Non-spherical Wrist Research Articles

A Closed-Form Inverse Kinematic Analytical Method for Seven-DOF Space Manipulator with Aspheric Wrist Structure

The seven-degree-of-freedom space manipulator, characterized by its redundant and aspheric wrist structure, is extensively used in space missions due to its exceptional dexterity and multi-joint capabilities. However, the non-spherical wrist structure presents challenges in solving inverse kinematics, as it cannot decouple joints using the Pieper criterion, unlike spherical wrist structures. To address this issue, this paper presents a closed-form analytical method for solving the inverse kinematics of seven-degree-of-freedom aspheric wrist space manipulators. The method begins by identifying the redundant joint through comparing the volumes of the workspace with different joints fixed. The redundant joint angle is then treated as a parametric joint angle, enabling the derivation of closed-form expressions for the non-parametric joint angles using screw theory. The optimal solution branch is identified through a comparative analysis of various self-motion manifold branches. Additionally, a hybrid approach, combining analytical and numerical methods, is proposed to optimize the parametric joint angle for a trajectory tracking task. Simulation results confirm the effectiveness of the proposed method.

An inverse kinematic method for non-spherical wrist 6DOF robot based on reconfigured objective function

An inverse kinematic method for non-spherical wrist 6DOF robot based on reconfigured objective function

Singularity Parametrization With a Novel Kinematic Decoupled Model for Non-Spherical Wrist Robots

Abstract Most of the current commercial collaborative robots present a non-spherical wrist, so they cannot utilize singularity handling techniques efficiently to avoid excessive safety stops while dynamically avoiding collisions. These robots usually require heavier algorithms due to their kinematics or online methods that shift the original singularities. Therefore, to enable more efficient computations on singularity handling and collision avoidance controllers, this paper proposes a novel method to characterize singular configurations of non-spherical wrist collaborative robots (6 and 7 degrees-of-freedom). This method is based on a new decoupled kinematic model that allows lighter kinematic computations and enables the joint-dependant characterization of the robot singularities to avoid shifting the singular configurations. Finally, the proposed kinematic model is particularized for a UR10e, where its kinematic behavior has been tested against two different literature models in simulation. In this manner, a novel singularity category (belonging to the internal singularities) is proposed, and a new closed set of characterized singular solutions is obtained.

Dynamic Parallel Mapping and Trajectory Planning of Robot Arm in Unknown Environment

A high real-time robot arm mapping and dynamic shortest path planning algorithm is proposed, which is used for low-cost depth cameras and robot arms. First of all, an inverse kinematics solution algorithm for a non-spherical wrist joint is proposed for the Kinova Mico2 manipulator. Based on the idea of position and attitude decoupling combined with the numerical solution, the solution of multiple sets of inverse kinematics is acquired. Secondly, a hand-eye system is established on the basis of the depth camera-RealSense. The point cloud is inversely solved through the depth map, which is pre-processed by the pass-through filtering and outlier removal algorithm. A scene parallel mapping method is designed to achieve the real-time reconstruction of the working scene for the robot arm, in which the maintenance of map and large matrix operations can be completed by GPU. Thirdly, a path planning algorithm with the shortest path for the manipulator end in Cartesian space is designed based on D* method and grid map. The attitude interpolation and smoothing are performed on the path points to obtain the executable joint trajectories on the time axis. Finally, the ROS system is used to build a simulation test verification environment, and the effectiveness of the related algorithms is verified through multiple simulation cases.

Inverse Kinematics of a Class of 6R Collaborative Robots with Non-Spherical Wrist

The spread of cobotsin common industrial practice has led constructors to prefer the development of collaborative features that are necessary to prevent injuries to operators over the realization of simple kinematic structures for which the joints-to-workspace mapping is well known. An example is given by the replacement in serial robots of spherical wrists with safer solutions, where the danger of crushing and shearing is intrinsically avoided. Despite this tendency, the kinematic map between actuated joints and the Cartesian workspace remains of paramount importance for robot analysis and programming, deserving the attention of the research community. This paper proposes a closed-form solution for the inverse kinematics of a class of 6R robotic arms with six degrees of freedom and non-spherical wrists. The solutions are worked out by a single polynomial, of minimum degree, in terms of one of the positioning parameters chosen for the description of the robot posture. The roots of such a polynomial are then back-substituted to determine all the remaining unknowns. A numerical example is finally shown to verify the validity of the proposed implementation for a commercial collaborative robot.

