the spacecraft and the test masses is proposed based on dual quaternions. A cooperative feedback control law based on a consistency algorithm is designed to achieve the consistent attitude tracking of multiple rigid bodies (spacecraft and test mass) and maintain the specific formation configuration. Moreover, the communication delays of the system are taken into account. The distributed coordination control law ensures almost global asymptotic convergence of the relative position and attitude error in the presence of communication delays. The simulation results demonstrate the effectiveness of the proposed control method, which meets the formation-configuration requirements for gravitational-wave detection missions.

Analysis of Strain Transfer in FBG-Based Embedded Optical Fiber 3-D Shape Sensor

The FBG-based embedded optical fiber 3-D shape sensor (FBG-EOFSS) composed of several different materials finds potential applications in various industrial and medical applications. The strain loss during the strain transfer affects the change of the fiber Bragg grating (FBG) sensor’s wavelength, which in turn deteriorates the position accuracy. In this article, first, we analyzed the strain transfer in FBG-EOFSS and derived the optical–mechanical transformation equation. Then, a strain transfer model combining mechanics, materials, and optics is developed based on the finite-element analysis (FEA) method. The FEA simulation results show that the strain transfer rate decreases by 27.7%/mm with the increase of the adhesive thickness under FBG. The optimal average strain transfer rate is about 0.97 when the elastic modulus of the adhesive is in the range of 109–1014 Pa. Moreover, the effect of the strain transfer on the position accuracy is analyzed. The relative position error of 3-D shape reconstruction increases by 8.4% with the strain transfer rate decreasing by 10%. Finally, an experimental system composed of the clamp, the displacement stage, and the FBG demodulator is developed. The strain sensitivity coefficients of bare FBGs and FBG sensors were tested quantitatively. The corresponding average strain transfer rate was calculated by the strain sensitivity coefficients. The results can potentially conduce to the design of 3-D shape sensors and improve the positioning accuracy.

Multi-frequency complex conductivity sparse imaging of plant root zone based on space-frequency correlation

The root zone provides indispensable water and nutrients for plants and monitoring the dynamics of the root zone is highly important. However, due to the opacity and complexity of this zone, in situ characterization of the root zone poses many challenges. A sparse Bayesian learning complex model based on spatial frequency correlation (SF-SBLC) was proposed for fast nondestructive imaging of the growth trends in the root zone of plants, and multi-frequency electrical impedance tomography (mfEIT) was used to reconstruct the complex conductivity distribution of the root zone. To achieve the best sparse coefficients and enhance the quality of the reconstructed images, the SF-SBLC learned and utilized the spatial and frequency correlations of the complex conductivities at different frequencies. The reconstruction algorithm was further optimized using a concave-convex process method and a multi-measure vector model, which decreased its time complexity. When compared to conventional mfEIT reconstruction algorithms, the experimental findings demonstrated that the SF-SBLC could greatly reduce imaging artifacts, generate higher reconstruction performance (in terms of the image correlation coefficient, relative image error, resolution, position error, shape deformation, and ringing), and shorten imaging time. Moreover, the SF-SBLC was able to recreate the root zone's shape, size, and location in both a nutrient solution and a horticulture substrate. Finally, the effective volume of the root zone is defined and calculated based on the 3D EIT image. This technique offers a prospective tool that might be useful for monitoring the root growth trends and expansion rates of potted plants.

Unmanned ground vehicle‐unmanned aerial vehicle relative navigation robust adaptive localization algorithm

