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Intervertebral kinematics can affect model-predicted loads and strains in the spine; therefore knowledge of expected vertebral kinematics error is important for understanding the limitations of model predictions. This study addressed how different kinematic models of the neck affect the prediction of intervertebral kinematics from markers on the head and trunk. Eight subjects executed head and neck extension-flexion motion with simultaneous motion capture and biplanar dynamic stereo-radiography (DSX) of vertebrae C1-C7. A generic head and neck model in OpenSim was scaled by marker data, and three versions of the model were used with an inverse kinematics solver. The models differed according to the number of independent degrees of freedom (DOF) between the head and trunk: 3 rotational DOF with constraints defining intervertebral kinematics as a function of overall head-trunk motion; 24DOF with 3 independent rotational DOF at each level, skull-T1; 48DOF with 3 rotational and 3 translational DOF at each level. Marker tracking error was lower for scaled models compared to generic models and decreased as model DOF increased. The largest mean absolute error (MAE) was found in extension-flexion angle and anterior-posterior translation at C1-C2, and superior-inferior translation at C2-C3. Model scaling and complexity did not have a statistically significant effect on most error metrics when corrected for multiple comparisons, but ranges of motion were significantly different from DSX in some cases. This study evaluated model kinematics in comparison to gold standard radiographic data and provides important information about intervertebral kinematics error that are foundational to model validity.

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It has long been recognized that segments of the protein main chain are like robotic manipulators and inverse kinematics methods from robotics have been applied to model loops to bridge gaps in protein comparative modelling. The complex internal motion of a redundant manipulator with fixed ends is called a self-motion and its character is determined by the relative position of its ends. Self-motions that are topologically equivalent (homotopic) occupy the same continous region of the configuration space. Topologically inequivalent (non-homotopic) regions are separated by co-regular surfaces and crossing a co-regular surface can result in a sudden dramatic change in the character of the self-motion. It is shown, using a five-residue type I ß-turn, that these concepts apply to protein segments and that as the ends of the five-residue segment come closer together, a co-regular surface is crossed, and the structure is locked in to becoming either a type I or type I' turn. It is also shown that the type II turn is topologically equivalent to the type I' turn, not the type I turn. These results have implications for both native-state protein dynamics and protein folding.

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Walking is the most common form of how animals move on land. The model organism Drosophila melanogaster has become increasingly popular for studying how the nervous system controls behavior in general and walking in particular. Despite recent advances in tracking and modeling leg movements of walking Drosophila in 3D, there are still gaps in knowledge about the biomechanics of leg joints due to the tiny size of fruit flies. For instance, the natural alignment of joint rotational axes was largely neglected in previous kinematic analyses. In this study, we therefore present a detailed kinematic leg model in which not only the segment lengths but also the main rotational axes of the joints were derived from anatomical landmarks, namely, the joint condyles. Our model with natural oblique joint axes is able to adapt to the 3D leg postures of straight and forward walking fruit flies with high accuracy. When we compared our model to an orthogonalized version, we observed that our model showed a smaller error as well as differences in the used range of motion (ROM), highlighting the advantages of modeling natural rotational axes alignment for the study of joint kinematics. We further found that the kinematic profiles of front, middle, and hind legs differed in the number of required degrees of freedom as well as their contributions to stepping, time courses of joint angles, and ROM. Our findings provide deeper insights into the joint kinematics of walking in Drosophila, and, additionally, will help to develop dynamical, musculoskeletal, and neuromechanical simulations.

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It is worthwhile to calculate the execution cost of a manipulator for selecting a planning algorithm to generate trajectories, especially for an agricultural robot. Although there are various off-the-shelf trajectory planning methods, such as pursuing the shortest stroke or the smallest time cost, they often do not consider factors synthetically. This paper uses the state-of-the-art Python version of the Robotics Toolbox for manipulator trajectory planning instead of the traditional D-H method. We propose a cost function with mass, iteration, and residual to assess the effort of a manipulator. We realized three inverse kinematics methods (NR, GN, and LM with variants) and verified our cost function's feasibility and effectiveness. Furthermore, we compared it with state-of-the-art methods such as Double A* and MoveIt. Results show that our method is valid and stable. Moreover, we applied LM (Chan λ = 0.1) in mobile operation on our agricultural robot platform.

