Trajectory Error Research Articles

Kinematics analysis of trajectory planning of four-degree-of-freedom robotic arm

This article describes the use of the Open MANIPULATOR-X open robotic platform with four degrees of freedom to model the forward and inverse kinematics of the robot arm. Algorithms for forward and inverse kinematics were developed, and simulations were conducted for comparative analysis. System verification and validation were performed, along with trajectory planning, error analysis, and structural optimization methods. The results obtained serve as a theoretical basis for future research into improving trajectory planning and optimizing robot design. The importance of using the MATLAB platform for kinematic modeling, simulation, and algorithm development is emphasized, contributing to the enhancement of robotics skills and innovation.

Advancing real-world visual SLAM: Integrating adaptive segmentation with dynamic object detection for enhanced environmental perception

The field of Visual Simultaneous Localization and Mapping (VSLAM) has long grappled with the limitations imposed by static environmental assumptions, a challenge that becomes increasingly pronounced in dynamic settings. Addressing this gap, our study introduces a pioneering technique, Accurate and Dynamic Reliable SLAM (YoloV8-SLAM), which represents a paradigm shift in VSLAM technology. This novel approach combines the prowess of dynamic object detection with advanced multi-view geometry, thereby elevating the system’s accuracy, robustness, and efficiency in varied dynamic scenarios. At the core of YoloV8-SLAM is an innovative adaptive segmentation process that skilfully merges geometric motion details from successive frames. This integration not only isolates dynamic objects with heightened precision but also ensures consistent mapping accuracy. The system employs the latest YoloV8 model, synergizing it with an Enhanced Multi-View Geometry algorithm. This combination is adept at handling a spectrum of dynamic conditions, further bolstered by a precise point selection mechanism that swiftly retrieves motion information, crucial for real-time applications. Our extensive evaluations demonstrate that YoloV8-SLAM significantly outperforms existing methods such as including DynaSLAM (Bescos et al., 2018), DM-SLAM (Cheng et al., 2020), RDS-SLAM (Liu et al., 2021), Blitz-SLAM (Fan et al., 2022), and OVD-SLAM (He et al., 2023). Notably, it achieves a 38–45% reduction in Absolute Trajectory Error and a 66–72% decrease in Relative Pose Error, underscoring its superior performance. The breakthrough of YoloV8-SLAM lies in its seamless amalgamation of cutting-edge machine learning with robust geometric principles. This fusion not only facilitates effective dynamic segmentation but also ensures stable structural reconstruction, even in highly dynamic environments. This work marks a substantial advancement in SLAM technology, particularly in addressing the complexities of dynamic and unrestricted settings. YoloV8-SLAM sets a new benchmark in the field and paves the way for future explorations in dynamic SLAM solutions, promising to revolutionize applications requiring high fidelity in real-world, ever-changing environments.

Advancement on target ranging and tracking by four-quadrant photon counting lidar

Single-photon lidar stands out as a promising technology for long-distance lidar applications, owing to its attributes of single-photon sensitivity and high repetition rate. Existing single-photon lidar systems typically rely on single-point scanning for positioning and tracking, necessitating intricate and precise scanning control. In pursuit of a more concise and efficient positioning, we incorporate the four-quadrant theory to articulate the signal formula of photon detection, and propose a novel single-photon four-quadrant positioning method. Our method, which includes signal preprocessing, compensation for longitudinal motion, extraction of pixel intensity, and acquisition of lateral motion, facilitates motion acquisition and positioning for targets. Through simulation calculations, we analyze and compare the effectiveness of each step of the method. With longitudinal and lateral speeds of 100 m/s and 50 m/s, respectively, the trajectory error is 1.7%, and the average speed error is 1.8%. Moreover, for various verification experiments, the trajectory errors are all below 4.2%, and the average speed errors remain under 5.4%, effectively verifying the validity of our method in acquiring the motion information and positioning of targets. It provides an excellent option for acquiring motion information and tracking small moving targets over long distances.