AbstractThe unmanned aerial vehicle (UAV) and the unmanned ground vehicle (UGV) can complete complex tasks through information sharing and ensure the mission execution capability of multiple unmanned carrier platforms. At the same time, cooperative navigation can use the information interaction between multi‐platform sensors to improve the relative navigation and positioning accuracy of the entire system. Aiming at the problem of deviation of the system model due to gross errors in sensor measurement data or strong manoeuvrability in complex environments, a robust and adaptive UGV‐UAV relative navigation and positioning algorithm is proposed. In this paper, the relative navigation and positioning of UGV‐UAV is studied based on inertial measurement unit (IMU)/Vision. Based on analyzing the relative kinematics model and sensor measurement model, a leader (UGV)‐follow (UAV) relative navigation model is established. In the implementation of the relative navigation and positioning algorithm, the robust adaptive algorithm and the non‐linear Kalman filter (extended Kalman filter [EKF]) algorithm are combined to dynamically adjust the system state parameters. Finally, a mathematical simulation of the accompanying and landing process in the UGV‐UAV cooperative scene is carried out. The relative position, velocity and attitude errors calculated by EKF, Robust‐EKF and Robust‐Adaptive‐EKF algorithms are compared and analyzed by simulating two cases where the noise obeys the Gaussian distribution and the non‐Gaussian distribution. The results show that under the non‐Gaussian distribution conditions, the accuracy of the Robust‐Adaptive‐EKF algorithm is improved by about two to three times compared with the EKF and Robust‐EKF and can almost reach the relative navigation accuracy under the Gaussian distribution conditions. The robust self‐adaptive relative navigation and positioning algorithm proposed in this paper has strong adaptability to the uncertainty and deviation of system modelling in complex environments, with higher accuracy and stronger robustness.

Mission Design and Orbit-Attitude Control Algorithms Development of Multistatic SAR Satellites for Very-High-Resolution Stripmap Imaging

This study designs a multistatic synthetic aperture radar (SAR) formation-flying system for very-high-resolution stripmap imaging (VHRSI) using manufacturable SAR microsatellites. Multistatic SAR formation specifications for VHRSI are derived based on the SAR image theory. For the simultaneous multi-satellite operation, the advantages of the autonomous orbit and attitude control are prominent in terms of the workload of the ground station or the efficient performance of missions. Therefore, the autonomous relative-orbit-control algorithm using relative orbital elements is developed to maintain the designed multistatic SAR formation. Additionally, an autonomous attitude-control algorithm for multistatic SAR imaging is designed by applying the optimal right-ascension of the descending node (RADN) sector concept. Finally, the resolution improvement of VHRSI is verified through multistatic SAR imaging simulations. The multistatic SAR formation is designed with three satellites separated by 7.5 km each in the along-track direction. Autonomous relative orbit control maintains the relative position error within 45 m (3σ). Additionally, the autonomous attitude control simulation verifies that the satellites perform attitude maneuvers suitable for the operation mode, and the pointing error is maintained within 0.0035° (3σ). The spatial resolution of the multistatic SAR system for VHRSI is 0.95 × 0.96 m, which satisfies the very-high-spatial-resolution requirement.

Assembly Strategy for Modular Components Using a Dual-Arm Space Robot with Flexible Appendages

Space robotic systems tend to be more flexible and equipped with some appendages, such as solar panels and communication antennas. The inevitable vibration in the flexible appendage will occur during space missions, and it in turn affects the attitude of the rigid base due to coupling dynamics. This study develops an assembly scheme for a dual-arm space robot with flexible appendages to assemble two modular components and to minimize the disturbance force caused by the manipulators to the base and flexible appendages. The assembly strategy consists of two stages, a preassembly stage which transports the two components to desired relative states, and a trajectory tracking stage to achieve the final assembly. In the first stage, based on a relative Jacobian matrix in the base frame, an optimal objective function is formulated in terms of the relative position and attitude errors between the two components. Thereby, more freedom of manipulators is released for minimizing disturbance forces. Notably, two virtual points are created to describe the relative position between the two components. In the second stage, two components are driven to follow a relative trajectory for the final assembly with an unchanged relative attitude. Finally, numerical simulations are conducted to demonstrate the efficiency of the proposed assembly strategy.

