Inverse Kinematic Model Research Articles

Geometric error identification and compensation for rotary worktable of gear profile grinding machines based on single-axis motion measurement and actual inverse kinematic model

Gear profile grinding accuracy is often restricted by geometric errors of the rotary worktable. This paper proposes a novel approach to improve the geometric accuracy of the worktable based on single-axis motion measurement and the actual inverse kinematic model (IKM). The volumetric error model of gear profile grinding machines is first established based on homogeneous transformation matrices (HTMs) and machine kinematic chains, and the actual IKM based compensation method is then proposed to offset the position-dependent geometric errors (PDGEs) of the worktable. It directly gives explicit analytical expressions of compensated motion commands for efficient compensation. Besides, a novel PDGEs identification approach based on single-axis motion measurement with a double ball bar (DBB) is presented for the worktable. This approach has improved identification accuracy and stronger robustness as the interference error of non-targeted axes is avoided. The influence of the installation errors of the workpiece ball on measurement results and the PDGEs on gear grinding errors were discussed. The experiments verified the effectiveness of the identification approach, and the geometric accuracy tests of the worktable validated the compensation method.

Enhancement in Quality Estimation of Resistance Spot Welding Using Vision System and Fuzzy Support Vector Machine

The current nondestructive testing methods such as ultrasonic, magnetic, or eddy current signals, and even the existing image processing methods, present certain challenges and show a lack of flexibility in building an effective and real-time quality estimation system of the resistance spot welding (RSW). This paper provides a significant improvement in the theory and practices for designing a robotized inspection station for RSW at the car manufacturing plants using image processing and fuzzy support vector machine (FSVM). The weld nuggets’ positions on each of the used car underbody models are detected mathematically. Then, to collect perfect pictures of the weld nuggets on each of these models, the required end-effector path is planned in real-time by establishing the Denavit-Hartenberg (D-H) model and solving the forward and inverse kinematics models of the used six-degrees of freedom (6-DOF) robotic arm. After that, the most frequent resistance spot-welding failure modes are reviewed. Improved image processing methods are employed to extract new features from the elliptical-shaped weld nugget’s surface and obtain a three-dimensional (3D) reconstruction model of the weld’s surface. The extracted artificial data of thousands of samples of the weld nuggets are divided into three groups. Then, the FSVM learning algorithm is formed by applying the fuzzy membership functions to each group. The improved image processing with the proposed FSVM method shows good performance in classifying the failure modes and dealing with the image noise. The experimental results show that the improvement of comprehensive automatic real-time quality evaluation of RSW surfaces is meaningful: the quality estimation could be processed within 0.5 s in very high accuracy.

Algebraic Method-Based Point-to-Point Trajectory Planning of an Under-Constrained Cable-Suspended Parallel Robot with Variable Angle and Height Cable Mast

To avoid impacts and vibrations during the processes of acceleration and deceleration while possessing flexible working ways for cable-suspended parallel robots (CSPRs), point-to-point trajectory planning demands an under-constrained cable-suspended parallel robot (UCPR) with variable angle and height cable mast as described in this paper. The end-effector of the UCPR with three cables can achieve three translational degrees of freedom (DOFs). The inverse kinematic and dynamic modeling of the UCPR considering the angle and height of cable mast are completed. The motion trajectory of the end-effector comprising six segments is given. The connection points of the trajectory segments (except for point P3 in the X direction) are devised to have zero instantaneous velocities, which ensure that the acceleration has continuity and the planned acceleration curve achieves smooth transition. The trajectory is respectively planned using three algebraic methods, including fifth degree polynomial, cycloid trajectory, and double-S velocity curve. The results indicate that the trajectory planned by fifth degree polynomial method is much closer to the given trajectory of the end-effector. Numerical simulation and experiments are accomplished for the given trajectory based on fifth degree polynomial planning. At the points where the velocity suddenly changes, the length and tension variation curves of the planned and unplanned three cables are compared and analyzed. The OptiTrack motion capture system is adopted to track the end-effector of the UCPR during the experiment. The effectiveness and feasibility of fifth degree polynomial planning are validated.