ADM-SLAM: Accurate and Fast Dynamic Visual SLAM with Adaptive Feature Point Extraction, Deeplabv3pro, and Multi-View Geometry.

Visual Simultaneous Localization and Mapping (V-SLAM) plays a crucial role in the development of intelligent robotics and autonomous navigation systems. However, it still faces significant challenges in handling highly dynamic environments. The prevalent method currently used for dynamic object recognition in the environment is deep learning. However, models such as Yolov5 and Mask R-CNN require significant computational resources, which limits their potential in real-time applications due to hardware and time constraints. To overcome this limitation, this paper proposes ADM-SLAM, a visual SLAM system designed for dynamic environments that builds upon the ORB-SLAM2. This system integrates efficient adaptive feature point homogenization extraction, lightweight deep learning semantic segmentation based on an improved DeepLabv3, and multi-view geometric segmentation. It optimizes keyframe extraction, segments potential dynamic objects using contextual information with the semantic segmentation network, and detects the motion states of dynamic objects using multi-view geometric methods, thereby eliminating dynamic interference points. The results indicate that ADM-SLAM outperforms ORB-SLAM2 in dynamic environments, especially in high-dynamic scenes, where it achieves up to a 97% reduction in Absolute Trajectory Error (ATE). In various highly dynamic test sequences, ADM-SLAM outperforms DS-SLAM and DynaSLAM in terms of real-time performance and accuracy, proving its excellent adaptability.

Research on tightly coupled SLAM method based on LiDAR/IMU

Abstract Aiming at the problems of insufficient accuracy and serious computational time-consumption of mainstream laser odometry schemes, this paper proposes an innovative solution, where the front end is based on the idea of iterative Kalman filtering, which realizes the tight coupling of inertial measurement unit (IMU) and LiDAR to obtain high-precision position and attitude estimation. The back-end optimization employs a factor graph approach, incorporating laser odometry, IMU preintegration, and loop closure detection factors. In comparison with state-of-the-art laser SLAM algorithms, the SLAM algorithm proposed in this paper reduces the absolute position error of trajectories by 9.61%, 91.03%, and 94.89% compared to Fast-lio2, Lego-loam, and a-loam, respectively.

Unified framework for geometric error compensation and shape-adaptive scanning in five-axis metrology systems

In response to the escalating demand for precise shape metrology of complex optical surfaces, this study unveils a unified geometric error compensation and trajectory planning framework tailored for high-accuracy five-axis scanning metrology systems, which remains a notably underexplored field compared to error compensation in machine tools. Founded on a unified geometric model, the proposed framework seamlessly integrates a versatile shape-adaptive trajectory planning strategy, a thorough global error sensitivity analysis approach, and an exhaustive geometric error compensation scheme. Leveraging inverse kinematics, an innovative shape-adaptive scanning trajectory generation strategy is mathematically formulated, thereby facilitating adaptable measurement trajectory generation for diverse surface geometries. Employing forward kinematics, an exhaustive geometric error model is established to extensively address the 53 distinct geometric errors in the metrology system. This proposed error model fundamentally augments conventional geometric error models in machine tool by managing not only the geometric errors from the motion system, but also those from the probe and workpiece. To streamline the error compensation procedure, a novel global error sensitivity analysis approach is introduced, identifying both system-oriented and process-oriented sensitive geometric errors for targeted compensation. Experimental validation using a standard ball, which achieved an exceptional 89.35% reduction in the root mean square of the measurement errors, further confirms the feasibility and effectiveness of the proposed framework. By offering an universal trajectory planning, sensitivity analysis and error compensation trinity for five-axis scanning metrology systems, this study sets the stage for precision advancements and design optimization across diverse configurations of metrology systems.