Visual SLAM Mapping Based on YOLOv5 in Dynamic Scenes

When building a map of a dynamic environment, simultaneous localization and mapping systems have problems such as poor robustness and inaccurate pose estimation. This paper proposes a new mapping method based on the ORB-SLAM2 algorithm combined with the YOLOv5 network. First, the YOLOv5 network of the tracing thread is used to detect dynamic objects of each frame, and to get keyframes with detection of dynamic information. Second, the dynamic objects of each image frame are detected using the YOLOv5 network, and the detected dynamic points are rejected. Finally, the global map is constructed using the keyframes after eliminating the highly dynamic objects. The test results using the TUM dataset show that when the map is constructed in a dynamic environment, compared with the ORB-SLAM2 algorithm, the absolute trajectory error of our algorithm is reduced by 97.8%, and the relative positional error is reduced by 59.7%. The average time consumed to track each image frame is improved by 94.7% compared to DynaSLAM. In terms of algorithmic real-time performance, this paper’s algorithm is significantly better than the comparable dynamic SLAM map-building algorithm DynaSLAM.

Localization and Mapping for UGV in Dynamic Scenes with Dynamic Objects Eliminated

SLAM (Simultaneous Localization and Mapping) based on lidar is an important method for UGV (Unmanned Ground Vehicle) localization in real time under GNSS (Global Navigation Satellite System)-denied situations. However, dynamic objects in real-world scenarios affect odometry in SLAM and reduce localization accuracy. We propose a novel lidar SLAM algorithm based on LOAM (Lidar Odometry and Mapping), which is popular in this field. First, we applied elevation maps to label the ground point cloud. Then we extracted convex hulls in point clouds based on scanlines as materials for dynamic object clustering. We replaced these dynamic objects with background point cloud to avoid accuracy reduction. Finally, we extracted feature points from ground points and non-ground points, respectively, and matched these feature points frame-to-frame to estimate ground robot motion. We evaluated the proposed algorithm in dynamic industrial park roads, and it kept UGV maximum relative position error less than 3% and average relative position error less than 2%.

Confocal probe localization algorithm based on region growing and endoscope size prior

Confocal laser endomicroscopy technology can obtain cell-level images in real time and in situ, which can assist doctors in real-time intraoperative diagnosis, but its non-invasiveness makes it difficult to relocate the optical biopsy site. The confocal probe localization algorithm can automatically calculate the coordinates of the probe tip, that is, the coordinates of the optical biopsy site. In this paper, a confocal probe localization algorithm based on region growing and endoscope size prior was proposed. The algorithm detected the probe region by region growing on the probe edge image, then searched for tip points based on a given probe axis, and iteratively optimized it. Finally, based on the single-degree-of-freedom motion characteristics of the probe, the three-dimensional coordinates of the tip of the probe were calculated by using the prior information of the size of the endoscope, which solved the scale uncertainty problem of the monocular camera. The confocal probe localization algorithm was tested on the dataset collected in this paper. The results showed that our algorithm no longer relied on the color information of the probe, avoided the influence of uneven illumination on the gray value of the probe pixels, and had a more robust location accuracy and running speed. Within the length of the probe extending out of the endoscope from 0 to 5 cm, the pixel error could be as low as 11.76 pixels, and the average relative position error could be as low as 1.66 mm, which can achieve the real-time and accurate localization of the confocal probe.

Design and evaluation of an active secondary mirror positioning system for a small telescope

This publication presents an active compensation system for the position of the secondary mirror of a small Ritchey–Chrétien telescope system. The goal is to maintain the optical imaging quality under varying gravitational and thermal influences, by compensation for the relative position deviations between the primary and secondary mirrors. An extensive analysis concerning the feasibility of such a system for a commercial off-the-shelf small telescope is performed and used as a basis for the design of the precision measurement and positioning system. The developed prototype uses dimensional metrology to capture relative position errors of the secondary mirror. A newly designed actuator with three degrees of freedom for the secondary mirror allows us to compensate for these deviations in a closed-loop control manner and ensures optimal positions of the two mirrors at all times. The support structure design requirements are reduced, allowing the utilization of more lightweight structures, as the artificial stiffness of the compensation system takes care of keeping the telescope mirrors in place. Furthermore, the measurement principle requires no light from the telescope, thus providing 100% of the collected light for the observation. The developed actuation and measurement principles are designed for simple scalability to larger representatives of small telescopes. The implemented setup is evaluated in various poses and temperature influences, successfully demonstrating that the calculated Strehl ratio is kept well above the diffraction limit of 80% for the used telescope system.

