Direct Kinematic Model Research Articles

Direct and Inverse Kinematics of a 3RRR Symmetric Planar Robot: An Alternative of Active Joints

Existing direct and inverse kinematic models of planar parallel robots assume that the robot’s active joints are all at the bases. However, this approach becomes excessively complex when modeling a planar parallel robot in which the active joints are within one single kinematic chain. To address this problem, our article unveils an alternative for a 3RRR symmetric planar robot modeling technique for the derivation of the robot workspace and the analysis of its direct and inverse kinematics. The workspace was defined using a system of inequalities, and the direct and inverse kinematics models were generated using vectorial analysis and an optimized geometrical approach, respectively. The resulting models are systematically presented and validated. Two final model renditions are delivered supplying a thorough equation analysis and an applicability discussion based on the importance of the robot’s mobile platform orientation. The advantages of this model are discussed in comparison to the traditional modeling approach: whereas conventional techniques require the solution of complex eighth-degree polynomials for the analysis of the active joint configuration of these robots, these models provide an efficient back-of-the-envelope analysis approach that requires the solution of a simple second-degree polynomial.

Dual-Loop Control of Cable-Driven Snake-like Robots

Snake-like robots, which have high degrees of freedom and flexibility, can effectively perform an obstacle avoidance motion in a narrow and unstructured space to complete assignments efficiently. However, accurate closed-loop control is difficult to achieve. On the one hand, this is because adding too many sensors to the robot will significantly increase its mass, size, and cost. On the other hand, the more complex structure of the hyper-redundant robot also challenges the more elaborate closed-loop control strategy. For these reasons, a cable-driven snake-like robot, which is compact and low cost, with force transducers and angle sensors, is designed in this article. The simpler and more direct kinematic model is studied, which applies to a widely used kinematics algorithm. Based on the kinematic model, the inverse dynamics are resolved. Finally, this article analyzes the sources of the motion errors and achieves dual-loop control through force-feedback and pose-feedback. The experiment results show that the robot’s structure and dual-loop control strategy function with high accuracy and reliability, meeting the requirements of engineering applications and high-precision control.

The effect of external loads and biological sex on coupling variability during load carriage

BackgroundLoad carriage is a fundamental requirement for military personnel that commonly results in lower-limb injuries. Coupling variability represents a potential injury mechanism for such repetitive tasks and its unknown whether external loads and biological sex affect coupling variability during load carriage. Research questionIs there a sex-by-load interaction during load carriage at self-selected walking speeds? MethodsTwenty-six participants (13 males, 13 females) completed three 10-minute treadmill-based trials wearing body-borne external load (0 %BM, 20 %BM, and 40 %BM) at load-specific self-selected walking speeds. A Vicon motion capture system tracked markers with a lower-body direct-kinematic model calculating sagittal-plane segment kinematics of the thigh, shank, and foot across 19 strides. Continuous relative phase standard deviation (CRPv) provided a measure of coupling variability for each coupling angle (Thigh-Shank and Shank-Foot). The CRPv for each load and sex was compared using statistical parametric mapping repeated measures ANOVA and paired t tests. ResultsSignificant sex-by-load interactions were reported for the Thigh-Shank coupling. Males demonstrated no significant load differences in CRPv, however, females displayed significantly higher CRPv in the 40 %BM than the 0 %BM condition. A significant main effect of load was observed in the Shank-Foot coupling, with the 40 %BM having significantly greater CRPv than the other load conditions. SignificanceBoth biological sex and external loads significantly affected CRPv during load carriage at self-selected walking speeds. Females demonstrated greater CRPv at the heavier loads, suggesting that the perturbation from the heavier mass increases coupling variability, which may also be amplified by a greater total passive load due to their relatively higher adipose tissue compared to males. The consistent CRPv in males suggests that higher relative loads may be required to change coupling variability. Collectively, these results suggest that external load affects the coupling variability of males and females differently, providing potential for injury screening and monitoring programs.