Formation Control of Autonomous Underwater Vehicles Using an Improved Nonlinear Backstepping Method

The characteristics of autonomous underwater vehicles include nonlinearity, strong coupling, multiple inputs and multiple outputs, uncertainty, strong disturbance, underdrive, and multiple constraints. Autonomous underwater vehicle cluster systems are associated with large-scale complex dynamic systems through local perception or network communication, which have the structural characteristics of “complex dynamic + association topology + interaction rules”. To solve the problem of formation trajectory tracking of underactuated autonomous underwater vehicles, a controller was designed on the basis of an improved nonlinear backstepping algorithm, cascade system theory, and the Lyapunov direct method. In this design, the formation is determined from the actual trajectory of the leader autonomous underwater vehicle. The formation control rate is determined using the backstepping method and Lyapunov theory. Nonlinear disturbance observers were added to ensure that the trajectory error of the formation control could be quickly reduced in a real case with interference. The stability and effectiveness of this method were verified through simulation experiments. The robustness of the control algorithm was verified using two simulation cases, and the simulation results show that the proposed control method can maintain the expected formation.

A Visual-Inertial Pressure Fusion-Based Underwater Simultaneous Localization and Mapping System.

Detecting objects, particularly naval mines, on the seafloor is a complex task. In naval mine countermeasures (MCM) operations, sidescan or synthetic aperture sonars have been used to search large areas. However, a single sensor cannot meet the requirements of high-precision autonomous navigation. Based on the ORB-SLAM3-VI framework, we propose ORB-SLAM3-VIP, which integrates a depth sensor, an IMU sensor and an optical sensor. This method integrates the measurements of depth sensors and an IMU sensor into the visual SLAM algorithm through tight coupling, and establishes a multi-sensor fusion SLAM model. Depth constraints are introduced into the process of initialization, scale fine-tuning, tracking and mapping to constrain the position of the sensor in the z-axis and improve the accuracy of pose estimation and map scale estimate. The test on seven sets of underwater multi-sensor sequence data in the AQUALOC dataset shows that, compared with ORB-SLAM3-VI, the ORB-SLAM3-VIP system proposed in this paper reduces the scale error in all sequences by up to 41.2%, and reduces the trajectory error by up to 41.2%. The square root has also been reduced by up to 41.6%.

Multi-mode adaptive control strategy for a lower limb rehabilitation robot.

Different patients have different rehabilitation requirements. It is essential to ensure the safety and comfort of patients at different recovery stages during rehabilitation training. This study proposes a multi-mode adaptive control method to achieve a safe and compliant rehabilitation training strategy. First, patients' motion intention and motor ability are evaluated based on the average human-robot interaction force per task cycle. Second, three kinds of rehabilitation training modes-robot-dominant, patient-dominant, and safety-stop-are established, and the adaptive controller can dexterously switch between the three training modes. In the robot-dominant mode, based on the motion errors, the patient's motor ability, and motion intention, the controller can adaptively adjust its assistance level and impedance parameters to help patients complete rehabilitation tasks and encourage them to actively participate. In the patient-dominant mode, the controller only adjusts the training speed. When the trajectory error is too large, the controller switches to the safety-stop mode to ensure patient safety. The stabilities of the adaptive controller under three training modes are then proven using Lyapunov theory. Finally, the effectiveness of the multi-mode adaptive controller is verified by simulation results.

Trajectory optimization of B-splines interpolation based on dynamic error adjustment

In this paper, we propose a motion planning algorithm based on the five-fold B-spline curve for multi-axis motion control systems with non-smooth trajectories, acceleration, plus acceleration over the limit, etc. We construct a smooth transition model for the micro-line segment G3 of the continuous five-fold B-spline curve. A derivation of the corresponding theoretical equation is given. Using the transition model, we propose an optimization method for dynamic adjustment of motion trajectory errors based on the velocity forward planning constraints by smoothing the transition after the trajectory of the micro-line segment for the forward planning velocity. Finally, the design flow for the forward planning of the velocity is given. Finally, the above algorithm is used to perform simulation experiments for the optimization algorithm. Experimental results show that the proposed optimization improves the accuracy of fitting motion trajectories under the constraints of acceleration and deceleration addition, which validates the proposed algorithm.