Comparison of Proportional and PWM Pneumatic Control in Terms of Positioning and Compressed Air Consumption

In this paper is shown a comparison of proportional pneumatic control and Pulse Width Modulation (PWM) pneumatic control in terms of positioning and compressed air consumption. All experimental tests were performed on a device for lifting and holding of the workpieces, which consists of one vertically mounted rodless cylinder with integrated vacuum gripper. In the case of the proportional pneumatic control, cylinder piston is always positioning in the correct position, but position losses are recurring during the time (in majority of cases, the position loss is 4 mm). As the control system constantly returns the cylinder piston to the desired position, that increases the compressed air consumption. In the case of the PWM pneumatic control, the position error is occurring (in majority of cases, the absolute value of the relative position error is less than 2%), but there is no position loss during the period of workpiece holding, i.e. there is no additional compressed air consumption. The compressed air consumption differential is approximately 18.6%. In addition, in case of Meter-out control in combination with previously defined types of control, the positioning is more accurate but the compressed air consumption slightly increases with decreasing the opening level of the one-way flow control valve.

Spatial Consistency Calibration Based on Phase Difference Minimization for Parallel Slightly Off-Axis Digital Holographic Microscopy

In this study, we propose a spatial consistency calibration method for slightly off-axis digital holographic microscopy (SO-DHM). The acquisition of relative position errors is summarized into a solution of a nonlinear optimization problem in which the root mean squared error of phase aberration of holograms is minimized. The particle swarm optimization algorithm is chosen to solve this optimization problem due to its simple structure, high convergence efficiency, and robust global search ability. Phase-only wavefronts based on phase aberration, which remove the influence of noise, are used for calibration. The simulation result indicates that the proposed method has subpixel-level precision, and the experiment demonstrates the effectiveness of the proposed method in the SO-DHM system.

ECC‐BERT: Classification of error correcting codes using the improved bidirectional encoder representation from transformers

The recent concept of contextual information in error correcting code (ECC) can significantly improve the capacity of the blind recognition of codes with deep learning (DL) approaches. However, the fundamental challenges of existing DL-based methods are inflexible structure and limited kernel size which bring great difficulties to exploit the characteristics of contextual information in ECC. To handle this problem, in this paper, a state-of-the-art framework for natural language processing (NLP), bidirectional encoder representation from transformers (BERT), is utilized in ECC classification scenarios. To strengthen the effectiveness of contextual information, the BERT model is improved by weighted relative positional encoding and error bit embedding. The proposed approach achieves higher classification accuracy than the methods based on Gauss-Jordan elimination and traditional deep learning schemes. Further simulation results show that the classification accuracy is affected by block length and the employment of weighted relative positional encoding and error bit embedding to a large extent.

Graph SLAM-Based 2.5D LIDAR Mapping Module for Autonomous Vehicles

This paper proposes a unique Graph SLAM framework to generate precise 2.5D LIDAR maps in an XYZ plane. A node strategy was invented to divide the road into a set of nodes. The LIDAR point clouds are smoothly accumulated in intensity and elevation images in each node. The optimization process is decomposed into applying Graph SLAM on nodes’ intensity images for eliminating the ghosting effects of the road surface in the XY plane. This step ensures true loop-closure events between nodes and precise common area estimations in the real world. Accordingly, another Graph SLAM framework was designed to bring the nodes’ elevation images into the same Z-level by making the altitudinal errors in the common areas as small as possible. A robust cost function is detailed to properly constitute the relationships between nodes and generate the map in the Absolute Coordinate System. The framework is tested against an accurate GNSS/INS-RTK system in a very challenging environment of high buildings, dense trees and longitudinal railway bridges. The experimental results verified the robustness, reliability and efficiency of the proposed framework to generate accurate 2.5D maps with eliminating the relative and global position errors in XY and Z planes. Therefore, the generated maps significantly contribute to increasing the safety of autonomous driving regardless of the road structures and environmental factors.

