Offset Wrist Research Articles

An analytical approach based on Dixon resultant for the inverse kinematics of 6R robot manipulators with offset wrists

6-revolute (6R) robot manipulators with offset wrists are widely applied in industrial scenarios. However, the autonomous and highly-precise manipulations of these robots are restricted for online industrial uses due to the lack of effective inverse kinematic methods. The inverse kinematic problem for 6R robot manipulators with offset wrists is addressed with a novel kinematic modelling and elimination approach in this study. To begin, kinematic models with non-redundant equations for joint variables are established An improved Dixon elimination approach is then introduced for inverse kinematic calculation to reduce the high computational cost and get rid of the singularity issues. The core is to efficiently extract the linear terms from variable sequences, such that the number of terms can be reduced in the polynomial equations. By further examining the characteristics of offset wrists, the fourth and fifth joint variables are eliminated from kinematic formulas, without increasing the polynomial degrees. The formulas are demonstrated to produce a polynomial with a single joint variable and a minimum degree using the elimination approach. Finally, experiments are carried out to verify the computing performance of the inverse kinematic problem. The main focus of this study is to develop a systematic and automatic procedure for solving the inverse kinematic problem for 6R robot manipulators with offset wrists and producing highly precise and efficient solutions by means of a novel modelling and elimination method.

An improved inverse kinematics solution for 6-DOF robot manipulators with offset wrists

AbstractEfficiently solving inverse kinematics (IK) of robot manipulators with offset wrists remains a challenge in robotics due to noncompliance with Pieper criteria. In this paper, an improved method to solve the IK for 6-DOF robot manipulators with offset wrists is proposed. This method is based on the Newton iteration technique, but it does not require a selection of initial estimation of joint variables. The solution is divided into two parts: the first part is to reconstruct a simplified structure with analytical IK solution, and the second part is to obtain a numerical solution by iteration. Further, a robot manipulator HSR-BR606 with an offset wrist is used as an example to specifically elaborate the mathematical procedure of the method and to investigate the algorithm in terms of accuracy, efficiency, and application of motion planning. A comparative experiment is conducted with a typical IK algorithm, which demonstrates a higher accuracy and shorter calculation time of the proposed method. The mean calculation time for a single IK solution required for this algorithm is only 4% of the comparison algorithm.

Compliance model of Exechon manipulators with an offset wrist

The stiffness of the Exechon hybrid manipulator is a crucial performance indicator as the manipulator is used as a 5-axis machine tool. Normally, the serial module of the Exechon is not included in the kinematic and stiffness analysis. In terms of kinematics, the parallel and serial modules are said to be decoupled, i.e. parallel module can be solved for position and the serial module can be used to compensate the parasitic orientation of the parallel platform. This is only possible when the serial module is a perfect spherical wrist. However, several models of Exechon technology have an offset wrist rather than a spherical one. Such an offset makes it impossible to obtain a kinematic decoupling.In all publications available in the literature, the Exechon is considered to have a perfect spherical wrist. Therefore, this paper presents the inverse kinematics and compliance model of Exechon manipulators with offset wrists. The unknown coefficients in the compliance model are determined by optimizing the model against experimental data. The resulting predictions are then compared against more experimental results to validate the model.

Human-Like Posture Correction for Seven-Degree-of-Freedom Robotic Arm

Abstract Owing to advancements in robotics, researchers have been focusing on integrating humanoid robots into actual environments. Most humanoid robots are equipped with seven-degree-of-freedom (DoF) arms that allow them to be flexible in different scenarios. The controller of a 7-DoF robotic arm must select one solution among the infinite sets of solutions for a given inverse kinematics problem. To date, no suitable approach has been developed for identifying appropriate human-like postures for a robotic arm with an offset wrist configuration. In this paper, we propose a novel algorithm that considers the movement of the human arm to consistently find a suitable human-like posture. First, a one-class support vector machine model is employed to classify human-like postures. Then, the algorithm uses the redundancy characteristic of a 7-DoF robotic arm with a linear regression model to enhance the search of human-like postures. Finally, the proposed algorithm is demonstrated in simulation, where it successfully optimized point-to-point trajectories by modifying only the endpoint posture.

