Inverse Kinematics Research Articles (Page 1)

Abstract To address the challenge of real-time detection and correction of assembly deviations during automated assembly processes, this study proposes an online assembly correction system based on a fiber Bragg grating (FBG) sensor array. The system utilizes an FBG array to continuously monitor changes in the strain field of the assembly structure, converting the measured wavelength shift Δλ into a spatial displacement vector for the fingers. Based on a rigid body kinematic model, the least-squares optimization algorithm was employed to solve the finger displacement into translation vector T and rotation angle θ of the misaligned assembly components. Real-time joint angle adjustment values were determined using inverse kinematic calculations of the robotic arm to achieve online position correction during the assembly process. The simulation validation confirmed the strain response under offset conditions. The experimental results demonstrate that the system can effectively detect assembly deviations in multiple directions. The correction algorithm had a high accuracy, with a displacement prediction error of ≤0.1 mm. The angle prediction deviation was small (standard deviation σ=0.30°, mean μ=0.02°), and there was no significant systematic deviation. This system achieves real-time monitoring and closed-loop correction of assembly deviations, thereby providing an effective solution for automated assembly tasks.

Taking the strong coupling characteristic between 4WISV’s lateral and yaw motion and the time-delay characteristic of the steering system into consideration can greatly improve the path-tracking accuracy of the Four-Wheel-Independent-Steering Vehicle (4WISV). However, most conventional control methods failed to fully analyze the kinematic relationship between path points and the vehicle and neglected the effect of the steering time-delay characteristic, which limits the improvement of 4WISV’s path-tracking accuracy. This article designs a kind of hierarchical path-tracking strategy (HPTS) and proposes the steering discrete time-delay model with the relaxation factor to solve the problems above. Specifically, the HPTS includes the tracking-motion control layer and the actuator regulating layer. The first layer introduces “kinematic inversion” in mechanics into path-tracking modeling to solve the desired motion commands by using the MPC controller. The second layer, considering the ramp convergence time-delay characteristic of the steering motor, is proposed to follow the motion commands from the first layer by using the improved LADRC controller. Ultimately, the real-time performance and the effectiveness of the HPTS are verified by the simulation and experimental platform. The results show that the HPTS proposed can improve 4WISV’s path-tracking accuracy (the lateral deviation reduced by 28.5% at least) while ensuring driving stability.

Abstract Percutaneous interventions, including biopsies, thermal ablations, and regional anesthesia, involve the insertion of an instrument into the patient’s body to remove tissue or manage pain. In this context, the use of a robotic assistant is suitable to guide the medical gestures, leading to a more time-effective intervention and better patient care. For this purpose, this article introduces a novel URRR-URR parallel mechanism. The constraint and mobility analysis of the mechanism is performed using screw theory. A methodology for determining the solution to its direct and inverse geometric models is presented. The forward and inverse kinematic Jacobian matrices of the mechanism are then expressed. Some singularities of the mechanism are identified and illustrated. Additionally, the design problem of the parallel manipulator (PM) under study is formulated as a bi-objective optimization problem. The first objective function is expressed in terms of the condition number of the forward and inverse Jacobian matrices. The second objective function deals with the mechanism size. Lastly, the nondominated Pareto-optimal solutions are obtained and three Pareto-optimal solutions are detailed.

Comparison of kinematics between markerless and marker-based motion capture systems for change of direction maneuvers.

Fission studies using quasi-free NN scattering reactions in inverse kinematics

Measurement of the 10B(d,n)11C reaction cross-section in the energy range of 0.05-0.57MeV in inverse kinematics.

A limitation of projected frontal area as an indicator of active drag in swimming: Focusing on tibial and femoral segments.

Machine learning-based inverse kinematics scalability for prismatic tensegrity structural manipulators

Horizontal control strategy of 3UPU/UP offshore parallel platform based on forward and inverse kinematic models

Objective To investigate the effects of fatigue on lower limb kinematics and kinetics during manual lifting tasks and to quantitatively analyze these effects in order to provide guidance for safe work practices. Methods Twenty healthy male college students performed lifting tasks with two load conditions (15 kg, low load; and 25 kg, high load) before and after fatigue. An eight-camera 3D motion capture system and two force plates were used to collect surface marker trajectories and ground reaction force data. Inverse kinematics and inverse dynamics analyses were conducted using OpenSim to calculate movement duration, joint angles, joint angular velocities, joint moments, joint power, and joint energy expenditure. Results (1) For the 15 kg lifting task, there were no significant differences in any parameter between pre- and post-fatigue conditions. (2) For the 25 kg task, compared to the pre-fatigue state, subjects exhibited decreased movement duration, increased joint range of motion, faster angular velocities, and elevated joint power and energy expenditure after fatigue. Conclusion Under low load conditions, the primary kinematic and kinetic parameters of the lower limb joints remained stable before and after fatigue, demonstrating strong fatigue resistance. In contrast, under high-load conditions, fatigue altered the lower limb movement patterns. The combined effect of high load and fatigue not only increased the burden on the musculoskeletal system but also led to a rise in potential injury risk, which requires further research for validation.