Prescribing joint co-ordinates during model preparation in OpenSim improves lower limb unplanned sidestepping kinematics

ObjectivesInvestigate how prescribing participant-specific joint co-ordinates during model preparation influences the measurement agreement of inverse kinematic (IK) derived unplanned sidestepping (UnSS) lower limb kinematics in OpenSim in comparison to an established direct kinematic (DK) model. DesignParallel forms repeatability. MethodsThe lower limb UnSS kinematics of 20 elite female athletes were calculated using: 1) an established DK model (criterion) and, 2) two IK models; one with (IKPC) and one without (IK0) participant-specific joint co-ordinates prescribed during the marker registration phase of model preparation in OpenSim. Time-varying kinematic analyses were performed using one dimensional (1D) statistical parametric mapping (α=0.05), where zero dimensional (0D) Root Mean Squared Error (RMSE) estimates were calculated and used as a surrogate effect size estimates. ResultsStatistical differences were observed between the IKPC and DK derived kinematics as well as the IK0 and DK derived kinematics. For the IKPC and DK models, mean kinematic differences over stance for the three dimensional (3D) hip joint, 3D knee joint and ankle flexion/extension (F/E) degrees of freedom (DoF) were 46±40% (RMSE=5±5°), 56±31% (RMSE=7±4°) and 3% (RMSE=2°) respectively. For the IK0 and DK models, mean kinematics differences over stance for the 3D hip joint, 3D knee joint and ankle F/E DoF were 70±53% (RMSE=14±11°), 46±48% (RMSE=8±7°) and 100% (RMSE=11°) respectively. ConclusionsPrescribing participant-specific joint co-ordinates during model preparation improves the agreement of IK derived lower limb UnSS kinematics in OpenSim with an established DK model, as well as previously published in-vivo knee kinematic estimates.

Empirical Quasi-Static and Inverse Kinematics of Cable-Driven Parallel Manipulators Including Presence of Sagging

Cable-driven parallel manipulators (CDPMs) have been of great interest to researchers in recent years because they have many advantages compared to the traditional parallel robot. However, in many studies they lack the cable’s elasticity that leads to flexible cables just being considered as extendable rigid links. Furthermore, an external force acts on the extremities of cable and the self-weight is relevant to the length of it. Experimentally, a small change in length produces a huge change in tension act on the entire cable. By this property, the adjusting length of cable is often added to the traditional inverse kinematic solution in order to reduce the tension force exerted on the cable. This means that the load on the actuator is also reduced. Because of the relationship between tension that acts on the cable and its length, the kinematic problem itself does not make sense without concerning the static or dynamic problems. There is often interest in planning forces for actuators and the length of cables based on a given quasi-static trajectory of the moving platform. The mentioned problem is combined with the quasi-static problem with the inverse kinematic problem of CDPM. In this study, we introduce a novel procedure to produce the quasi-static model and inverse kinematic model for CDPM with the presence of sagging by using both an analytic approach and empirical approach. The produced model is time-efficient and is generalized for spatial CDPM. To illustrate the performance of the proposed model, the numerical and experimental approaches are employed to determine particular solutions in the feasible solutions set produced by our model in order to control the two redundant actuators’ CDPM tracking on a certain desired trajectory. Its results are clearly described in the experimental section.

Sensor-free Force Control of Tendon-driven Ablation Catheters through Position Control and Contact Modeling.

