Trajectory Error Research Articles

Integrated design of sun-synchronous orbit and launch vehicle trajectory for operationally responsive space

For the operationally responsive space mission with the known launch point and target area, based on the simplified trajectory, the design method of the sun-synchronous orbit is given by the orbit dynamics, considering the mutually constrained relationship between the satellite orbit and the launch vehicle trajectory. Then, with the orbit parameters as the input, the trajectory model obtains the actual trajectory parameters. Considering the error between the actual and simplified trajectory parameters, the actual trajectory parameters are used to correct the simplified trajectory. Finally, by iterative calculation, the parameters of sun-synchronous orbit and launch vehicle trajectory for operationally responsive space are obtained with the finite trajectory error. For a typical example, the parameters are calculated by the method, which is verified by the STK simulation, demonstrating the feasibility and practicability of the method. The design method can provide theoretical support for the orbit and trajectory design of operationally responsive space.

Retracted: Motion Trajectory Error of Robotic Arm Based on Neural Network Algorithm

Retracted: Motion Trajectory Error of Robotic Arm Based on Neural Network Algorithm

Research on Positioning Accuracy of Mobile Robot in Indoor Environment Based on Improved RTABMAP Algorithm

Visual simultaneous localization and mapping is a widely used technology for mobile robots to carry out precise positioning in the environment of GNSS technology failure. However, as the robot moves around indoors, its position accuracy will gradually decrease over time due to common and unavoidable environmental factors. In this paper, we propose an improved method called RTABMAP-VIWO, which is based on RTABMAP. The basic idea is to use an Extended Kalman Filter (EKF) framework for fusion attitude estimates from the wheel odometry and IMU, and provide new prediction values. This helps to reduce the local cumulative error of RTABMAP and make it more accurate. We compare and evaluate three kinds of SLAM methods using both public datasets and real indoor scenes. In the dataset experiments, our proposed method reduces the Root-Mean-Square Error (RMSE) coefficient by 48.1% compared to the RTABMAP, and the coefficient is also reduced by at least 29.4% in the real environment experiments. The results demonstrate that the improved method is feasible. By incorporating the IMU into the RTABMAP method, the trajectory and posture errors of the mobile robot are significantly improved.

GMIW-Pose: Camera Pose Estimation via Global Matching and Iterative Weighted Eight-Point Algorithm

We propose a novel approach, GMIW-Pose, to estimate the relative camera poses between two views. This method leverages a Transformer-based global matching module to obtain robust 2D–2D dense correspondences, followed by iterative refinement of matching weights using ConvGRU. Ultimately, the camera’s relative pose is determined through the weighted eight-point algorithm. Compared with the previous best two-view pose estimation method, GMIW-Pose reduced the Absolute Trajectory Error (ATE) by 24% on the TartanAir dataset; it achieved the best or second-best performance in multiple scenarios of the TUM-RGBD and KITTI datasets without fine-tuning, among which ATE decreased by 22% on the TUM-RGBD dataset.

Automatic registration with continuous pose updates for marker-less surgical navigation in spine surgery

Established surgical navigation systems for pedicle screw placement have been proven to be accurate, but still reveal limitations in registration or surgical guidance. Registration of preoperative data to the intraoperative anatomy remains a time-consuming, error-prone task that includes exposure to harmful radiation. Surgical guidance through conventional displays has well-known drawbacks, as information cannot be presented in-situ and from the surgeon’s perspective. Consequently, radiation-free and more automatic registration methods with subsequent surgeon-centric navigation feedback are desirable. In this work, we present a marker-less approach that automatically solves the registration problem for lumbar spinal fusion surgery in a radiation-free manner. A deep neural network was trained to segment the lumbar spine and simultaneously predict its orientation, yielding an initial pose for preoperative models, which then is refined for each vertebra individually and updated in real-time with GPU acceleration while handling surgeon occlusions. An intuitive surgical guidance is provided thanks to the integration into an augmented reality based navigation system. The registration method was verified on a public dataset with a median of 100% successful registrations, a median target registration error of 2.7 mm, a median screw trajectory error of 1.6°and a median screw entry point error of 2.3 mm. Additionally, the whole pipeline was validated in an ex-vivo surgery, yielding a 100% screw accuracy and a median target registration error of 1.0 mm. Our results meet clinical demands and emphasize the potential of RGB-D data for fully automatic registration approaches in combination with augmented reality guidance.