This work focuses on the derivation and validation of inverse kinematics equations for a planar ball-plate robot, a critical step for its precise control. The robot's kinematic model was developed considering a simplified equilateral triangular base and mobile platform. We detail the mathematical procedures for determining the z-coordinates of the platform's points and establishing the unit vector normal to the platform, which are fundamental for the inverse kinematics solution. The derived equations allow for the calculation of the joint angles necessary to achieve a desired ball position on the plate. For modeling and simulation, Matlab and Simulink were utilized. The robot's SolidWorks design was exported to Simulink using the Simscape Multibody Link tool, and a PID controller was integrated to achieve realistic simulated behavior. Simulation results demonstrate that the derived inverse kinematics equations accurately guide the robot, with the simulated ball trajectory closely matching the desired circular path. Furthermore, computer vision techniques, implemented with OpenCV in Python, were employed for real-time detection and tracking of both the platform and the ball. This visual feedback system provides crucial positional data, allowing for the potential closure of the control loop for adaptive visual control. This project successfully combines precise inverse kinematics with visual feedback, laying a robust foundation for advanced control systems in planar ball-plate robots.

This paper introduces TETRArm, a four-legged parallel manipulator endowed with kinematic redundancy. The redundancy of the robot is leveraged by incorporating two internal degrees of freedom into the moving platform of a non-redundant spatial parallel manipulator. This contribution demonstrates how a generalized coordinate can function identically in both inverse and forward instantaneous kinematics. Due to the complexity of the resulting equations, the forward position analysis is solved numerically. The instantaneous kinematics of the robot is examined using screw theory. In that concern, the velocity and acceleration expressions for the eight-degree-of-freedom parallel manipulator are systematically derived through the cancellation of passive joint rates via the Klein form. Numerical applications complement the theoretical findings.

ABSTRACT With the growing demand for precise and efficient control of robotic arms in the era of Industry 4.0, traditional methods for solving the inverse kinematics problem face significant limitations in terms of accuracy, computational speed, and adaptability to complex robotic configurations. This paper proposes a novel approach for solving the inverse kinematics problem by integrating the Improved Dung Beetle Optimization (IDBO) algorithm with Backpropagation Neural Networks (BPNN). This hybrid method is applied to Newton‐Raphson (NR) iterative algorithms for computing the kinematic solutions of robotic arms, effectively enhancing both optimization efficiency and solution accuracy. The IDBO algorithm, an advanced version of the traditional Dung Beetle Optimization (DBO), incorporates innovative strategies that improve convergence speed and balance local and global search capabilities, making it an effective tool for optimizing the weights and biases of the neural network. As a case study, the UR5e robotic arm is modeled using the Denavit‐Hartenberg convention. The proposed IDBO‐BPNN method is benchmarked against traditional and other optimization algorithms through simulations, demonstrating superior performance in terms of convergence speed, solution accuracy, and computational stability. Notably, the IDBO‐BPNN‐NR approach significantly reduces computation time, achieving an 80.6% reduction compared to the Random Iteration Point‐NR method and a 66.6% reduction compared to the Fixed Starting Point‐NR method. By comparing the solution parameters obtained using the IDBO‐BPNN‐NR algorithm and the Fixed Starting Point‐NR algorithm across robotic arms with varying degrees of freedom and structural configurations, the robust generalization capability of the proposed method is further validated. The results indicate that this hybrid approach is highly suitable for real‐time robotic applications, offering a scalable, efficient, and accurate solution to the inverse kinematics problem.