Towards a Discrete Snake-Like Robot Based on SMA-Actuated Tristable Modules for Follow the Leader Control Strategy

Snake-like robots applications include surveillance and exploration of confined environments where human presence is incompatible. The attractiveness of this type of mechatronic structure is notably linked to the modular character and the hyper-redundancy of their architecture, which gives it both mechanical robustness and great manoeuvrability. However, due to the large number of degrees-of-freedom, the use of advanced mathematical models are needed to asses the motion patterns and to simulate it. A new snake-like robot architecture is introduced in this paper together with the development methodology of a replicable multistable module. The interest of this contribution lies in the combination of the mechanical stability of the modules with an easy-to-use direct kinematic model, thus avoiding the need of complex control strategies. The design of one module exploiting the three stable states of a tristable flexible mechanism so as to orient the articulation of the module at three distinct stable angles is first presented. Then a prototype of a modular snake-like robot is built and experimentally evaluated. The prototype consists of 4 modules that can be individually oriented by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pm$</tex-math></inline-formula> 7.1 degrees. Each module measures 51.5 × 32 mm and weighs 2.5g. Thereby, this work provides the first results on the feasibility of this robotic architecture which consists of several multistable modules. A good agreement between the working space estimated with the direct kinematic model and experimental measurements is obtained. According to the fact that these are preliminary results, there is a 1.5% error between the experimental results and the models.

Developing application techniques of kinematics and simulation model for InMoov robot

In this work, the direct and inverse kinematic analysis of both robot arms are investigated based on the analytical and informational representation. The results of the study will be used to provide the functionality of gesturing by a robot in sign language, both Kazakh and other languages, used in educational systems, especially in children's institutions and societies for deaf people. A simulation model of the movement of the robot's arms in the workspace has been studied and built. The developed model will be further implemented and used as mathematical and information support for the created robot. The developed library contains implementations of forward kinematics and iterative algorithms for inverse kinematics. The InMoov robot is a platform widely used in research tasks, supported by the MyRobotLab package. A direct kinematic model for the left and right hands of the robot has been studied. Based on the Python programming language, the working space for robot manipulators was calculated, using the matpilotlib library, an iteration method algorithm was developed to find the probable path of robot manipulators in space. A model of a structured artificial neural network (ANN) is proposed, which is used to find a solution to the inverse kinematics of the InMoov robot with six degrees of freedom (4-dof). The applied ANN model is a multilayer perceptron neural network (MLPNN) in which the learning rule of the Adam-a gradient diskend type is applied. To solve this problem, the problem of finding the best ANN configuration was studied. It has been established that a multilayer parseptron neural network gives the minimum mean square error. The regression coefficient analysis, which shows a 95.6 % fit of all communication variables, is acceptable for obtaining the inverse kinematics of the InMoov robot.

Development of interface for kinematic analysis of a delta-type parallel robot

The development and implementation process of a computer interface for the kinematic analysis of a parallel robot, in delta configuration, and its application to a previously formed prototype are exposed. Being identified the associated equations, and deduced the respective geometric parameters. On the other hand, the synthesis of the direct and inverse kinematic models, with the Matlab software, guarantees the calculation of a specific Cartesian position, in the end effector of the robot used, once certain joint values have been assigned to it, or vice versa. Finally, a user-friendly graphical interface is created, whose functions are: data entry, resolution of the models described, issuance of the corresponding results, representation of the robot used and its physical manipulation. The results obtained in the real location of the end effector with respect to the values deduced by the interface, are competitive for both models analyzed, even though the prototype used operates by means of servomotors. An average position error of 0.083 cm per axis and overall of 0.006 cm is observed during the tests developed.

Coupling Numerical Deformable Models in Global and Reduced Coordinates for the Simulation of the Direct and the Inverse Kinematics of Soft Robots

In this letter, we propose a method to combine the Finite Element Method (FEM) with Discrete Cosserat Modeling (DCM) to capture the mechanics and the actuation of soft robots. The FEM is used to simulate the non-linear behavior of the volume of the soft structure while the cable/rod used for the actuation is modeled using the DCM. The two models are linked using kinematic constraints without imposing meshing rules. We demonstrate that both direct and inverse kinematic models can be obtained by quadratic optimization. The originality of this coupling is that the FEM model uses global coordinates (the position of the nodes of its mesh in space) where the Cosserat model uses local coordinates (successive strain values). The coupling of these mechanical models allows to combine the best of each parametrization. On the one hand, FEM allows to capture the behavior of the volume structure of the robot while accounting for its geometry with a complex mesh. On the other hand, the DCM allows efficient modeling of 1D structures such as rods, (concentric) tubes, cables, etc. that are used to deform the volume structure of the soft robots. DCM handles large deformation, torsion and (in)-extensibility and is efficient to compute. Moreover, the approach is compatible with complementarity constraints introduced when modeling contact and friction of the robot with its environment as well as the self-collision.