Automated Method for SLAM Evaluation in GNSS-Denied Areas

The automated inspection and mapping of engineering structures are mainly based on photogrammetry and laser scanning. Mobile robotic platforms like unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs), but also handheld platforms, allow efficient automated mapping. Engineering structures like bridges shadow global navigation satellite system (GNSS), which complicates precise localization. Simultaneous localization and mapping (SLAM) algorithms offer a sufficient solution, since they do not require GNSS. However, testing and comparing SLAM algorithms in GNSS-denied areas is difficult due to missing ground truth data. This work presents an approach to measuring the performance of SLAM in indoor and outdoor GNSS-denied areas using a terrestrial scanner Leica RTC360 and a tachymeter to acquire point cloud and trajectory information. The proposed method is independent of time synchronization between robot and tachymeter and also works on sparse SLAM point clouds. For the evaluation of the proposed method, three LiDAR-based SLAM algorithms called KISS-ICP, SC-LIO-SAM, and MA-LIO are tested using a UGV equipped with two light detection and ranging (LiDAR) sensors and an inertial measurement unit (IMU). KISS-ICP is based solely on a single LiDAR scanner and SC-LIO-SAM also uses an IMU. MA-LIO, which allows multiple (different) LiDAR sensors, is tested on a horizontal and vertical one and an IMU. Time synchronization between the tachymeter and SLAM data during post-processing allows calculating the root mean square (RMS) absolute trajectory error, mean relative trajectory error, and the mean point cloud to reference point cloud distance. It shows that the proposed method is an efficient approach to measure the performance of SLAM in GNSS-denied areas. Additionally, the method shows the superior performance of MA-LIO in four of six test tracks with 5 to 7 cm RMS trajectory error, followed by SC-LIO-SAM and KISS-ICP in last place. SC-LIO-SAM reaches the lowest point cloud to reference point cloud distance in four of six test tracks, with 4 to 12 cm.

Trajectory tracking intelligent controller for differential wheel mobile robot

This paper presents the design and development of a Neural Netwwork-Adaptive backstepping (NN-Adaptive backstepping) controller to track the trajectory of a differentially controlled mobile robot. The controller is designed based on the robot dynamics equation and on the basis of the Backstepping controller. The effectiveness of the proposed controller is verified by simulation on different trajectories and compared with the backstepping controller. Model results The simulation shows that the proposed controller achieves quality better than the Backstepping controller in different trajectories. The tracking performance of the NN-Adaptive backstepping controller compared to the Backstepping controller is clearly improved (performance improved by over 52%), which means that the proposed controller trajectory error output will decrease by this percentage.

Compound Control of Trajectory Errors in a Non-Resonant Piezo-Actuated Elliptical Vibration Cutting Device.

To improve the machining quality of the non-resonant elliptical vibration cutting (EVC) device, a compound control method for trajectory error compensation is proposed in this paper. Firstly, by analyzing the working principle of non-resonant EVC device and considering the elliptical trajectory error caused by piezoelectric hysteresis, a dynamic PI (Prandtl-Ishlinskii) model relating to voltage change rate and acceleration was established to describe the piezoelectric hysteresis characteristics of EVC devices. Then, the parameters of the dynamic PI model were identified by using the particle swarm optimization (PSO) algorithm. Secondly, based on the dynamic PI model, a compound control method has been proposed in which the inverse dynamic PI model is used as the feedforward controller for the dynamic hysteresis compensation, while PID (proportion integration differentiation) feedback is used to improve the control accuracy. Finally, trajectory-tracking experiments have been conducted to verify the feasibility of the proposed compound control method.