Optimal path crossing the orientation exclusion zone of a robot with offset wrist

AbstractAn unexpected path reversal is discovered for a serial robot with an offset-axis wrist over a finite range of proximity to the wrist singularity. This is replicated by a kinematic model. A prior spherical-wrist method transits the singularity with limited joint rate and acceleration under a constant rate of tool traversal. Accurate position is maintained by controlling a small deviation in orientation. Extensions to the method for an offset wrist (1) find the least-maximum deviation, (2) identify and locate where a path reversal occurs, and (3) use this point to control step size in a high-order predictor-correction path following procedure.

Serial-robot Wrist-singularity Mitigation Along Alternative Optimally Adjusted Paths

Abstract Adjusting the displacement path of a serial robot encountering the wrist singularity to pass either through the singularity or around it mitigates its adverse effects. Both such path adjustments are commonly called singularity avoidance and are applied here to either a spherical or an offset wrist. These adjustments avoid high joint rates that can occur at singularity encounter. A recent through-the singularity method limits joint rates and accelerations in the robot with either a spherical or offset wrist when conducting a constant rate of traversal of the tool manipulated by the robot. A kinematic model adding multiple virtual joints allows a modified high-order path-following algorithm to maintain accurate tool position while achieving an optimal level of tool deviation in orientation. Whereas a path reversal resulting from a turning-point type singularity had been revealed for an offset wrist over a finite range of close-approach, these conditions are met when connecting the isolated path segments. Procedures are developed here with this capability for an around-the-singularity path. Choosing between the through and around-singularity alternatives offers the overall optimum.

Chaos-based Vortex Search algorithm for solving inverse kinematics problem of serial robot manipulators with offset wrist

Vortex Search (VS) algorithm is a single-solution-based optimization algorithm that requires the high maximum number of iterations (NOI) to solve optimization problems. In this study, two methods were proposed to reduce the required maximum NOI of the VS algorithm. These methods are based on using ten chaos maps with the VS algorithm and provide improvements in the exploration and exploitation abilities of the algorithm for reducing the required maximum NOI. Ten chaos-based VS algorithms (CVSs) were obtained by combining these methods with the VS algorithm. The performances of the CVS algorithms were tested by fifty benchmark functions. The results were evaluated in terms of some statistical values and a pairwise statistical test, Wilcoxon Signed-Rank Test. According to the results, it was found that the CVS algorithm obtained by using the Gauss–Mouse chaos map was the best algorithm. And also, it was shown that the proposed CVS algorithm performs better than the classical VS algorithm, even when its maximum NOI was ten times less than the maximum NOI of the VS algorithm. Additionally, the effects of the proposed methods in the exploration and the exploitation abilities of the VS algorithm were visually shown and a comparison about algorithm processing time was presented. In order to test the performance of the proposed CVS algorithm in solving the real-world optimization problems, the inverse kinematics problem of a six Degrees Of Freedom (DOF) serial robot manipulator with offset wrist was solved with both the proposed CVS algorithm and the VS algorithm for two different types of trajectories. The results showed that the proposed algorithm outperforms the VS algorithm in terms of the objective function values and position errors of the end-effector of the serial robot manipulator.

Inverse kinematics solutions for industrial robot manipulators with offset wrists

In this paper, the inverse kinematics solutions for 16 industrial 6-Degrees-of-Freedom (DOF) robot manipulators with offset wrists are solved analytically and numerically based on the existence of the closed form equations. A new numerical algorithm is proposed for the inverse kinematics of the robot manipulators that cannot be solved in closed form. In order to illustrate the performance of the New Inverse Kinematics Algorithm (NIKA), the simulation results attained from NIKA are compared with those obtained from well-known Newton–Raphson Algorithm (NRA). The inverse kinematics solutions of two robot manipulators with offset wrists are given as examples. In order to have a complete idea, the inverse kinematics solution techniques for 16 industrial robot manipulators are also summarized in a table.

