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

Fu, Zhongtao; Yang, Wenyu; Yang, Zhen

doi:10.1115/1.4024239

Cited by 53 publications

(33 citation statements)

References 70 publications

(94 reference statements)

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“…As mentioned above; the analytical solution for 1 can be obtained as follows; firstly, 9 0 = _ matrix can be written as in Eq. (7).…”

Section: Inverse Kinematicsmentioning

confidence: 99%

“…Some of these methods can be given as follows; Koker [6] employed an artificial neural network and genetic algorithm-based method in order to solve the inverse kinematic problem of a six-joint Stanford robot manipulator. Fu et al [7] proposed a geometric algebraic method to solve the inverse kinematic problem of a 6R (R: Rotary Joint) robot mechanism with an offset wrist. Kucuk and Bingül [8] handled the inverse kinematic problem of sixteen basic six DOF serial robot manipulators with offset wrists and presented a numerical solution technique for analytically unresolved problems.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

5-DOF serial robot manipulator design, application and inverse kinematic solution through analytical method and simple search technique

Uzuner¹,

Akkuş²,

Toz³

2020

Pamukkale J Eng Sci

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ÖzIn this study a five Degrees of Freedom (DOF) serial robot manipulator was designed and implemented. The inverse kinematics problem, which has not exact analytical solution (only one inverse kinematic solution for a predefined end effector position in three dimensional space), of the robot mechanism was solved by using the combination of the analytical method and a simple search method. In order to use the proposed method in real-time applications, the method is designed so that it can be used to solve the inverse kinematics problem for the next point of the end-effector while the mechanism is working. Moreover, so that to control the implemented mechanism, a user interface program was written by using Visual Basic programming language. Finally, the proposed inverse kinematic solution method was tested on two different trajectories, an arc shaped trajectory that composed of 58 points and a linear trajectory divided into 29 points. The obtained results revealed that the proposed method can be used successfully in solving the inverse kinematic problem of the designed mechanism.Bu çalışmada, beş serbestlik derecesine (SD) sahip bir seri robot manipülatörü tasarlanmış ve test edilmiştir. Robot mekanizmasının kesin analitik çözümü (üç boyutlu uzayda önceden tanımlanmış bir uç işlevcisi konumu için yalnızca bir ters kinematik çözümü) olmayan ters kinematik problemi, analitik yöntem ve bir basit arama metodu kombinasyonu kullanılarak çözülmüştür. Önerilen yöntem, gerçek zamanlı kullanılabilmesi için mekanizma çalışırken uç işlevcinin gideceği bir sonraki nokta için çözüm yapılabilecek şekilde tasarlanmıştır. Gerçekleştirilen mekanizmayı kontrol etmek için Visual Basic programlama dili kullanılarak bir kullanıcı arayüzü programı yazılmıştır. Son olarak, önerilen ters kinematik çözüm yöntemi 58 noktadan oluşan yay şeklinde bir yörünge ve 29 noktaya bölünmüş doğrusal bir yörünge olmak üzere iki farklı yörüngede test edilmiştir. Elde edilen sonuçlar, önerilen yöntemin tasarlanan mekanizmanın ters kinematik problemini çözmede başarıyla kullanılabileceğini ortaya koymuştur.

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“…As mentioned above; the analytical solution for 1 can be obtained as follows; firstly, 9 0 = _ matrix can be written as in Eq. (7).…”

Section: Inverse Kinematicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

5-DOF serial robot manipulator design, application and inverse kinematic solution through analytical method and simple search technique

Uzuner¹,

Akkuş²,

Toz³

2020

Pamukkale J Eng Sci

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show abstract

“…However, the problem of inverse kinematics can be dealt with well since several extensive related investigations of kinematics were discussed using several geometry algebra (GA) approaches [87,88]. For example, Fu et al [23] applied theory of GA to kinematic modeling of 6R robot manipulators, so a group of closed-form kinematic equations was generated to reformulate the generalized eigenvalue problem [4]. The merit of GA approach is to have a universal meaningfulness on geometric intuition, compu-tation and real time for all serial robot manipulators.…”

Section: Geometry Algebra Analysismentioning

confidence: 99%

A review on kinematic analysis and dynamic stable control of space flexible manipulators

Jing

Huang

2019

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A review on state of the art of kinematic analysis and dynamic stable control of space flexible manipulators (SFMs) is presented. Specially, SFM as a significant assembled part of autonomous space robotics (ASRs) play an important role in precision-positioning and accurateness-controlling for space engineering application since this lightweight structure possesses a high-efficient payload-to-arm weight ratio. Further, the existing studies of kinematic analysis and dynamic stable control of SFMs are critically examined to ascertain the trends of research and to identify unsolved problems through comparing with different methods. Motivated by the current research results of the two aspects, some suggestions for future research are given concisely in our published literature: (1) a fast eliminate solution algorithm of forward kinematics is presented. (2) Two observer-based control methods are suggested after dynamic modeling of SFMs. (3) How to choose a suitable closed-loop strategy to describe system dynamic features is discussed in a comparison study of the two proposed observer-based control methods.

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“…Raghavan and Roth transform the kinematics equations into a 16 degree polynomial using the half-angle tangent of joint variables and calculate the solutions [7]. Z. Fu, W. Yang and Z. Yang apply the theory of Geometric Algebra to the kinematic modeling of 6R robot manipulators and generate closed-form kinematics equations, reformulate as a generalized eigenvalue problem, and then yield 16 solutions [8]. The above approaches involve complicated computations and may not be suitable in real time applications.…”

Section: Introductionmentioning

confidence: 99%

Inverse kinematics of robot manipulators with offset wrist

Kung

Lee

et al. 2015

2015 International Conference on Advanced Robotics and Intelligent Systems (ARIS)

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Ahstract-The inverse kinematics for a robot manipulator with offset wrist is formulated as a minimization problem in this paper to reduce its complexity and accelerate the computation speed. A specific type of robot such as Yaskawa MA1400, which has an offset between the last two axes, is chosen for analysis.Given an initial guess angle of last joint, all the 6 joint angles can be easily found through analytical solution. The output value is compared with the initial guess. An error function with only one variable is then defined and Newton-Raphson method is applied to search for the solution where the error goes to zero.To check the validity of the algorithm, forward kinematics is first computed and the position and orientation of end-effector are then applied in the inverse kinematics to solve the joint angles back. The computation converges within 5 iterations in cases when the angle 85 is far away from zero and the accuracy is within 10. 10 degree. When 85 approaches zero, searching direction is slightly modified to achieve convergence for the algorithm. The number of iterations increases for the same accuracy. The results show that the approach presented in this paper greatly reduces the computation time and is suitable for real time application.

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

Cited by 53 publications

References 70 publications

5-DOF serial robot manipulator design, application and inverse kinematic solution through analytical method and simple search technique

5-DOF serial robot manipulator design, application and inverse kinematic solution through analytical method and simple search technique

A review on kinematic analysis and dynamic stable control of space flexible manipulators

Inverse kinematics of robot manipulators with offset wrist

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