Vision Sensing-Based Online Correction System for Robotic Weld Grinding

The service cycle and dynamic performance of structural parts are affected by the weld grinding accuracy and surface consistency. Because of reasons such as assembly errors and thermal deformation, the actual track of the robot does not coincide with the theoretical track when the weld is ground offline, resulting in poor workpiece surface quality. Considering these problems, in this study, a vision sensing-based online correction system for robotic weld grinding was developed. The system mainly included three subsystems: weld feature extraction, grinding, and robot real-time control. The grinding equipment was first set as a substation for the robot using the WorkVisual software. The input/output (I/O) ports for communication between the robot and the grinding equipment were configured via the I/O mapping function to enable the robot to control the grinding equipment (start, stop, and speed control). Subsequently, the Ethernet KRL software package was used to write the data interaction structure to realize real-time communication between the robot and the laser vision system. To correct the measurement error caused by the bending deformation of the workpiece, we established a surface profile model of the base material in the weld area using a polynomial fitting algorithm to compensate for the measurement data. The corrected extracted weld width and height errors were reduced by 2.01% and 9.3%, respectively. Online weld seam extraction and correction experiments verified the effectiveness of the system’s correction function, and the system could control the grinding trajectory error within 0.2 mm. The reliability of the system was verified through actual weld grinding experiments. The roughness, Ra, could reach 0.504 µm and the average residual height was within 0.21 mm. In this study, we developed a vision sensing-based online correction system for robotic weld grinding with a good correction effect and high robustness.

Tuning path tracking controllers for autonomous cars using reinforcement learning.

This article proposes an adaptable path tracking control system, based on reinforcement learning (RL), for autonomous cars. A four-parameter controller shapes the behaviour of the vehicle to navigate lane changes and roundabouts. The tuning of the tracker uses an 'educated' Q-Learning algorithm to minimize the lateral and steering trajectory errors, this being a key contribution of this article. The CARLA (CAR Learning to Act) simulator was used both for training and testing. The results show the vehicle is able to adapt its behaviour to the different types of reference trajectories, navigating safely with low tracking errors. The use of a robot operating system (ROS) bridge between CARLA and the tracker (i) results in a realistic system, and (ii) simplifies the replacement of CARLA by a real vehicle, as in a hardware-in-the-loop system. Another contribution of this article is the framework for the dependability of the overall architecture based on stability results of non-smooth systems, presented at the end of this article.

Semantic visual simultaneous localization and mapping (SLAM) using deep learning for dynamic scenes.

Simultaneous localization and mapping (SLAM) is a fundamental problem in robotics and computer vision. It involves the task of a robot or an autonomous system navigating an unknown environment, simultaneously creating a map of the surroundings, and accurately estimating its position within that map. While significant progress has been made in SLAM over the years, challenges still need to be addressed. One prominent issue is robustness and accuracy in dynamic environments, which can cause uncertainties and errors in the estimation process. Traditional methods using temporal information to differentiate static and dynamic objects have limitations in accuracy and applicability. Nowadays, many research trends have leaned towards utilizing deep learning-based methods which leverage the capabilities to handle dynamic objects, semantic segmentation, and motion estimation, aiming to improve accuracy and adaptability in complex scenes. This article proposed an approach to enhance monocular visual odometry's robustness and precision in dynamic environments. An enhanced algorithm using the semantic segmentation algorithm DeeplabV3+ is used to identify dynamic objects in the image and then apply the motion consistency check to remove feature points belonging to dynamic objects. The remaining static feature points are then used for feature matching and pose estimation based on ORB-SLAM2 using the Technical University of Munich (TUM) dataset. Experimental results show that our method outperforms traditional visual odometry methods in accuracy and robustness, especially in dynamic environments. By eliminating the influence of moving objects, our method improves the accuracy and robustness of visual odometry in dynamic environments. Compared to the traditional ORB-SLAM2, the results show that the system significantly reduces the absolute trajectory error and the relative pose error in dynamic scenes. Our approach has significantly improved the accuracy and robustness of the SLAM system's pose estimation.