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A single depth camera provides a fast and easy approach to performing biomechanical assessments in a clinical setting; however, there are currently no established methods to reliably determine joint angles from these devices. The primary aim of this study was to compare joint angles as well as the between-day reliability of direct kinematics to model-constrained inverse kinematics recorded using a single markerless depth camera during a range of clinical and athletic movement assessments.A secondary aim was to determine the minimum number of trials required to maximize reliability. Eighteen healthy participants attended two testing sessions one week apart. Tasks included treadmill walking, treadmill running, single-leg squats, single-leg countermovement jumps, bilateral countermovement jumps, and drop vertical jumps. Keypoint data were processed using direct kinematics as well as in OpenSim using a full-body musculoskeletal model and inverse kinematics. Kinematic methods were compared using statistical parametric mapping and between-day reliability was calculated using intraclass correlation coefficients, mean absolute error, and minimal detectable change. Keypoint-derived inverse kinematics resulted in significantly smaller hip flexion (range = -9 to -2°), hip abduction (range = -3 to -2°), knee flexion (range = -5° to -2°), and greater dorsiflexion angles (range = 6-15°) than direct kinematics. Both markerless kinematic methods had high between-day reliability (inverse kinematics ICC 95 %CI = 0.83-0.90; direct kinematics ICC 95 %CI = 0.80-0.93). For certain tasks and joints, keypoint-derived inverse kinematics resulted in greater reliability (up to 0.47 ICC) and smaller minimal detectable changes (up to 13°) than direct kinematics. Performing 2-4 trials was sufficient to maximize reliability for most tasks. A single markerless depth camera can reliably measure lower limb joint angles, and skeletal model-constrained inverse kinematics improves lower limb joint angle reliability for certain tasks and joints.

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The advent of Industry 4.0 has significantly promoted the field of intelligent manufacturing, which is facilitated by the development of new technologies are emerging. Robot technology and robot intelligence methods have rapidly developed and been widely applied. Manipulators are widely used in industry, and their control is a crucial research topic. The inverse kinematics solution of manipulators is an important part of manipulator control, which calculates the joint angles required for the end effector to reach a desired position and posture. Traditional inverse kinematics solution algorithms often face the problem of insufficient generalization, and iterative methods have challenges such as large computation and long solution time. This paper proposes a reinforcement learning-based inverse kinematics solution algorithm, called the MAPPO-IK algorithm. The algorithm trains the manipulator agent using the MAPPO algorithm and calculates the difference between the end effector state of the manipulator and the target posture in real-time by designing a reward mechanism, while considering Gaussian distance and cosine distance. Through experimental comparative analysis, the feasibility, computational efficiency, and superiority of this reinforcement learning algorithm are verified. Compared with traditional inverse kinematics solution algorithms, this method has good generalization and supports real-time computation, and the obtained result is a unique solution. Reinforcement learning algorithms have better adaptability to complex environments and can handle different sudden situations in different environments. This algorithm also has the advantages of path planning, intelligent obstacle avoidance, and other advantages in dynamically processing complex environmental scenes.

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The biomechanical-model-based approach with a contact model offers advantages in estimating ground reaction forces (GRFs) and ground reaction moments (GRMs), as it does not rely on the need for training data and gait assumptions. However, this approach faces the challenge of long computational times due to the inclusion of optimization processes. To address this challenge, the present study developed a new optical motion capture (OMC)-based method to estimate GRFs, GRMs, and joint torques without prolonged computational times. The proposed approach performs the estimation process by distributing external forces, as determined by a multibody model, between the left and right feet based on foot deformations, thereby predicting the GRFs and GRMs without relying on optimization techniques. In this study, prediction accuracies during level walking were confirmed by comparing a general analysis using a force plate with the estimation results. The comparison revealed excellent or strong correlations between the prediction and the measurements for all GRFs, GRMs, and lower-limb-joint torques. The proposed method, which provides practical estimation with low computational cost, facilitates efficient biomechanical analysis and rapid feedback of analysis results, contributing to its increased applicability in clinical settings.

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This paper introduces a novel approach to bipedal robot gait generation by proposing a higher-order form through the parameter equation of first-order Bessel interpolation. The trajectory planning for the bipedal robot, specifically for stepping up or down stairs, is established based on a three-dimensional interpolation equation. The experimental prototype, Roban, is utilized for the study, and the structural sketch of a single leg is presented. The inverse kinematics expression for the leg is derived using kinematic methods. Employing a position control method, the angle information is transmitted to the robot's joints, enabling the completion of both downstairs simulation experiments and physical experiments with the Roban prototype. The analysis of the experimental process reveals a noticeable phenomenon of hip and ankle joint tilting in the robot. This observation suggests that low-cost bipedal robots driven by servo motors exhibit low stiffness characteristics in their joints.