In the present study, a sensor-free force control framework for tendon-driven steerable catheters was proposed and validated. The hypothesis of this study was that the contact force between the catheter tip and the tissue could be controlled using the estimated force with a previously validated displacement-based viscoelastic tissue model. The tissue model was used in a feedback control loop. The model estimated the contact force based on a realtime estimation of catheter-tissue indentation depth performed by a data-driven inverse kinematic model. To test the hypothesis, a tendon-driven catheter (φ6 × 40mm) and a robotic catheter intervention system were prototyped and characterized. Three validation studies were performed to test the performance of the proposed system with static and dynamic inputs. The results showed that the system was capable of reaching to the desired force with a root-mean-square error of 0.03 ± 0.02N for static tests and 0.05 ± 0.04N for dynamic inputs. The main contribution of this study was providing a computationally efficient and sensor-free force control schema for tendon-driven catheters.

Rolling based locomotion on rough terrain for a wheeled quadruped using centroidal dynamics

This paper proposes a new wheel motion generator to track the centroidal motion of one quadruped-on-wheel robot which has the ability to cross various rough terrains with the model based whole-body torque control. The generator is used to track the whole-robot centroidal motion reference. Firstly, the wheel contact model and the whole-body inverse kinematics model are derived using spatial vectors. The wheel motion is extracted out mathematically depending on the base and the legged motions, which serves as the kinematics model. Then the wheel motion generator is developed by combining both the kinematics model and the robot centroidal momentum/dynamics model. The models are decomposed into three components relating to the base motion, the legged motion and the wheel motion. The adaptive wheel motion references are derived in a detailed mathematical way and several algorithms are developed for the model decompositions. Finally, the robot is simulated to be driven on various rough terrains using the operational space control framework mixed with our proposed compatible prioritized impedance controller. The required torque for multiple tasks is generated by the feed-forward and feedback controllers while fulfilling the contact constraints.

Accuracy analysis and synthesis of asymmetric parallel mechanism based on Sobol-QMC

Aiming at the aircraft composite skin grinding, a new three degree-of-freedom (DOF) parallel mechanism with asymmetrical structure (TAM) is proposed to replace manual grinding. The TAM is achieved by integrating one of active limbs into the passive limb while keeping the required DOF unchanged, which is divided into two closed-loop chains: telescopic rod and parallelogram. The inverse kinematics models of the two chains are established according to closed-loop vector method. Thus, the actuation and the constraint Jacobian matrix are obtained. Based on the perturbation principle, the error modeling of the TAM is built. Adopting the constraint Jacobian matrix, 15 uncompensated errors are distinguished from the error model. In order to improve the working accuracy of the TAM, accuracy analysis and synthesis are necessary for all the uncompensated errors. The mapping function reflects the influence of uncompensated errors on the pose accuracy. The global sensitivity evaluation indexes are established by mapping function. Since Sobol sequences are superior in uniformity and convergence, the Quasi-Monte Carlo method based on Sobol sequences (Sobol-QMC) is introduced for sensitivity analysis. Taking the minimum manufacturing and installation costs as the optimization target, the objective function of accuracy synthesis is constructed. Ultimately, the reasonable tolerance zone of each uncompensated error is calculated by genetic algorithm. Simulation is performed by Sobol-QMC to verify the rationality of the optimization. The results show the probability is above 97% where most pose errors are in [[Formula: see text], [Formula: see text]] within the workspace. Therefore, accuracy synthesis is correct and practical.

Synthesis of the Inverse Kinematic Model of Non-Redundant Open-Chain Robotic Systems Using Groebner Basis Theory