Weighted quasi-stable combined adjustment of two-order horizontal control network using posteriori variance to determine the weight

To address the difficulty in reasonably determining the datum in the combined adjustment of a two-order horizontal control network, a new weighted quasi-stable adjustment method is proposed that uses posteriori variance to determine the weight of the datum. First, the most suitable classic datum is selected from the high-order control points to fix the coordinate system, and the posterior variance matrix of the high-order control points is obtained by the classical free network adjustment. Then, keeping the coordinates of the high-order control points unchanged and taking them as the quasi-stable datum, the datum weight matrix is determined according to the posterior variance matrix, and weighted quasi-stable combined adjustment is performed to effectively use all the high-order control points to restrain the error accumulation in the low-order network. Finally, to achieve better conformity between the coordinates of the high-order control points and the low-order observations, the weighted quasi-stable combined adjustment is carried out iteratively until the posteriori variance matrix remains unchanged before and after the adjustment. The proposed method is applied to the combined adjustment of the route plane control network and track control network of high-speed railway as well as the ground and tunnel control networks of a particle accelerator. The adjustment result of this method is compared with the adjustment results of classical free network and annexed network. Experimental results show that the root-mean-square of positional error of the proposed method is close to the result of the annexed network adjustment and better than the result of the classical free network adjustment; the error accumulation is also effectively restrained. The relative positional error of this method is smaller than that in the annexed network, which shows that the proposed method can effectively reduce the influence of high-order control points with initial error on relative positional error.

UAV-Aided Relative Localization of Terminals

Accurate location information is essential for many emerging applications of the Internet of Things. Compared with absolute positions, relative positions of nodes are often more relevant in tasks such as formation control and autonomous driving. In this article, we propose a relative localization scheme for terminals aided by unmanned aerial vehicles. We first derive the performance limit of the relative position error as the constrained Cramér-Rao lower bound (CRLB), and proved that the equivalent Fisher information of a subnetwork retains all the information for its relative localization. We then develop a distributed localization algorithm based on local geometry transforming for the proposed scheme with low computation complexity. Moreover, an iterative descent algorithm is designed for joint power and spectrum allocation for relative localization. Numerical results show that the proposed localization algorithm significantly outperforms existing algorithms and the optimal allocation scheme can reduce the relative CRLB by about 50% compared with the uniform allocation scheme.

Coordinative coupled attitude and orbit control for satellite formation with multiple uncertainties and actuator saturation

This paper studies the coordinative coupled attitude and orbit control system (AOCS) of a satellite formation composed of one microsatellite and two 3U CubeSats. It is described as a highly nonlinear and coupled system subject to actuator saturation and multiple uncertainties including parametric perturbations and external disturbances. To address this issue, the centralized architecture and leader-following method are adopted in the formation firstly. The closed-loop system of each satellite member is divided into orbit and attitude control loops respectively. The coupling relationship between orbit and attitude is introduced as a constraint of the control law. Then a robust controller consisting of a nominal controller, a robust compensator and an advanced proportional–derivative (APD) controller is proposed to achieve high-accuracy formation control. The robust compensator is constructed from an auxiliary system and a finite-time observer to compensate the influence of an equivalent lumped disturbance. The APD controller is developed to achieve desired performances under actuator saturation. Stability analysis indicates that both relative position errors and attitude tracking errors can converge asymptotically. Finally, numerical simulations are carried out to verify the effectiveness of proposed control law in both relatively-stationary and fly-around scenarios.

The geometrical analysis of localization error characteristic in stereo vision systems.