Synchronization of delayed stochastic reaction–diffusion Hopfield neural networks via sliding mode control

Synchronization of stochastic reaction–diffusion Hopfield neural networks with s-delays via sliding mode control is investigated in this article. To begin with, we choose suitable functional space for state variables, then the system is transformed into a functional differential equation in an infinite-dimensional Hilbert space by using appropriate functional analysis technique. Based on above preliminary preparation, sliding mode control (SMC) is constructed to drive the error trajectory into the designed switching surface. Specifically, the switching surface is constructed as linear combination of state variables, which is related to control gains. Then novel SMC law is designed which involving delay, reaction diffusion term, and reaching law. Furthermore, the criterion of mean-square exponential synchronization for stochastic delayed reaction–diffusion Hopfield neural networks with s-delays is given in the form of matrix form. This criterion is less restrictive and easy to check in computer. Meanwhile, a different novel Lyapunov–Krasovskii functional (LKF) mixed with Itô’s formula, Young inequality, Hanalay inequality is employed in this proof procedure. At last, a numerical example is presented to validate the availability of theoretical result. The simulation is based on the finite difference method, and numerical result coincides with the theoretical result proposed.

Implementation and Evaluation of Walk-in-Place Using a Low-Cost Motion-Capture Device for Virtual Reality Applications.

Virtual reality (VR) is used in many fields, including entertainment, education, training, and healthcare, because it allows users to experience challenging and dangerous situations that may be impossible in real life. Advances in head-mounted display technology have enhanced visual immersion, offering content that closely resembles reality. However, several factors can reduce VR immersion, particularly issues with the interactions in the virtual world, such as locomotion. Additionally, the development of locomotion technology is occurring at a moderate pace. Continuous research is being conducted using hardware such as treadmills, and motion tracking using depth cameras, but they are costly and space-intensive. This paper presents a walk-in-place (WIP) algorithm that uses Mocopi, a low-cost motion-capture device, to track user movements in real time. Additionally, its feasibility for VR applications was evaluated by comparing its performance with that of a treadmill using the absolute trajectory error metric and survey data collected from human participants. The proposed WIP algorithm with low-cost Mocopi exhibited performance similar to that of the high-cost treadmill, with significantly positive results for spatial awareness. This study is expected to contribute to solving the issue of spatial constraints when experiencing infinite virtual spaces.

Reduction in Trajectory Error by Generating Smoother Trajectory for the Time-Efficient Navigation of Mobile Robot

Reduction in Trajectory Error by Generating Smoother Trajectory for the Time-Efficient Navigation of Mobile Robot

Fixed-time trajectory tracking for autonomous surface vehicles via output feedback under various constraints

This paper proposes a novel fixed-time output feedback trajectory tracking control method suitable for autonomous surface vehicles (ASVs). Firstly, various complex uncertainty terms, such as unknown external disturbances, unmodeled errors, and actuator faults are considered in this paper. And these terms are uniformly converted into the total uncertainty terms through model transformation for convenience. Then, a fixed-time extended state observer (FTESO) with the newly expanded state is designed to observe and estimate the total uncertainty terms. Next, the saturation dynamic filter (SDF) is adopted to address the input saturation, and the saturation factors of SDF are incorporated into the trajectory error calculation to reduce the torque mutation caused by an excessive error in the control input. Finally, a fixed-time control law is proposed by taking into account the ASV system error and FTESO estimation state. Simulation experiments show that this method has excellent control performance, and this conclusion is validated through stability proof and case comparison.