Performance Comparison of Two Architectures of 6R Articulated Robots

This paper presents a comparison between two different 6R articulated robot architectures, one with a spherical wrist and the other with a non-spherical wrist and three consecutive parallel axes, which are found mainly in collaborative arms. The performance of the two architectures has been evaluated in terms of linear and rotational velocity using the Kinematic Directional Index (KDI). The results highlight the relation between the robot’s velocity along a direction and the joint velocities. In this way, the proposed approach allows the evaluation of the best performance in a direction and the joints that limit the considered motion.

A computation effective singularity avoidance method for the underwater manipulator with a non-spherical wrist

In order to perform increasingly complex underwater tasks, we have designed a hydraulic underwater non-spherical wrist manipulator with a binocular vision system and a six-dimensional force sensor mounted behind the end-effector, which can improve the path accuracy and automation capabilities of the system. The system lays a foundation for the high precision and autonomous deep-sea operation and can improve its intelligence level. In this paper, we focus on solving the singularity avoidance problem of the hydraulic underwater manipulator for accurate control, and propose a computationally efficient singularity avoidance method to improve the path accuracy of the manipulator with the non-spherical wrist. Firstly, the singular configurations of the manipulator are analyzed. Secondly, the Jacobian is decomposed into sub-block matrices to obtain the singular factors according to the singular configurations. Thirdly, the singularities are avoided by the approximate damped reciprocal method. Theoretical analysis shows that the computation costs of the proposed method are only one-third to one-half of that of the traditional methods. The simulation results prove that the proposed method can largely improve the path accuracy of the manipulator with less computation costs, which shows that our method would have a certain significance in improving the precision and real-time response of deep-sea operations.

Model-based kinematic and non-kinematic calibration of a 7R 6-DOF robot with non-spherical wrist

This paper presents a model-based kinematic and non-kinematic calibration method for a 7R 6-DOF robot with non-spherical wrist. By using the proposed method, kinematic errors, compliance errors from external load and self-gravity are particularly compensated. Firstly, kinematic error model is built based on modified DH (MDH) model, meanwhile calibration models for compliance and inertial parameters are derived by proper linearization of stiffness model. Secondly, to derive a suitable minimal model for practical application, model reduction and parameter identifiability analysis are conducted by considering parameter properties defined in controller. Finally, a step-by-step procedure for error parameter estimation is proposed with laser tracker as measuring device: (1) kinematic parameter errors are identified when the robot is not loaded. (2) compliance parameters are identified when the robot is loaded. (3) inertial parameters are calibrated together with kinematic errors, if deformations from self-gravity need to be compensated. Simulations and experiments on a 7R 6-DOF industrial painting robot are conducted to verify that the proposed calibration method can improve accuracy of the robot under no load and loaded conditions.

Inverse Kinematics Solution Algorithm of a 6R Robot with Non-spherical Wrist

Inverse Kinematics Solution Algorithm of a 6R Robot with Non-spherical Wrist

Inverse Kinematics of a 7-DOF Spraying Robot with 4R 3-DOF Non-spherical Wrist

In this paper, an Inverse Kinematics (IK) algorithm combining the analytical method and the numerical one is proposed to solve the IK problem of a 7-DOF spraying robot with 4R 3-DOF non-spherical wrist. Firstly, the 7-DOF spraying robot is transformed into a 7-DOF robot with 3R spherical wrist and the arm angle is used as the redundancy parameter. The approximate IK solution is calculated analytically using offset angle method by means of approximation. Secondly, the approximate solution is taken as the initial value of the iterative algorithm and by updating the joint angles through the damped least-square method with augmented Jacobian matrix, the final exact solution is obtained after a few iterations. Three simulation experiments show that the proposed algorithm not only has high computational efficiency and accuracy, but also can obtain multiple solutions and show the self-motion characteristics of the 7-DOF robot. The novel algorithm may be implemented in real-time control of the 7-DOF spraying robot.