The parameters of a stereo camera directly determine the accuracy of a stereo vision positioning system. In this paper, the relationship between camera parameter error and positioning error is established by using the geometric analysis method with a clear physical meaning. The error models of the relative position error and camera resolution error of the stereo camera are established. The relative position error of the stereo camera is represented by the rotation and translation of the coordinate system, and the positioning error is derived from image coordinates through the pinhole camera model. For the camera resolution error, the two pixels of the stereo camera are projected into an octahedral uncertain region in space. We use geometric methods to derive the maximum size of the octahedron in the three-axis direction. The maximum size in the three-axis direction is used to evaluate the impact of camera resolution errors. The depth of field and angle of view are used to represent the measured area. The effects of resolution error and camera parameters on the measurement error of each axis are analyzed. Finally, a large number of simulations verified our conclusion. By comparing the effects of the magnitude of the error, we can conclude that the baseline and pixel size of the camera have a greater impact on the positioning accuracy.

A Novel Cooperative Control System of Multi-Missile Formation Under Uncontrollable Speed

This article investigates a novel cooperative control system based on the sliding mode variable structure control theory for multi-missile formation flight. It is desired in practice to form and maintain the formation under the premise of uncontrollable missile speed. First, under the inertial coordinate system, we obtain the model of the formation control problem using the relative position of the leader to the follower. Then, we perform acceleration conversion and combine it to this model, getting the form of the formation problem model in the ballistic coordinate system. The finished model is useful for researchers to design the formation controller on this basis. Besides, the sliding mode variable structure control theory is used to design the formation controller for the system not considering disturbances and considering disturbances. Then we use the Lyapunov stability theory to analyze the stability of the formation control system. Finally, we compare our method with another method which requires controllable speed. According to numerical simulations, the method proposed in this article can achieve similar relative position errors under the condition of uncontrollable speed. And the robustness, versatility and formation adaptability of the method we propose are confirmed by simulation results.

Neural Network-Based Pose Estimation for Noncooperative Spacecraft Rendezvous

This article presents the Spacecraft Pose Network (SPN), the first neural network-based method for on-board estimation of the pose, i.e., the relative position and attitude, of a known noncooperative spacecraft using monocular vision. In contrast to other state-of-the-art pose estimation approaches for spaceborne applications, the SPN method does not require the formulation of hand-engineered features and only requires a single grayscale image to determine the pose of the spacecraft relative to the camera. The SPN method uses a convolutional neural network (CNN) with three branches to solve the problem of relative attitude estimation. The first branch of the CNN bootstraps a state-of-the-art object detection algorithm to detect a 2-D bounding box around the target spacecraft in the input image. The region inside the 2-D bounding box is then used by the other two branches of the CNN to determine the relative attitude by initially classifying the input region into discrete coarse attitude labels before regressing to a finer estimate. The SPN method then estimates the relative position by using the constraints imposed by the detected 2-D bounding box and the estimated relative attitude. Further, with the detection of 2-D bounding boxes of subcomponents of the target spacecraft, the SPN method is easily generalizable to estimate the pose of multiple target geometries. Finally, to facilitate integration with navigation filters and perform continuous pose tracking, the SPN method estimates the uncertainty associated with the estimated pose. The secondary contribution of this article is the generation of the Spacecraft PosE Estimation Dataset (SPEED), which is used to train and evaluate the performance of the SPN method. SPEED consists of synthetic as well as actual camera images of a mock-up of the Tango spacecraft from the PRISMA mission. The synthetic images are created by fusing OpenGL-based renderings of the spacecraft's 3-D model with actual images of the Earth captured by the Himawari-8 meteorological satellite. The actual camera images are created using a seven degrees-of-freedom robotic arm, which positions and orients a vision-based sensor with respect to a full-scale mock-up of the Tango spacecraft with submillimeter and submillidegree accuracy. The SPN method, trained only on synthetic images, produces degree-level relative attitude error and cm-level relative position errors when evaluated on the actual camera images with a different distribution not used during training.