Curvature Scale Space LiDAR Odometry And Mapping (LOAM)

The LiDAR Odometry and Mapping (LOAM) algorithm ranks in second place in the Karlsruhe Institute of Technology and Toyota Technological Institute (KITTI), Visual Odometry/SLAM Evaluations. It utilizes a feature extraction algorithm based on the evaluation of the curvature of points under test, to produce estimated smooth and non-smooth regions within typically laser based Point Cloud Data (PCD). This feature extractor (FE) however, does not take into account PCD spatial or detection uncertainty, which can result in the divergence of the LOAM algorithm. Therefore, this article proposes the use of the Curvature Scale Space (CSS) algorithm as a replacement for LOAM’s current feature extractor. It justifies the substitution, based on the CSS algorithm’s similar computational complexity but improved feature detection repeatability. LOAM’s current feature extractor and the proposed CSS feature extractor are tested and compared with simulated and real data, including the KITTI odometry-laser data set. Additionally, a recent deep learning based LiDAR Odometry (LO) algorithm, the Convolutional Auto-Encoder (CAE)-LO algorithm, will also be compared, using this data set, in terms of its computational speed and performance. Performance comparisons are made based on the Absolute Trajectory Error (ATE) and Cardinalized Optimal Linear Assignment (COLA) metrics. Based on these metrics, the comparisons show significant improvements of the LOAM algorithm with the CSS feature extractor compared with the benchmark versions.

Tuning the Proportional-Integral-Derivative Control Parameters of Unmanned Aerial Vehicles Using Artificial Neural Networks for Point-to-Point Trajectory Approach.

Nowadays, trajectory control is a significant issue for unmanned micro aerial vehicles (MAVs) due to large disturbances such as wind and storms. Trajectory control is typically implemented using a proportional-integral-derivative (PID) controller. In order to achieve high accuracy in trajectory tracking, it is essential to set the PID gain parameters to optimum values. For this reason, separate gain values are set for roll, pitch and yaw movements before autonomous flight in quadrotor systems. Traditionally, this adjustment is performed manually or automatically in autotune mode. Given the constraints of narrow orchard corridors, the use of manual or autotune mode is neither practical nor effective, as the quadrotor system has to fly in narrow apple orchard corridors covered with hail nets. These reasons require the development of an innovative solution specific to quadrotor vehicles designed for constrained areas such as apple orchards. This paper recognizes the need for effective trajectory control in quadrotors and proposes a novel neural network-based approach to tuning the optimal PID control parameters. This new approach not only improves trajectory control efficiency but also addresses the unique challenges posed by environments with constrained locational characteristics. Flight simulations using the proposed neural network models have demonstrated successful trajectory tracking performance and highlighted the superiority of the feed-forward back propagation network (FFBPN), especially in latitude tracking within 7.52745 × 10-5 RMSE trajectory error. Simulation results support the high performance of the proposed approach for the development of automatic flight capabilities in challenging environments.

Tracking control of a flexible‐link manipulator based on an improved barrier function adaptive sliding mode

AbstractIn this paper, a novel controller designed for robust tracking control of a flexible‐link manipulator operating in the presence of parameter uncertainties and external disturbances within the joint space is introduced. The proposed controller employs an adaptive sliding mode control approach, incorporating an improved barrier function, to ensure that trajectory errors remain within predefined performance bounds. This design enhances the tracking performance without overestimating control‐switching gains. Additionally, a fixed‐time adaptive sliding mode control, featuring a rapid nonsingular terminal sliding mode variable, is introduced to expedite the convergence rate of the system state during the initial stages. The efficacy of the proposed control scheme is established through the Lyapunov method, demonstrating finite‐time convergence of the trajectory error to a specified neighborhood of zero. Experimental validation on a flexible‐link system supports the effectiveness and advantages of the proposed control strategy, as evidenced via comparisons with two existing adaptive control schemes.