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Introduction: Redundant robots offer greater flexibility compared to non-redundant ones but are susceptible to increased collision risks when the end-effector approaches the robot's own links. Redundant degrees of freedom (DoFs) present an opportunity for collision avoidance; however, selecting an appropriate inverse kinematics (IK) solution remains challenging due to the infinite possible solutions. Methods: This study proposes a reinforcement learning (RL) enhanced pseudo-inverse approach to address self-collision avoidance in redundant robots. The RL agent is integrated into the redundancy resolution process of a pseudo-inverse method to determine a suitable IK solution for avoiding self-collisions during task execution. Additionally, an improved replay buffer is implemented to enhance the performance of the RL algorithm. Results: Simulations and experiments validate the effectiveness of the proposed method in reducing the risk of self-collision in redundant robots. Conclusion: The RL enhanced pseudo-inverse approach presented in this study demonstrates promising results in mitigating self-collision risks in redundant robots, highlighting its potential for enhancing safety and performance in robotic systems.

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The inverse kinematics (IK) problem addresses how both humans and robotic systems coordinate movement to resolve redundancy, as in the case of arm reaching where more degrees of freedom are available at the joint versus hand level. This work focuses on which coordinate frames best represent human movements, enabling the motor system to solve the IK problem in the presence of kinematic redundancies. We used a multi-dimensional sparse source separation method to derive sets of basis (or source) functions for both the task and joint spaces, with joint space represented by either absolute or anatomical joint angles. We assessed the similarities between joint and task sources in each of these joint representations, finding that the time-dependent profiles of the absolute reference frame's sources show greater similarity to corresponding sources in the task space. This result was found to be statistically significant. Our analysis suggests that the nervous system represents multi-joint arm movements using a limited number of basis functions, allowing for simple transformations between task and joint spaces. Additionally, joint space seems to be represented in an absolute reference frame to simplify the IK transformations, given redundancies. Further studies will assess this finding's generalizability and implications for neural control of movement.

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This study investigated the validity of using OpenSim to measure muscle-tendon unit (MTU) length of the bi-articular lower limb muscles in several postures (shortened, lengthened, a combination of shortened and lengthened involving both joints, neutral and standing) using 3D freehand ultrasound (US), and to propose new personalized models. MTU length was measured on 14 participants and 6 bi-articular muscles (semimembranosus SM, semitendinosus ST, biceps femoris BF, rectus femoris RF, gastrocnemius medialis GM and gastrocnemius lateralis GL), considering 5 to 6 postures. MTU length was computed using OpenSim with three different models: OS (the generic OpenSim scaled model), OS + INSER (OS with personalized 3D US MTU insertions), OS + INSER + PATH (OS with personalized 3D US MTU insertions and path obtained from one posture). Significant differences in MTU length were found between OS and 3D US models for RF, GM and GL (from - 6.3 to 10.9%). Non-significant effects were reported for the hamstrings, notably for the ST (- 1.5%) and BF (- 1.9%), while the SM just crossed the alpha level (- 3.4%, p = 0.049). The OS + INSER model reduced the magnitude of bias by an average of 4% for RF, GM and GL. The OS + INSER + PATH model showed the smallest biases in length estimates, which made them negligible and non-significant for all the MTU (i.e. ≤ 2.2%). A 3D US pipeline was developed and validated to estimate the MTU length from a limited number of measurements. This opens up new perspectives for personalizing musculoskeletal models using low-cost user-friendly devices.

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At present, most of the research on hip exoskeleton robots adopts the method of decoupling analysis of hip joint motion, decoupling the ball pair motion of hip joint into rotational motion on sagittal plane, coronal plane and cross section, and designing it into series mechanism. Aiming at the problems of error accumulation and man-machine coupling in series mechanism, a parallel hip rehabilitation exoskeleton structure is proposed based on the bionic analysis of human hip joint. The structure model is established and the kinematics analysis is carried out. Through the OpenSim software, the curve of hip flexion and extension, adduction and abduction angle in a gait cycle is obtained. The inverse solution of the structure is obtained by the D-H coordinate system method. The gait data points are selected and compared with the inverse solution obtained by ADAMS software simulation. The results show that the inverse solution expression is correct. The parallel hip exoskeleton structure can meet the requirements of the rotation angle of the hip joint of the human body, and can basically achieve the movement of the hip joint, which is helpful to improve the human-computer interaction performance of the exoskeleton.