Reliability of walking and stair climbing kinematics in a young obese population using a standard kinematic and the CGM2 model

Background:Recently, the successor of the Conventional Gait Model, the CGM2 was introduced. Even though achievable reliability of gait kinematics is a well-assessed topic in gait analysis for several models, information about reliability in difficult study samples with high amount of subcutaneous fat is scarce and to date, not available for the CGM2. Therefore, this study evaluated the test–retest reliability of the CGM2 model for difficult data with high amount of soft tissue artifacts. Research question:What is the test–retest reliability of the CGM2 during level walking and stair climbing in a young obese population? Is there a clinically relevant difference in reliability between a standard direct kinematic model and the CGM2? Methods:A retrospective test–retest dataset from eight male and two female volunteers was used. It comprised standard 3D gait analysis data of three walking conditions: level walking, stair ascent and descent. To quantify test–retest reliability the Standard Error of Measurement (SEM) was calculated for each kinematic waveform for a direct kinematic model (Cleveland clinic marker set) and the CGM2. Results:Both models showed an acceptable level of test–retest reliability in all three walking conditions. However, SEM ranged between two and five degrees (∘) for both models and, thus, needs consideration during interpretation. The choice of model did not affect reliability considerably. Differences in SEM between stair climbing and level walking were small and not clinically relevant (<1°). Significance:Results showed an acceptable level of reliability and only small differences between the models. It is noteworthy, that the SEM was increased during the first half of swing in all walking conditions. This might be attributed to increased variability resulting for example from inaccurate knee and ankle axis definitions or increased variability in the gait pattern and needs to be considered during data interpretation.

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.

Closed-form solution for direct and inverse kinematic models of a parallel manipulator for robotic orbital welding

This paper presents a closed-form solution for direct and inverse kinematic models of a four-degree-of-freedom parallel manipulator designed for weld torch positioning of orbital welding of metallic pipes. The mathematical model was developed, implemented and simulated considering the geometric parameters of the prototype. The proposed closed-form solution showed that the mathematical model matched the behavior of the manipulator, confirming that the motion was entirely defined through the mathematical and geometric relations, without the requirement of iterations or numerical solutions. The closed-form solution also offered a simpler approach for the mechanical behavior of the manipulator, making it feasible to implement a less complex-coded routine in the embedded microcontroller due to its lower computational requirements.

RMoCap: an R language package for processing and kinematic analyzing motion capture data

Package RMoCap is an advanced open-source tool for scientists, engineers and computer graphics familiar with R language who work with motion capture (MoCap) technology. Package provides them with MoCap data handling, statistical processing, visualizing and analysis. Package uses well-established MoCap file exchange format and can be easily integrated with most of the motion analysis workflows. Among functions available in RMoCap, there are procedures for conversion between hierarchical and direct kinematic models, data averaging, correcting direction of motion, 3D interactive visualization and advanced analysis using Dynamic Time Warping. This paper covers all advanced algorithms that are implemented in RMoCap. This article also introduces direct to hierarchical kinematic conversion algorithm that is a new, never-before-published method. We also introduce extension of motion direction correction method that makes possible to process data that does not contain information about acceleration. All examples showed in this paper can be reproduced using replication code and data sources that are included to this package.