One of the most important elements of a robot’s control system is its Inverse Kinematic Model (IKM), which calculates the position and velocity references required by the robot’s actuators to follow a trajectory. The methods that are commonly used to synthesize the IKM of open-chain robotic systems strongly depend on the geometry of the analyzed robot. Those methods are not systematic procedures that could be applied equally in all possible cases. This project presents the development of a systematic procedure to synthesize the IKM of non-redundant open-chain robotic systems using Groebner Basis theory, which does not depend on the geometry of the robot’s structure. The inputs to the developed procedure are the robot’s Denavit–Hartenberg parameters, while the output is the IKM, ready to be used in the robot’s control system or in a simulation of its behavior. The Groebner Basis calculation is done in a two-step process, first computing a basis with Faugère’s F4 algorithm and a grevlex monomial order, and later changing the basis with the FGLM algorithm to the desired lexicographic order. This procedure’s performance was proved calculating the IKM of a PUMA manipulator and a walking hexapod robot. The errors in the computed references of both IKMs were absolutely negligible in their corresponding workspaces, and their computation times were comparable to those required by the kinematic models calculated by traditional methods. The developed procedure can be applied to all Cartesian robotic systems, SCARA robots, all the non-redundant robotic manipulators that satisfy the in-line wrist condition, and any non-redundant open-chain robot whose IKM should only solve the positioning problem, such as multi-legged walking robots.

Didactic use of genetic algorithms: a model for teaching robotics

The study of articulated robots in higher education necessarily goes through the development of their kinematic models. The inverse kinematic model is usually described algebraically, although this representation is often difficult to obtain. Thus, the use of genetic algorithms in teaching robotics can be very attractive, since they allow students to easily develop models and predict the behavior of robots before their formal development. This way, the results of this work present a relatively fast way to simulate the inverse kinematic model, allowing the designer to have a broader view of the structure of a robot, coming to identify points that must be corrected or that can be optimized. It can be concluded that the use of genetic algorithms in robotics teaching is viable, having as main advantages their easy computational implementation and precision in the representation of kinematic models. .

New insights into lumbar flexion tests based on inverse and direct kinematic musculoskeletal modeling

Measurement of maximal lumbar flexion is considered to be a crucial element in the assessment of lumbar spine mechanics in situations as diverse as physiotherapy, orthopaedics, ergonomics, sport or aging. However, currently, there is no consensus on a reference test.This study aims to characterise five maximal lumbar flexion tests (four classical tests and a new, specifically-developed test designed to constrain pelvic retroversion) based on a three-dimensional, participant-specific musculoskeletal model.Twenty-six male and female participants performed the five tests. Movements were modelled in OpenSim to estimate change in length in lumbar, hamstring and gluteus muscles, together with lumbar flexion and pelvic tilt. These so-called “inverse” kinematic results were compared using a two-way ANOVA (sex×test). In a second step, lumbar muscle change in length was computed using a direct kinematic method.Lumbar flexion and lumbar muscle change in length were found to be greater when participants were in seated postures, with little pelvic retroversion. Female participants were observed to have less lumbar flexion than male participants (77±14° and 91±12°, respectively). Hip extensor muscles (hamstrings and gluteus) were fully stretched during each of the five tests. Our results highlight the specific roles of hamstrings, gluteus and lumbar muscles into reaching maximal lumbar flexion.Coupling inverse and direct kinematic methods proved to be a useful tool to enhance our knowledge of lumbar tests. Our findings help to characterise the role of the muscles involved in lumbar flexion, and we propose some recommendations for improving and standardising these tests.

Learning the Kinematics of a Manipulator Based on VQTAM

The kinematics of a robotic manipulator is critical to the real-time performance and robustness of the robot control system. This paper proposes a surrogate model of inverse kinematics for the serial six-degree of freedom (6-DOF) robotic manipulator, based on its kinematics symmetry. Herein, the inverse kinematics model is derived via the training of the Vector-Quantified Temporal Associative Memory (VQTAM) network, which originates from Self-Organized Mapping (SOM). During the processes of training, testing, and estimating of this neural network, a priority K-means tree search algorithm is utilized, thus improving the training efficacy. Furthermore, Local Linear Regression (LLR), Local Weighted Linear Regression (LWR), and Local Linear Embedding (LLE) algorithms are, respectively, combined with VQTAM to obtain three improvement algorithms, all of which aim to further optimize the prediction accuracy of the networks for subsequent comparison and selection. To speed up the solving of the least squared equation, which is common among the three algorithms, Singular Value Decomposition (SVD) is introduced. Finally, data from forward kinematics, in the form of the exponential product of a motion screw, are obtained, and are used for the construction and validation of the VQTAM neural network. Our results show that the prediction effect of the LLE algorithm is better than others, and that the LLE algorithm is a potential surrogate model to estimate the output of inverse kinematics.