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The inverse kinematics plays a vital role in the planning and execution of robot motions. In the design of robotic motion control for NAO robot arms, it is necessary to find the proper inverse kinematics model. Neural networks are such a data-driven modeling technique that they are so flexible for modeling the inverse kinematics. This inverse kinematics model can be obtained by means of training neural networks with the dataset. This training process cannot be achieved without the presence of the dataset. Therefore, the contribution of this research is to provide the dataset to develop neural networks-based inverse kinematics model for NAO robot arms. The dataset that we created in this paper is named ARKOMA. ARKOMA is an acronym for ARif eKO MAuridhi, all of whom are the creators of this dataset. This dataset contains 10000 input-output data pairs in which the end-effector position and orientation are the input data and a set of joint angular positions are the output data. For further application, this dataset was split into three subsets: training dataset, validation dataset, and testing dataset. From a set of 10000 data, 60 % of data was allocated for the training dataset, 20 % of data for the validation dataset, and the remaining 20 % of data for the testing dataset. The dataset that we provided in this paper can be applied for NAO H25 v3.3 or later.

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Scapular kinematic estimates are altered by soft tissue artefacts, therefore experimental and numerical methods should be developed to improve their accuracy. This study aimed to assess the influence of weights applied to the scapula markers within a closed-loop multibody kinematic optimization on scapular kinematic estimates. Fifteen healthy volunteers performed static postures mimicking analytical, daily living and sport movements. Scapulo-thoracic angles were computed either from a scapula locator as the reference, or from a closed-loop multibody-kinematic optimization (MKO) including a participant-specific point-on-ellipsoid scapulothoracic joint. Weights applied to scapula markers in the MKO were optimized to minimize the difference in scapular orientation from the reference. Optimizing weighting sets significantly (p < 0.0001) improved scapular orientation from 0.9° to 12.1° in comparison to scapular kinematics estimated with non-optimized weighting sets. The mean optimized weighting set contained no neglectable weight for all markers from the acromion to the medial border of the scapular spine but showed no significant difference (p = 0.547) compared to homogeneous weights. Optimized weighting sets were participant- and movement- specific. To conclude, homogenous weights applied on redundant markers located from acromion to scapular medial border spine are recommended when estimating scapular kinematics in upper limb MKO.

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Soft robots are interesting examples of hyper-redundancy in robotics. However, the nonlinear continuous dynamics of these robots and the use of hyper-elastic and visco-elastic materials make modeling these robots more complicated. This study presents a geometric inverse kinematics (IK) model for trajectory tracking of multi-segment extensible soft robots, where each segment of the soft actuator is geometrically approximated with a rigid links model to reduce the complexity. In this model, the links are connected with rotary and prismatic joints, which enable both the extension and rotation of the robot. Using optimization methods, the desired configuration variables of the soft actuator for the desired end-effector positions were obtained. Furthermore, the redundancy of the robot is applied for second task applications, such as tip angle control. The model's performance was investigated through kinematics and dynamics simulations and numerical benchmarks on multi-segment soft robots. The results showed lower computational costs and higher accuracy compared to most existing models. The method is easy to apply to multi-segment soft robots in both 2D and 3D, and it was experimentally validated on 3D-printed soft robotic manipulators. The results demonstrated the high accuracy in path following using this technique.

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Robotic devices are gaining popularity for the physical rehabilitation of stroke survivors. Transition of these robotic systems from research labs to the clinical setting has been successful, however, providing robot-assisted rehabilitation in home settings remains to be achieved. In addition to ensure safety to the users, other important issues that need to be addressed are the real time monitoring of the installed instruments, remote supervision by a therapist, optimal data transmission and processing. The goal of this paper is to advance the current state of robot-assisted in-home rehabilitation. A state-of-the-art approach to implement a novel paradigm for home-based training of stroke survivors in the context of an upper limb rehabilitation robot system is presented in this paper. First, a cost effective and easy-to-wear upper limb robotic orthosis for home settings is introduced. Then, a framework of the internet of robotics things (IoRT) is discussed together with its implementation. Experimental results are included from a proof-of-concept study demonstrating that the means of absolute errors in predicting wrist, elbow and shoulder angles are 0.89180,2.67530 and 8.02580, respectively. These experimental results demonstrate the feasibility of a safe home-based training paradigm for stroke survivors. The proposed framework will help overcome the technological barriers, being relevant for IT experts in health-related domains and pave the way to setting up a telerehabilitation system increasing implementation of home-based robotic rehabilitation. The proposed novel framework includes:•A low-cost and easy to wear upper limb robotic orthosis which is suitable for use at home.•A paradigm of IoRT which is used in conjunction with the robotic orthosis for home-based rehabilitation.•A machine learning-based protocol which combines and analyse the data from robot sensors for efficient and quick decision making.