Programming and wireless control of a wafer manipulation SCARA robot using a mobile device

The research performed by the authors had the purpose of developing a control and programming application for a 3-axes SCARA robot designed for wafer manipulation and integrating it with a mobile device capable of wireless communication. The mobile device was then used to command axis movements, internal signals and for programming. The application was developed as a user-interface capable of communicating with robot’s controller and converting the user inputs into controller commands. In order to achieve position control, the direct kinematic model of the robot was developed. Furthermore, the application was integrated with the V-REP virtual simulation platform in order to achieve simulation and offline programming capabilities - the V-REP software provided the 3-D environment and the kinematics modelling functions required to perform the simulation while receiving commands from the developed application. Finally, a few demonstrative applications were configured in order to test the functionality of the system. The research has important implications in the field of industrial wireless communication, being a step towards more flexible robotic applications, full integration of remote operation technologies and easier access to remote production facilities.

A New 4-DOF Fully Parallel Robot With Decoupled Rotation for Five-Axis Micromachining Applications

We present a novel 4-DOF (degrees of freedom) parallel robot designed for five-axis micromachining applications. Two of its five telescoping legs operate simultaneously, thus acting as an extensible parallelogram linkage, and in conjunction with two other legs control the position of the tooltip. The fifth leg controls the tilt of the end-effector (a spindle), while a turntable fixed at the base of the robot controls the swivel of the workpiece. The robot is capable of tilting its end-effector up to 90 deg, for any tooltip position. In this paper, we study the mobility of the new parallel kinematic machine (PKM), describe its inverse and direct kinematic models, then study its singularities, and analyze its workspace. Finally, we propose a potential mechanical design for this PKM utilizing telescopic actuators as well as the procedure for optimizing it. In addition, we discuss the possibility of using constant-length legs and base-mounted linear actuators in order to increase the volume of the workspace.

Self-motion conditions for a 3-PPPS parallel robot with delta-shaped base

This paper presents the self-motion conditions of the 3-PPPS parallel robot with an equilateral mobile platform and an equilateral-shaped base. The study of the direct kinematic model shows that this robot admits self-motion of the Cardanic type as the 3-RPR planar parallel robot where the first revolute joint of each leg is actuated or the PamINSA parallel robot. This property explains why the direct kinematic model admits an infinite number of solutions in the center of the workspace but has never been studied until now. The condition of this singularity is described and the location of the self-motion in the workspace with respect to all the singularities is then presented. The quaternion parameters are used to represent the singularity surfaces and the self-motion conditions in the workspace.

Kinematic Calibration of a Three Degrees-of-Freedom Parallel Manipulator With a Laser Tracker

Kinematic calibration is commonly used to improve the accuracy of a parallel mechanism. This paper presents an effective method for calibrating an overconstrained three degrees-of-freedom parallel manipulator employing a direct kinematic model. An error-mapping function is formulated from the differential of its kinematic model which is established through vector chains with the geometrical errors. To simplify the measurement of the error, the positioning and orientation error of the moving platform is replaced by the positioning error of the tool center point, which can be measured by a laser tracker accurately. Three different objective functions F1, F2, and F∞, respectively, representing 1-norm, 2-norm, and inf-norm of the error vector are used to identify the geometrical parameters of the manipulator. The results of computer simulation show that parameters after kinematic calibration through minimizing the objective function F2 is highly accurate and efficient. A calibration experiment is carried out to verify the effectiveness of the method. The maximum residual of calibration points reduces greatly from 3.904 to 0.256 mm during parameter identification. The positioning errors of all points on and inside the space surrounded by the calibration points are smaller than 0.4 mm after error compensation.

Anthropomorphic Features for On-Line Signatures.

Many features have been proposed in on-line signature verification. Generally, these features rely on the position of the on-line signature samples and their dynamic properties, as recorded by a tablet. This paper proposes a novel feature space to describe efficiently on-line signatures. Since producing a signature requires a skeletal arm system and its associated muscles, the new feature space is based on characterizing the movement of the shoulder, the elbow and the wrist joints when signing. As this motion is not directly obtained from a digital tablet, the new features are calculated by means of a virtual skeletal arm (VSA) model, which simulates the architecture of a real arm and forearm. Specifically, the VSA motion is described by its 3D joint position and its joint angles. These anthropomorphic features are worked out from both pen position and orientation through the VSA forward and direct kinematic model. The anthropomorphic features' robustness is proved by achieving state-of-the-art performance with several verifiers and multiple benchmarks on third party signature databases, which were collected with different devices and in different languages and scripts.