Methodology and Research of Intelligent New Energy Vehicle Motion Control System based on Fuzzy Adaptive

To resolve the difficult control issue of intelligent new energy automobile in the process of vehicle control, the study starts from the vehicle motion mode and splits the vehicle control into two parts, transverse control and longitudinal control. Among them, the longitudinal speed control is controlled by an improved adaptive PID model, while the lateral angle control is dominated by an indistinct adaptive PID model, afterwards longitudinal speed control is combined with the lateral angle control for joint control. Finally, the study uses the actual lane simulation to verify the three perspectives of transverse control, longitudinal control and joint control respectively. It shows that the longitudinal control and lateral control are well realized with the improved adaptive PID model control effect at 8km, 15km and 20km per hour. Meanwhile, maximum trajectory error of the combined direction and transverse dominate is always lower than 0.5m at vehicle speeds of 8km/h, 16km/h and 20km/h in the integrated road environment and the combined longitudinal speed and transverse angle control performance is good in the curves. This shows that the model designed by the research can realize adaptive real-time precision control.

Optimal splicing of multi-segment analytical trajectories for electric sails

In this paper, the analytical approximation, and the corresponding modified solution of the two-dimensional propelled trajectory of the electric sail with fixed pitch angle are spliced for the optimal design of the transfer orbit. Based on the linear perturbation theory, the analytical approximate propelled trajectory of the electric sail launched from a general heliocentric elliptical orbit can be obtained. Interestingly, this semi-analytic solution is no longer limited to the circular orbit assumption. Therefore, the optimal transfer trajectories between different heliocentric orbits can be obtained by splicing the analytical propelled trajectories with different pitch angles. Significantly, for such a problem that requires a large amount of iterative computation, compared to numerical integration, the analytical solution can greatly reduce the calculation time. In addition, the method of using pitch angles as the main optimization variables can greatly improve optimization efficiency. Moreover, based on the high accuracy of the modified analytical approximation, the optimal trajectory obtained by the proposed method is extremely close to the optimal real solution obtained by the shooting method and numerical integration. For the electric sail with a characteristic acceleration of 0.03 mm/s2, the approximation error of the optimal trajectories in the multi-target mission obtained by the proposed method and the integral shooting method is as low as 10−6∼10−4. For multiple variable targets, the difference of indicators is approximately 10−5∼10−4. Furthermore, compared with numerical integration, the proposed analytical method can reduce the calculation time of multi-target optimization problems by at least 80 %. Notably, with extremely low accuracy loss and calculation time, the proposed method is applicable to the rapid design of optimal transfer trajectory of electric sail-based spacecraft in multi-target mission scenarios.

Event-triggered adaptive prescribed performance tracking for nonlinear time-varying systems with unknown control directions

This article deals with the adaptive prescribed performance tracking for nonlinear time-varying systems. To handle multiple unknown control directions, a novel lemma is established by using a general class of Nussbaum functions. To handle unknown time-varying parameters, the congelation of variables method is employed. Different novel functions are introduced to achieve prescribed performance tracking and finite-time prescribed performance tracking, respectively. Meanwhile, the problem of explosion of complexity is avoided by utilizing the command filter and the compensation mechanism. For reasons of saving network resources and reducing communication burden, a new event-triggered mechanism is proposed, which can circumvent the Zeno behavior. Then, an event-triggered adaptive prescribed performance tracking control scheme is constructed and is extended to event-triggered finite-time adaptive prescribed performance tracking, both of which guarantee that all closed-loop signals are bounded and the trajectory of the tracking error can be limited to the prescribed region. Finally, the availability of the control scheme is demonstrated by two examples.

Accurately predicting the tool influence function to achieve high-precision magnetorheological finishing using robots.