Solution of Inverse Kinematics for 6R Robot Manipulators With Offset Wrist Based on Geometric Algebra

In this paper, we present an efficient method based on geometric algebra for computing the solutions to the inverse kinematics problem (IKP) of the 6R robot manipulators with offset wrist. Due to the fact that there exist some difficulties to solve the inverse kinematics problem when the kinematics equations are complex, highly nonlinear, coupled and multiple solutions in terms of these robot manipulators stated mathematically, we apply the theory of Geometric Algebra to the kinematic modeling of 6R robot manipulators simply and generate closed-form kinematics equations, reformulate the problem as a generalized eigenvalue problem with symbolic elimination technique, and then yield 16 solutions. Finally, a spray painting robot, which conforms to the type of robot manipulators, is used as an example of implementation for the effectiveness and real-time of this method. The experimental results show that this method has a large advantage over the classical methods on geometric intuition, computation and real-time, and can be directly extended to all serial robot manipulators and completely automatized, which provides a new tool on the analysis and application of general robot manipulators.

Inverse Kinematics Analysis of 5-DOF Robot Manipulators Based on Virtual Joint Method

To solve the inverse kinematics problem of a robot manipulator without closed form solutions, one-dimensional iterative method is very useful. However, for a 5-DOF robot manipulator, because of the uncontrolable and uncertain orientation vectors, it's difficult to analytically express all joint variables by one of them, therefore one-dimensional iterative method can not be directedly used. By adding an appropriate virtual joint to it, a 5-DOF manipulator can be changed into a 6-DOF one so that the uncertain orientation vectors can be pre-given, and the difficulty is solved. To illustrate this virtual joint method a 5-DOF serial robot manipulator with prismatic arm joint and offset wrist is discussed in this paper as an example.

Inverse Displacement Analysis of 6R Robots with Offset Wrists Based on Decoupling Degrees of Freedom at the Cutoff Points

There are no closed-form inverse displacement solutions for 6R robots with offset wrists. These robotic offset wrists are classified as side offset,top offset,and front offset. To solve the problem of inverse displacement analysis of 6R robots with front offset wrists,according to the geometric character of robotic mechanisms,the robotic kinematic chain is cut into two branches at the origin of the joint coordinate or at the intersection point of the axes of the adjacent coordinates. In this way,one component of degrees of freedom for the two branches becomes decoupled at the cutoff point,so the relationships among the joint variables can be easily deduced. The transcendental equations containing 6 variables are turned into a nonlinear equation containing 1 variable,and the numerical solution for the inverse displacement analysis is obtained by using one dimensional iterative search.

Singularities of a Manipulator With Offset Wrist

The singularities of manipulators with offset wrists are difficult to enumerate. This article presents a numerical study to illuminate singularity problems when using an offset wrist with an articulated regional arm. Ironically, the regional manipulator singularity problem is worsened when using a singularity-free offset wrist. No wrist singularities exist (they are forced by design to lie outside of joint limits). However, the existing regional arm singularities become skewed from the well-known singular configurations of common manipulators. The wrist offset also skews the well-known wrist singularities (though they hopefully still lie outside of joint limits, their locations are no longer easily determined). Thus, a zero-offset singularity-free wrist is preferable with regard to overall manipulator singularities.

Real-time inverse kinematics for robots with offset and reduced wrist

The paper deals with the inverse transformation of coordinates for robotic manipulators with high payload capacity, which are widely used in welding applications. Such manipulators are usually equipped with 3 d.o.f. offset wrists or 2 d.o.f. reduced wrists, that do not satisfy the Pieper condition that ensures the existence of a closed-form solution of the inverse kinematics. Two reliable iterative algorithms are proposed to solve the problem in real time. The algorithms have been implemented in commercial robot controllers and software packages for the computer-aided design of welding robotic cells.

Real-Time Inverse Kinematics for Robots with Offset and Reduced Wrist

The paper deals with inverse transformation of coordinates for robotic manipulators with high payload capacity that are widely used in welding applications. Such manipulators are usually equipped with 3 d.o.f. offset wrists or 2 d.o.f reduced wrists that do not satisfy Pieper condition that ensure existence of inverse kinematics closed-form solution. Two reliable iterative algorithms are proposed to solve the problem in real time. The proposed algorithms have been implemented in commercial robot controllers and software packages for computer-aided design of welding robotic cells.