Reliability of joint kinematic calculations based on direct kinematic and inverse kinematic models in obese children

BackgroundIn recent years, the reliability of inverse (IK) and direct kinematic (DK) models in gait analysis have been assessed intensively, but mainly for lean populations. However, obesity is a growing issue. So far, the sparse results available for the reliability of clinical gait analysis in obese populations are limited to direct kinematic models. Reliability error-margins for inverse kinematic models in obese populations have not been reported yet. Research questionsIs there a difference in the reliability of IK models compared with a DK model in obese children? Are there any differences in the joint kinematic output between IK and DK models? MethodsA test-retest study was conducted using three-dimensional gait analysis data from two obese female and eight obese male participants from an earlier study. Data were analyzed using a DK model and two OpenSim-based IK models. Test-retest reliability was compared by calculating the Standard Error of Measurement (SEM) along with similar absolute reliability measures. A Friedman Test was used to assess whether there were any significant differences in the reliability between the models. Kinematic output of the models was compared by using Statistical Parametric Mapping (SPM). ResultsNo significant differences were found in the reliability between the DK and IK models. The SPM analysis indicated several significant differences between both IK models and the DK approach. Most of these differences were continuous offsets. SignificanceReliability values showed clinically acceptable error-margins and were comparable between all models. Therefore, our results support the careful use of IK models in overweight or obese populations, e.g. for musculoskeletal modelling studies. The inconsistent kinematic output can mainly be explained by different model conventions and anatomical segment coordinate frame definitions.

Design and control of an active suspension system for unmanned agricultural vehicles for field operations

In the design of both autonomously and remotely controlled unmanned agricultural vehicles it is important to use an efficient suspension system that enables free transit over uneven terrain. Most mobile robotic systems use either a direct or inverse kinematic structural model in order to accurately determine the position of the end effectors or joints. However, this increases the complexity of the system and requires greater computational effort. In this context, the objective of this work was to investigate a new strategy that integrates the concepts of zero moment point and fuzzy logic into the control system of a wheel-legged vehicle used in agricultural field operations. The control system was able to maintain the stability and working height of the vehicle within the established standards without the need for a kinematic model, thus offering a simpler solution to the problem.

Vision System-Based Design and Assessment of a Novel Shoulder Joint Mechanism for an Enhanced Workspace Upper Limb Exoskeleton.

Exoskeletons arise as the common ground between robotics and biomechanics, where rehabilitation is the main field in which these two disciplines find cohesion. One of the most relevant challenges in upper limb exoskeleton design relies in the high complexity of the human shoulder, where current devices implement elaborate systems only to emulate the drifting center of rotation of the shoulder joint. This paper proposes the use of 3D scanning vision technologies to ease the design process and its implementation on a variety of subjects, while a motion tracking system based on vision technologies is applied to assess the exoskeleton reachable workspace compared with an asymptomatic subject. Furthermore, the anatomic fitting index is proposed, which compares the anatomic workspace of the user with the exoskeleton workspace and provides insight into its features. This work proposes an exoskeleton architecture that considers the clavicle motion over the coronal plane whose workspace is determined by substituting the direct kinematics model with the dimensional parameters of the user. Simulations and numerical examples are used to validate the analytical results and to conciliate the experimental results provided by the vision tracking system.

The inter-tester repeatability of a model for analysing elbow flexion-extension during overhead sporting movements.

This study investigates the inter-tester repeatability of an upper limb direct kinematic (ULDK) model specifically for the reporting of elbow flexion-extension (FE) during overhead sporting movements, such as cricket bowling. The ULDK model consists of an upper arm and a forearm connected with a 6° of freedom elbow joint. The ULDK model was assessed for inter-tester repeatability by calculating elbow FE during cricket bowling in two sessions, with unique testers applying the kinematic marker set in each session. Analysis of both elbow FE time-varying waveforms (statistical parametric mapping = 0% time different) and extracted discrete events (no statistical differences, strong correlations > 0.9) support that this model is inter-tester repeatable at assessing elbow FE within the context of cricket bowling. This model is recommended as a framework in future studies for measuring elbow kinematics during other overhead sporting tasks, with recommendations for further participant-specific considerations. Graphical abstract ᅟ.