Industrial robots with six degrees-of-freedom have significant potential for use in optical manufacturing owing to their flexibility, low cost, and high space utilisation. However, the low trajectory accuracy of robots affects the manufacturing accuracy of optical components when combined with magnetorheological finishing (MRF). Moreover, general robot trajectory-error compensation methods cannot compensate for the running errors of large robots with high precision. To address this problem, a three-dimensional (3D) tool influence function (TIF) model based on inverse distance interpolation is developed in this study to accurately predict the TIF of different polishing gaps. A high-precision robot-MRF polishing strategy based on variable TIFs and surface shape accuracy of polished optics is proposed to achieve high-precision manufacturing without compensating for trajectory errors. Subsequently, the accuracy of a ϕ420 mm fused silica mirror is experimentally verified to be from 0.11 λ RMS to 0.013 λ RMS. This validates that the robot-MRF can achieve high-precision polishing without compensating for trajectory errors. Furthermore, the proposed model will promote the applications of industrial robots in optical manufacturing and will serve as a reference in the field of intelligent optical manufacturing.

Modeling and analysis of the equivalent convex mandrel of the three-dimensional braiding carbon fiber composite robotic arm

The third robotic arm (drive housing) of a six-axis industrial robot often has a vertical inwardly concave surface to facilitate the installation of spatially vertical drive motors. With the inwardly concave surface of the robotic arm it is difficult to realize three-dimensional (3D) braiding directly, and based on this problem, an equivalent convex mandrel is added to the concave mandrel. The mathematical model of the concave mandrel is established, and the mathematical expression of the concave mandrel is obtained. In any cross-section perpendicular to the x-axis, the equivalent outwardly convex cross-sectional line is obtained according to the condition that the length of the outwardly convex and concave mandrel cross-sectional line is equal. All outwardly convex cross-sectional lines form a smooth surface of the equivalent convex mandrel. By the numerical calculation method, the braiding trajectory and the downward pressure trajectory are predicted for various take-up speeds. The length error of the braiding trajectory and the downward pressure trajectory are within 5%, which verifies the accuracy of the convex mandrel. The variation pattern of the braiding angle is smooth, verifying the braidability of the convex mandrel. The experimental results show that the outwardly convex carbon fiber fabric can be pressed down to fit the surface of the concave mandrel. Therefore, a carbon fiber composite arm with an inwardly concave surface can be manufactured by 3D braiding with the addition of an equivalent convex mandrel.

Correcting gradient chain induced fat quantification errors in radial multi-echo Dixon imaging using a gradient modulation transfer function

Purpose: Multi-echo Stack-of-stars (SoS) radial k-space trajectories with golden angle ordering are becoming popular for free-breathing abdominal Dixon imaging and proton density fat fraction (PDFF) mapping. Gradient chain imperfections including eddy currents and system delays are known to affect the image quality of radial imaging and to confound the estimation of PDFF mapping. This work proposes a retrospective trajectory correction method based on a simple gradient modulation transfer function (GMTF) measurement to predict and correct gradient chain induced k-space trajectory errors.Methods: The GMTF was measured using the standard hardware of a 3 Tesla scanner on a phantom using the thin slice method and was applied to a 3D radial SoS Dixon imaging sequence. The impact of the GMTF-based correction on image reconstruction and PDFF quantification was investigated using numerical simulations and validated on experimental phantom data as well as on in vivo leg and liver data of healthy volunteers.Results: Correcting the k-space trajectories with the measured GMTF during image reconstruction reduced PDFF quantification errors for phantom and in vivo acquisitions. A Bland-Altman comparison of the measured PDFF phantom and reference data confirmed that the GMTF correction narrowed down the limits of agreement (LoA) from 1.3% ± 8.1% (uncorrected) to 1.9% ± 5.4% (GMTF-corrected) over the full PDFF range (0%–100%) and from −0.26% ± 2.8% (uncorrected) to 0.12% ± 1.5% (GMTF-corrected) within the 0%–50% PDFF range. Liver PDFF estimation was improved by reducing the standard deviation of the mean liver PDFF and the bias of the mean liver PDFF for all subjects.Conclusion: The proposed GMTF-based k-space trajectory correction is a fast alternative method for avoiding PDFF quantitation errors caused by gradient-system induced k-space trajectory errors in 3D radial multi-echo gradient-echo acquisitions.