Using the Dakhov granitometamorphic block (Neoproterozoic – Paleozoic) as an example consideration is being given to exhumation mechanisms of the Hercynian basement complexes within the epi-platform orogen of the Greater Caucasus. The block forms a horst-like uplift and is located in the junction area between the Central and Western Caucasus segments, where the pericline of the Paleozoic core of the orogen is tectonically overlain by the Cimmerian (Lower to Middle Jurassic) and Alpine (Middle Jurassic to Cenozoic) structural-formational complexes. The geologicalstructural and particularly the structural-kinematic studies have shown that the Dakhov uplift sits in the transpressional dextral strike-slip fault zone that is a branch of the long-lived Pshekish-Tyrnyauz suture zone. The sandstones and shales of the Cimmerian complex commonly found north and south of the Dakhov uplift, are complicated by the nappeoverthrust structures with divergent displacements occurred relative to the axis of Dakhov block uplift and associated with sliding collapse of the overlying Jurassic strata into the adjacent depressions. The Dakhov block itself is a structural element of a shear zone, which forms a shear duplex and participates in the formation of large Z-shaped shear-contact axonoclines complicating the northern part and the eastern pericline of the uplift, as well as its bordering Jurassic strata. The northern part of the uplift still contains a fragment of a serpentinite-gneiss melange zone that formed during the Hercynian tectogenesis. This zone exhibits signs of kinematic inversions in fault structures, related to rotation phenomena of large domains of metamorphic rocks.The isolation of the Dakhov uplift within the Hercynian basement structure was caused by the presence of a rheologically weakened Hercynian suture zone (serpentinite-gneiss melange) therein. During the Cimmerian dextral slipstrike movements, this zone was reactivated and experienced planar bending, which gave rise to the formation of asymmetric Z-shaped axonoclines. Rotational shear deformations in the area of converging flanks of these axonoclines contributed to the development of an extensional shear duplex, in which the Dakhov crystalline block was uplifted. The Cimmerian exhumation of the Dakhov crystalline block occurred as a result of the combined action of two interconnected heterogeneous processes: transpressional deformation of the basement and gravity sliding of the Lower to Middle Jurassic cover sediments. The processes involved in the Late Alpine orogeny, which began at the Neogene-Quaternary boundary, proceeded simultaneously with the collapse of the growing Greater Caucasus orogen. One of the forms of collapse occurrence in the study area was the development of tectono-gravitational detachments and sliding of the Alpine cover sediment down the northern slope of the orogen that causes the pre-Alpine basement rocks, including the Dakhov crystalline block, to be exposed on the modern relief surface.

This study describes the design and implementation process of a 3-DOF robotic arm designed to automatically stack objects based on coordinates using the inverse kinematics method. The system combines the use of servo motors, proximity sensors, and an Arduino Nano microcontroller to detect the presence of objects and adjust the angle of each joint, enabling precise object placement. Unlike traditional approaches that use fixed motion paths, the method proposed in this study dynamically calculates joint angles according to the height and position of the targeted stack. System testing demonstrated stable performance in stacking objects at five different coordinate points, with travel times ranging from 7.78 to 8.74 seconds and perfect placement success rates in every trial. Analysis of servo angle data indicates that the robot arm is capable of automatically adjusting its movements in response to changes in stack height, ensuring system accuracy and reliability. As such, this automation solution offers a cost-effective alternative for small-scale stacking applications that require flexibility and real-time position adjustment capabilities.

Anterior cruciate ligament (ACL) injuries are common, and re-injuries remain high despite advances in rehabilitation. Return-to-sport (RTS) assessments focus on strength, clinical and hop tests, and time-based criteria but often exclude objective movement quality measures. Biomechanical deficits during jump-landings can persist post-reconstruction, contributing to re-injury risk. Fatigue further alters neuromuscular control, potentially exacerbating risk-related movement patterns, yet most RTS tests are conducted in non-fatigued states. This study introduces a motion dataset of 2199 trials across six bilateral (countermovement jump, drop jump) and unilateral (forward hop, countermovement jump, cross-over hop, 90° medial rotation hop) jump-landing tasks, performed under fatigued and non-fatigued conditions. The dataset includes 3D motion capture and ground reaction force data, including full-body inverse kinematics data (joint angles: knee, hip flexion, abduction, rotation, ankle flexion, trunk and pelvis) processed in OpenSim software for 43 participants comprising individuals with prior ACL injury (n = 21) and healthy controls (n = 22). The dataset enables detailed analyses of jump-landing biomechanics under fatigue, aiming to improve RTS decision-making to reduce re-injury risk.