A novel inverse kinematics method for 6-DOF robots with non-spherical wrist

A novel numerical method is proposed to solve the inverse kinematics for 6-DOF robots with non-spherical wrist in this paper, which firstly simplifies the non-spherical wrist structure to a spherical one. In each iteration of the algorithm, the inverse solution of simplified robot is firstly used to calculate the end pose of actual robot to estimate the end position error between the calculated end pose and the target pose. And then the inverse solution of simplified robot gradually approaches the desired solution by compensating for the end position error. Additionally, the failure of proposed method caused by the reduction of robot workspace due to structure simplification is analyzed and then the offsetting of known end pose is introduced to improve the robustness of algorithm. Finally, numerical experiments for two typical robots prove the effectiveness of proposed method; a comparative study shows the advantages of proposed algorithm over Newton-Raphson (NR) algorithm; and the performance in processing continuous trajectories demonstrates its good practicability.

The optimized algorithm based on machine learning for inverse kinematics of two painting robots with non-spherical wrist.

This paper studies the inverse kinematics of two non-spherical wrist configurations of painting robot. The simplest analytical solution of orthogonal wrist configuration is deduced in this paper for the first time. For the oblique wrist configuration, there is no analytical solution for the configuration. So it is necessary to solve by general method, which cannot achieve high precision and high speed as analytic solution. Two general methods are optimized in this paper. Firstly, the elimination method is optimized to reduce the solving speed to 20% of the original one, and the completeness of the method is supplemented. Based on the Gauss damped least squares method, a new optimization method is proposed to improve the solving speed. The enhanced step length coefficient is introduced to conduct studies with the machine learning correlation method. It has been proved that, on the basis of ensuring the stability of motion, the number of iterations can be effectively reduced and the average number of iterations can be less than 5 times, which can effectively improve the speed of solution. In the simulation and experimental environment, it is verified.

Singularity analysis and treatment for a 7R 6-DOF painting robot with non-spherical wrist

Singularity is a fundamental problem in robotics which seriously affects the motion control, path planning, and off-line programing of the robot. In this paper, the singularities of a 7R 6-DOF painting robot with non-spherical wrist are analyzed in detail, and a new avoidance method is proposed. Firstly, the singularities are decoupled into the position singularities and the orientation singularities by introducing a virtual wrist center. All singularity conditions for both cases are identified based on a rational transformation between the 7R 6-DOF robot and the equivalent 6R robot with spherical wrist. Secondly, the position singularities are regarded as inescapable singularities, and unusable regions are defined in the workspace to deal with these singularities. Thirdly, the orientation singularities are regarded as escapable singularities. Based on the definition of functional redundancy for painting application, the Twist-decomposition approach (TWA) is extended to handle the orientation singularities. As the main improvement, a new and simple singularity criterion is proposed to overcome the drawback of the existing algorithm. In the end, two simulations for a 7R 6-DOF painting robot are implemented to demonstrate the effectiveness of the proposed method.

The inverse kinematics of a 7R 6-degree-of-freedom robot with non-spherical wrist

The 7R 6-degree-of-freedom robots with hollow non-spherical wrist have been proven more suitable to spray painting. However, the inverse kinematics of this robot is still imperfect due to the coupling between position and orientation of the end-effector. In this article, a reliable numerical iterative algorithm for the inverse kinematics of a 7R 6-degree-of-freedom robot is proposed. Based on the geometry of the robot, the inverse kinematics is converted into a one-dimensional iterative research problem. Since the Jacobian matrix is not utilized, the proposed algorithm possesses good convergence, even for singular configurations. Moreover, the multiple-solution problem in the inverse kinematics is also discussed. By introducing three robot configuration indicators which are prespecified by a user, the correct solution could be chosen from all the possible solutions. In order to verify the accuracy and efficiency of the proposed algorithm, several simulations are implemented on a practical 7R 6-degree-of-freedom painting robot. The result shows that the proposed algorithm is more advantageous for a continuous trajectory.