2DLIW-SLAM:2D LiDAR-inertial-wheel odometry with real-time loop closure

Due to budgetary constraints, indoor navigation typically employs two-dimensional (2D) LiDAR rather than 3D LiDAR. However, the utilization of 2D LiDAR in simultaneous localization and mapping (SLAM) frequently encounters challenges related to motion degeneracy, particularly in geometrically similar environments. To address this problem, this paper proposes a robust, accurate, and multi-sensor-fused 2D LiDAR SLAM system specifically designed for indoor mobile robots. To commence, the original LiDAR data undergoes meticulous processing through point and line extraction. Leveraging the distinctive characteristics of indoor environments, line–line constraints are established to complement other sensor data effectively, thereby augmenting the overall robustness and precision of the system. Concurrently, a tightly-coupled front-end is created, integrating data from the 2D LiDAR, inertial measurement unit, and wheel odometry, thus enabling real-time state estimation. Building upon this solid foundation, a novel global feature point matching-based loop closure detection algorithm is proposed. This algorithm proves highly effective in mitigating front-end accumulated errors and ultimately constructs a globally consistent map. The experimental results indicate that our system fully meets real-time requirements. When compared to cartographer, our system not only exhibits lower trajectory errors but also demonstrates stronger robustness, particularly in degeneracy problem. We open source our methods here: https://github.com/LittleDang/2DLIW-SLAM.

Validation and Safety Profile of a Novel, Noninvasive Fiducial Attachment for Stereotactic Robotic-Guided Stereoelectroencephalography: A Case Series.

We developed, tested, and validated a novel, noninvasive, Leksell G frame-based fiducial attachment, for use in stereotactic registration for stereoelectroencephalography (sEEG). Use of the device increased the number of fixed reference points available for registration, while obviating the need for additional scalp incisions. We report here on our experience and safety profile of using the device. We collected registration data using the fiducial device across 25 adult and pediatric patients with epilepsy consecutively undergoing robotic-guided sEEG for invasive epilepsy monitoring, treated between May 2022 and July 2023. ROSA One Brain was used for trajectory planning and electrode implantation. Postoperative clinical and radiographic data were computed and quantified, including mean registration error for all patients. Entry point, target point (TP), and angular errors were measured. Descriptive statistics and correlation coefficients for error were calculated. Twenty-five patients underwent robotic-guided sEEG implantation (11 patients, bilateral; 10 patients, left unilateral; 4 patients, right). The mean number of electrodes per patient was 18 ± 3. The average mean registration error was 0.77 ± 0.11 mm. All patients were implanted with Ad-Tech depth electrodes. No clinically relevant complications were reported. Analysis of trajectory error was performed on 446 electrodes. The median entry point error was 1.03 mm (IQR 0.69-1.54). The median TP error was 2.26 mm (IQR 1.63-2.93). The mean angular error was 0.03 radians (IQR 0.02-0.05). There was no significant correlation between root mean square error and lead error. Root mean square error did not appreciably change over time, nor were there any significant changes in average angular, entry point, or TP error metrics. A novel, noninvasive, Leksell G frame-based fiducial attachment was developed, tested, and validated, facilitating O-arm-based stereotactic registration for sEEG. This simple innovation maintained an excellent accuracy and safety profile for sEEG procedures in epilepsy patients, with the added advantages of providing additional reference points for stereotactic registration, without requiring additional scalp incisions.

Robust loop closure detection and relocalization with semantic-line graph matching constraints in indoor environments

Loop closure detection (LCD) plays an essential role in the Simultaneous Localization and Mapping (SLAM) process, effectively reducing cumulative trajectory errors. However, conventional LCD methods often encounter challenges when dealing with variations in illumination, changes in viewpoint, and environments with weak textures. This is due to their reliance on low-level geometric or image features. To address these issues, we propose a robust LCD method named SL-LCD, which integrates semantic information and line features to fully leverage the semantic content and line attributes within indoor scenes, thereby establishing a reliable feature correspondence between query images and loop closure images. For the retrieval of candidate closed-loop images, we construct a semantic-line-segment topological graph and introduce a graph matching algorithm to perform the LCD task. This approach fully exploits image features and spatial information to achieve closed-loop detection in complex indoor scenes. Furthermore, we present a semantic voxel-based generalized ICP (SVGICP) closed-loop relocalization algorithm tailored for challenging and complex indoor scenes, enhancing the accuracy of closed-loop relocalization in such scenarios. Experimental results demonstrate that the SL-LCD algorithm proposed in this paper surpasses state-of-the-art methods, accurately detecting closed loops, and effectively eliminating trajectory drift.