IntroductionThe sit-to-stand (STS) movement represents a mechanically demanding task, particularly informative in patients with knee osteoarthritis. While three-dimensional optoelectronic motion capture is the gold standard for analyzing joint biomechanics, the influence of protocol selection remains poorly characterized in the context of STS. This study investigated protocol-induced variability in knee kinematics and kinetics by evaluating two widely used marker sets: the anatomical-based IOR and the cluster-based CAST, each combined with either inverse kinematics or a six degrees-of-freedom joint model.Materials and MethodsTwenty-four patients (mean age of 67 ± 5 years and BMI of 28.9 ± 3.8 kg/m2) with end-stage KOA (Kellgren-Lawrence grade 3 or 4) performed three STS trials, and biomechanical outputs were compared across the four resulting protocols using Mean Absolute Variability (MAV), Mean Absolute Differences (MAD), and Statistical Parametric Mapping (SPM).ResultsResults revealed substantial variability across protocols, with the highest discrepancies observed in the sagittal plane: peak MAV reached 23.99° for knee flexion angle and 0.24 Nm/kg for knee flexion moment. Frontal and transverse parameters also showed clinically meaningful differences, particularly for knee adduction and internal rotation angles, with MAD values exceeding established thresholds. Differences were amplified when both markers set, and modeling strategy varied. In this context, cluster-based configurations showed reduced variability. SPM analyses revealed temporally localized differences, particularly at the initiation and final stabilization phases of the movement.ConclusionThese findings emphasize the critical role of protocol selection in motion analysis and its direct impact on the interpretation of knee biomechanics during functional tasks, highlighting the importance of adopting consistent and robust methodological frameworks to ensure clinical reliability and cross-study comparability.Clinical Trial Registrationhttps://clinicaltrials.gov/, identifier NCT06634654.

This paper presents a novel numerical algorithm for inverse kinematics (IK) in robotic arms with offset wrists to address the challenges in IK solutions caused by biased parameters. Initially, the problem is simplified by categorizing robotic arms into two standard types and applying rotation or translation transformations to the terminal link. This approach is used for a robotic arm with a biased wrist, allowing for the acquisition of joint angles that approximate the desired solution. Subsequently, the initial Hessian matrix is corrected by incorporating the Jacobian matrix and regularization terms. Furthermore, the step size of the scaled memoryless augmented Broyden-Fletcher-Goldfarb-Shanno (SMABFGS) algorithm is dynamically adjusted to avoid convergence to local optima by integrating a momentum-based gradient descent (GD) method. The joint angles are iteratively refined to facilitate the convergence of the robotic arm’s end effector toward the desired pose. Finally, the algorithm’s accuracy in solving discrete end-effector poses is validated through a simulation experiment of IK with randomly sampled end poses. Additionally, a trajectory-tracking experiment is conducted on a physical robotic arm with an offset wrist to demonstrate its effectiveness and real-time performance in practical robotic operations.Supplementary InformationThe online version contains supplementary material available at 10.1038/s41598-025-19054-y.

Abstract Establishing a communication mechanism for service and assistive robots to help the disabled and old age population through Human-Robot Interaction (HRI) is still a challenging task for further study. This research explores a vision and gesture-based control strategy, taking into account static and dynamic human gestures and full-body pose estimation without the use of any wearable devices. The human action recognition algorithm is coupled with an object detector algorithm to automatically perform a robotic task. The Deep Learning (DL) techniques, MediaPipe with Long Short-Term Memory (LSTM) model and You Only Look Once (YOLO) v9 algorithms are implemented for human gesture recognition and object detection respectively. For the robotic manipulation task, there are eight object classes, each uniquely associated with one of eight corresponding human gesture classes. These gestures are categorized into two types: four static gestures and four dynamic gestures. The dataset of object and gesture classes is prepared from scratch in this study. Based on the particular human gesture or action, the Intel RealSense depth camera provides position and depth information of the detected object, and the robotic arm picks and places that object using its Inverse Kinematics (IK) solution. The prediction outcomes and experimental demonstrations suggest that the proposed study performs quite well as compared to the recently used related studies and exhibits remarkable performance in establishing a real-time HRI system.

Fruit picking in complex orchard environments is limited by the low detection and recognition accuracy due to clustered background, illumination variation, and partial occlusion. To improve the picking performance, a hierarchical visual grasping architecture based on You Look Only Once (YOLO) algorithm and adaptive error compensation is proposed. The upper layer uses YOLOv5 and inverse kinematics to recognize and localize the target. Ant colony optimization is specifically used for hyperparameter tuning of YOLOv5 to improve the detection accuracy. The middle layer dynamically compensates for the output torque of the joint actuator through the feedback linearization method. The lower layer finishes precise grasping through nonlinear mapping model between the pulse width modulation signal and the servo angle. Experimental results validate that the proposed architecture outperforms traditional methods by reaching 98.2% and 97.7% recognition accuracy in obstacle-free scenarios and complex environments, a higher grasping success rate, and a lower positioning deviation.