A rapid performance evaluation approach for lower mobility hybrid robot based on gravity-center position.

This article develops a rapid performance evaluation approach for lower mobility hybrid robot, which provides guidance for manipulator evaluation, design, and optimization. First, a general position vector model of gravity center for the lower mobility hybrid robot in the whole workspace is constructed based on a general inverse kinematic model. A performance evaluation index based on gravity-center position is then proposed, where the coordinates pointing to the supporting direction are selected as the evaluation index of the robot performance. Furthermore, the credibility of the evaluation approach is verified from a 5-DOF hybrid robot (TriMule) by comparing with the condition number and the first natural frequency. Analysis results demonstrate that the evaluation index can not only reflect the performance spatial distribution in the whole workspace but also is sensitive to the performance difference caused by mass distribution. The proposed performance evaluation approach provides a new index for the rapid design and optimization of the cantilever robot.

A new solution for machining with RA-PKMs: Modelling, control and experiments

In this paper, a novel 5-Degree of Freedom (DOF) Redundantly Actuated (RA) Parallel Kinematic Manipulator (PKM) called SPIDER4 is presented. The main purpose of this manipulator is to perform machining tasks such as drilling and milling. All the mathematical models including the forward and inverse kinematic models, as well as the inverse dynamic model were developed. Owing to machining tasks require high precision, a RISE Feedforward controller is proposed for desired trajectory tracking. To show the performance and effectiveness of the proposed control scheme, real-time experiments were performed. The obtained results of the proposed controller compared to the standard RISE controller are presented and discussed. They confirm that the proposed controller outperforms the standard one.

An Autonomous Path Controller in a System on Chip for Shrimp Robot

This paper presents a path planning and trajectory tracking system for a BlueBotics Shrimp III®, which is an articulate mobile robot for rough terrain navigation. The system includes a decentralized neural inverse optimal controller, an inverse kinematic model, and a path-planning algorithm. The motor control is obtained based on a discrete-time recurrent high order neural network trained with an extended Kalman filter, and an inverse optimal controller designed without solving the Hamilton Jacobi Bellman equation. To operate the whole system in a real-time application, a Xilinx Zynq® System on Chip (SoC) is used. This implementation allows for a good performance and fast calculations in real-time, in a way that the robot can explore and navigate autonomously in unstructured environments. Therefore, this paper presents the design and implementation of a real-time system for robot navigation that integrates, in a Xilinx Zynq® System on Chip, algorithms of neural control, image processing, path planning, and inverse kinematics and trajectory tracking.

Inverse Kinematics Analysis of Hybrid-Driven Special Five-Bar Mechanism for Shield Machine

To simplify the inverse kinematics model of special five-bar mechanism based on Assur group, a inverse kinematics model is proposed by using vector analysis method and Euler’s formula, which is expressed by all explicit equations and establishes a direct relation between the output motion and the input motion. A numerical example and a computer simulation were conducted to verify the mathematical model. Results show that the motion law of control bar l4 obtained directly from the mathematical model is consistent with the result from ADAMS simulation, and the mathematical model of the special five-bar mechanism is correct and can be used to analyze the motion law of the drive bar and the control bar directly according to the motion parameters of the output point.