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Compared with non-redundant manipulators, the self-motion of 7-DOF redundant manipulators results in an infinite number of inverse kinematics solutions for a desired end-effector pose. This paper proposes an efficient and accurate analytical solution for inverse kinematics of SSRMS-type redundant manipulators. This solution is applicable to SRS-type manipulators with the same configuration. The proposed method involves introducing an alignment constraint to restrain the self-motion and to decompose the spatial inverse kinematics problem into three independent planar subproblems simultaneously. The resulting geometric equations depend on the part of the joint angles, respectively. These equations are then computed recursively and efficiently using the sequences of (θ1,θ7), (θ2,θ6), and (θ3,θ4,θ5), generating up to sixteen sets of solutions for a given desired end-effector pose. Additionally, two complementary methods are proposed for overcoming the possible singular configuration and judging unsolvable poses. Finally, numerical simulations are conducted to investigate the performance of the proposed approach in terms of average calculation time, success rate, average position error, and the ability to plan a trajectory with singular configurations.

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The compound continuum robot employs both concentric tube components and cable-driven continuum components to achieve its complex motions. Nevertheless, the interaction between these components causes coupling, which inevitably leads to reduced accuracy. Consequently, researchers have been striving to mitigate and compensate for this coupling-induced error in order to enhance the overall performance of the robot. This paper leverages the coupling between the components of the compound continuum robot to accomplish specific surgical procedures. Specifically, the internal concentric tube component is utilized to induce motion in the cable-driven external component, which generates coupled motion under the constraints of the cable. This approach enables the realization of high-precision surgical operations. Specifically, a kinematic model for the proposed robot is established, and an inverse kinematic algorithm is developed. In this inverse kinematic algorithm, the solution of a highly nonlinear system of equations is simplified into the solution of a single nonlinear equation. To demonstrate the effectiveness of the proposed approach, simulations are conducted to evaluate the efficiency of the algorithm. The simulations conducted in this study indicate that the proposed inverse kinematic (IK) algorithm improves computational speed by a significant margin. Specifically, it achieves a speedup of 2.8 × 103 over the Levenberg-Marquardt (LM) method. In addition, experimental results demonstrate that the coupled-motion system achieves high levels of accuracy. Specifically, the repetitive positioning accuracy is measured to be 0.9 mm, and the tracking accuracy is 1.5 mm. This paper is significant for dealing with the coupling of the compound continuum robot.

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The main problem with a robotic system arm is its sensitivity to time delays in the control process. Due to this problem, it is necessary to further optimize the control process of the system. One solution is to deal with the control accuracy and response speed issues of robotic arm joints, to improve the system's response performance and enhance the system's anti-interference ability. This paper proposes a speed feedforward and position control scheme for robotic arm joint control. The conclusion section shows that compared to traditional five-degree-of-freedom robotic arm systems, the addressed robotic arm control system has a lower tracking delay and better dynamic response performance. It can improve the system's response performance while also enhancing its anti-interference ability.

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The replacement of humans by machines has gradually become a technological trend. In this study, a dual robotic arm was used in the belt conveyor operation system to track the screw and nut assembly using mutual visual tracking and positioning technology. Moreover, this study simulated the automatic assembly process using a dual robotic arm in a smart factory. An inverse kinematics operation was constructed using a geometric method to control the dual robotic arm to track the screw and nut assembly on the conveyor belt in real time using mutual visual tracking and positioning technology based on a single-lens charge-coupled device of a robotic arm. This study utilized a dual robotic arm to grab the screw and nut using fuzzy visual tracking control. After completing the grabbing of the screw and nut with tracking and positioning errors of 8%, the dual robotic arms continued to complete the assembly of the screw and nut. Therefore, through the establishment technology of mutual visual tracking and positioning of the dual robotic arm in this study, assembly tasks can be efficiently completed in related fields in the future.