DIG-SLAM: an accurate RGB-D SLAM based on instance segmentation and geometric clustering for dynamic indoor scenes

Simultaneous localization and mapping (SLAM) has emerged as a critical technology enabling robots to navigate in unknown environments, drawing extensive attention within the robotics research community. However, traditional visual SLAM ignores the presence of dynamic objects in indoor scenes, and dynamic point features of dynamic objects can lead to incorrect data correlation, making the traditional visual SLAM is difficult to accurately estimate the camera’s pose when the objects in the scenes are moving. Using only point features cannot fully extract geometric information in dynamic indoor scenes, reducing the system’s robustness. To solve this problem, we develop a RGB-D SLAM system called DIG-SLAM. Firstly, the objects’ contour regions are extracted using the YOLOv7 instance segmentation method, serving as a prerequisite for determining dynamic objects and constructing a semantic information map. Meanwhile, the line features are extracted using the line segment detector algorithm, and the redundant line features are optimized via K-means clustering. Secondly, moving consistency checks combined with instance partitioning determine dynamic regions, and the point and line features of the dynamic regions are removed. Finally, the combination of static line features and point features optimizes the camera pose. Meanwhile, a static semantic octree map is created to provide richer and higher-level scene understanding and perception capabilities for robots or autonomous systems. The experimental results on the Technische Universität München dataset show that the average absolute trajectory error of the developed DIG-SLAM is reduced by 28.68% compared with the dynamic semantic SLAM. Compared with other dynamic SLAM methods, the proposed system shows better camera pose estimation accuracy and system’s robustness in dynamic indoor environments and better map building in real indoor scenes.

Robust prescribed performance trajectory tracking control with improved fast nonsingular terminal sliding surface of robot manipulators

This paper investigates the high-precision model-free control of robot manipulators. To this end, a model-free robust prescribed performance controller with an improved fast nonsingular terminal sliding mode surface (IFNTSM) and unknown system dynamics estimator (USDE) has been designed. An USDE method is employed to estimate model informations and further to achieve model-free control, which can avoid complex mathematical model calculation. Compared with some other model-free control methods like time-delay control (TDC) and neural-networks control (NNC), the USED does not require acceleration signal and is easy to implement. Then the prescribed performance control (PPC) has been used to limit error trajectory, which means the error can be pre-limit in a constraint band. A new transform function (TF) is designed for PPC, it has unlimited domain and can still maintain stability although tracking error will exceed PPC boundary sometimes, but the PPC with traditional TF will crash in this case. This is a great improvement for the stability of system compared with traditional TF. An improved fast nonsingular terminal sliding mode surface (IFNTSM) with a new adaptive law is proposed to accelerate convergence rate and improve steady-state accuracy on the sliding manifold. Finally, a practical finite-time controller (PFTC) has been constructed to drive sliding variable to a set centered on zero within a finite time, which means the convergence time can be calculated depending on the initial state. The transient response time can be shorten compared with traditional asymptotic stable. Abundant simulations and experimental results also verified the effectiveness of the proposed scheme.

OTE-SLAM: An Object Tracking Enhanced Visual SLAM System for Dynamic Environments.

With the rapid development of autonomous driving and robotics applications in recent years, visual Simultaneous Localization and Mapping (SLAM) has become a hot research topic. The majority of visual SLAM systems relies on the assumption of scene rigidity, which may not always hold true in real applications. In dynamic environments, SLAM systems, without accounting for dynamic objects, will easily fail to estimate the camera pose. Some existing methods attempt to address this issue by simply excluding the dynamic features lying in moving objects. But this may lead to a shortage of features for tracking. To tackle this problem, we propose OTE-SLAM, an object tracking enhanced visual SLAM system, which not only tracks the camera motion, but also tracks the movement of dynamic objects. Furthermore, we perform joint optimization of both the camera pose and object 3D position, enabling a mutual benefit between visual SLAM and object tracking. The results of experiences demonstrate that the proposed approach improves the accuracy of the SLAM system in challenging dynamic environments. The improvements include a maximum reduction in both absolute trajectory error and relative trajectory error by 22% and 33%, respectively.