Workspace Identification of Stewart Platform

The workspace identification of 6-DOF Stewart Platform has been done in this paper through inverse kinematic modeling. This Stewart Platform has six linear cylinder–piston actuators connected within fixed and the moving platform. The motions of the moving platform such as surge, sway, heave, roll, pitch and yaw have been generated from the combined motions of piston of actuators. The mathematical formulations for Inverse-Kinematic modeling of Stewart Platform have been formulated to find out the individual piston motion for the required platform motion. The platform motions and the actuator motions have been studied for the workspace identification of the Stewart Platform.

Receding-Horizon Vision Guidance with Smooth Trajectory Blending in the Field of View of Mobile Robots

Applying computer vision to mobile robot navigation has been studied for over two decades. One of the most challenging problems for a vision-based mobile robot involves accurately and stably tracking a guide path in the robot limited field of view under high-speed manoeuvres. Pure pursuit controllers are a prevalent class of path tracking algorithms for mobile robots, while their performance is rather limited to relatively low speeds. In order to cope with the demands of high-speed manoeuvres, a multi-loop receding-horizon control framework, including path tracking, robot control, and drive control, is proposed in this paper. This is done within the vision guidance of differential-driving wheeled mobile robots (DWMRs). Lamé curves are used to synthesize a trajectory with G 2 -continuity in the field of view of the mobile robot for path tracking, from its current posture towards the guide path. The platform twist—point velocity and angular velocity—is calculated according to the curvature of the Lamé-curve trajectory, then transformed into actuated joint rates by means of the inverse-kinematics model; finally, the motor torques needed by the driving wheels are obtained based on the inverse-dynamics model. The whole multi-loop control process, initiated from Lamé-curve blending to computational torque control, is conducted iteratively by means of receding-horizon guidance to robustly drive the mobile robot manoeuvring close to the guide path. The results of numerical simulation show the effectiveness of our approach.

An Application of a 3-RRRS 6 DOF Parallel Manipulator

A new drive simulator is designed and fabricated through three legged, 6-DOF RRRS (Revolute- Revolute- Revolute- Spherical) parallel manipulator having three 1-DOF joints which are of revolute type and the middle joint being passive. The three legs are placed equilaterally on the base. Base joint rotates about a vertical axis whereas the other two joints rotate parallel to horizontal plane. The main objective of this drive simulator is to reduce the overall cost of a drive simulator which is done by replacing the conventional drive simulators having linear actuators with ones having rotatory actuators. Conventional drive simulators are 6 legged and each actuator is a linear actuator. The proposed design of drive simulator is having 3 legs which leads to increase in workspace and since prismatic actuators are replaced by rotary actuators the overall cost is also reduced. For the proposed drive simulator, inverse kinematics model is generated in a closed form way and workspace of the fabricated drive simulator is verified and workspace volume is calculated for all possible orientations and plotted. Kinematic control is done through Arduino based on inverse kinematics model.

Design and simulation of a robotic arm for manufacturing operations in the railcar industry

As part of the application of the Fourth Industrial Revolution (FIR) to manufacturing activities, robotic solutions are integrated into the cyber physical systems and the production systems to enhance the automation of the manufacturing processes. This will further enhance high productivity with reduced manufacturing cycle time and overall cost. This work discusses the modelling and simulation of a robotic arm for manufacturing operations in the railcar industry. The Computer Aided Design (CAD) and the Finite Element Analysis (FEA) were carried out using the Solidworks 2017 under different loading conditions. The results of the finite element analysis showed the robotic arm is unlikely to yield or fail under different loading conditions as examined using the Von Mises failure analysis criterion. The negligible magnitude of the strain and displacement distributions imply that the robotic arm will be able to perform the gripping, handling and assembly operations with high degree of precision and accuracy during the manufacturing processes. Furthermore, using the inverse kinematics model in the MATLAB 2018 b environment, the kinematic motion and trajectory of the robotic arm along the X-Y coordinates show the movement of the robotic arm along a well-defined path, which indicates that the arm is highly flexible, characterized by smooth motion along the predetermined path during the manufacturing operations. Hence, this will promote the development of products with high quality in an efficient and fast process.