Inverse Kinematics of a 7R 6-DOF Robot with Nonspherical Wrist Based on Transformation into the 6R Robot

The 7R 6-DOF robots with hollow nonspherical wrist have been proven more suitable for spray painting applications. However, the inverse kinematics of this kind of robot is still imperfect due to the coupling between position and orientation of the end-effector (EE). In this paper, a new and efficient algorithm for the inverse kinematics of a 7R 6-DOF robot is proposed. The proposed inverse kinematics algorithm is a two-step method. The geometry of the 7R 6-DOF robot is analyzed. A comparison between the 7R 6-DOF robot and the well-known equivalent 6R robot is made. Based on this comparison, a rational transformation between these two kinds of robots is constructed. Then the general inverse kinematics algorithm of the equivalent 6R robot is applied to calculate the approximate solutions of the 7R 6-DOF robot, in the first step. The Damped Least-Squares (DLS) method is employed to derive the exact solutions, in the second step. The accuracy and efficiency of the algorithm are tested on a 7R 6-DOF painting robot. The results show that the proposed algorithm is more advantageous in the case without an approximate solution, such as the initial point of a continuous trajectory.

Structural Design and Kinematics Analysis of Oblique Crossing 3DOF NC Spindle

Based on the study of 3R oblique non-spherical wrist and the analysis of the NC machine spindle’s function, the concept of a oblique crossing 3DOF NC spindle was offered and the 3D model of this 3DOF NC spindle was made with Solidworks software. At the same time, the kinematics model of this 3DOF NC spindle was setup with D-H parameter method and the kinematics & workspace of this 3DOF NC spindle were analyzed and simulated. Simulation results indicated that this 3DOF NC spindle, with compacted-structure, low inertness and considerable flexibility, could be in any gesture in the 3D space, and could expand the work range of the NC machine.

Experiments of kinematic control on a redundant robot manipulator with nonspherical wrist

This article reports the results of an experimental investigation of real-time kinematic control on a seven-joint industrial robot manipulator having a nonspherical wrist. Closed-loop inverse kinematics algorithms are utilized, namely, an algorithm based on the manipulator geometric Jacobian and a two-stage algorithm based on analytical Jacobians of reduced dimensions. A damped least-squares technique with varying damping factor is adopted to provide numerical robustness of the solution in the neighborhood of kinematic singularities. Redundancy is solved by employing an augmented task space approach with task priority. Case studies are developed to compare the performance of the two algorithms. © 1996 John Wiley & Sons, Inc.

An Efficient Inverse Kinematic Solution with a Closed Form for Five-Degree-of-Freedom Robot Manipulators with a Non-Spherical Wrist

Summary In this paper, the efficient approach which was developed for computing an inverse kinematic solution with a closed form has been extended from a six-degree-of-freedom to a five-degree-of-freedom robot manipulator with a none spherical wrist. The TR 4000S spray paintinq robot manipulator has been used as an example to describe the principles. The inverse kinematic computation with a closed form solution shows that it is very systematic and efficient and easily carried out.

A joint-space command generator for Cartesian control of robotic manipulators

Many recently developed control schemes for robotic manipulators require as inputs the desired position, velocity, and in some cases, acceleration of each joint of the manipulator. However, it is most natural to specify the desired trajectory of the end effector in Cartesian coordinates. Thus it is desirable to have a command generator which has as input a desired Cartesian trajectory, and as output a vector of joint positions, velocities, and accelerations that correspond to the demanded trajectory. Such a command generator is presented in the form of a nonlinear feedback system that has the advantage of being related to a linear system. The linear system can be used to compute precise bounds on the performance of the nonlinear system. Simulation results for a nonspherical wrist manipulator are given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>