Algorithm for the Inverse Kinematics Calculation of 6-DOF Robots Based on Screw Theory and Paden-Kahan Sub-problems

Qian, Donghai

doi:10.3901/jme.2009.09.072

Cited by 16 publications

(7 citation statements)

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“…Right inverse kinematics can multiply by equation ( 6) to obtain [8]: are known, while θ is unknown to solve in equation (6). In general, equation ( 6) has no closed form solution, Paden-Kahan presents solution problem of the whole kinematics inverse can be decomposed into several sub problems with a clear geometric meaning, and has been widely used in [9,10].…”

Section: Manipulator Kinematics Based On Poementioning

confidence: 99%

Kinematics of a 6-DOF Feeding and Unloading Manipulator

Zhao

Di²,

Shou

et al. 2014

KEM

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In order to improve the efficiency of kinematics modeling in analyzing robots, this document used Lie groups and screw theory to describe rigid motion of the robot system, established a kinematic model of operating arm based on Product of Exponentials (POE) formula, and analyzed forward and inverse kinematics of chain topology structure robot, as well as several sub-inverse problem of inverse kinematics. A 6-DOF series-wound configuration loading and unloading manipulator has been used as an example, its kinematics equations are established by POE formula combined with screw theory, the special configuration of end effector under a specific task planning are calculated using Mathematica software. By contrast with D-H parameters method, we can draw a conclusion that POE formula and D-H parameters method are essentially equivalent. However, POE formula and motion screw have more definite geometric and physical meaning, neat expression form, convenient algebraic operation, are able to overcome limitations, such as calculation complexity and singularity in solving process, can meet kinematic analysis and real-time control of robot.

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Section: Manipulator Kinematics Based On Poementioning

confidence: 99%

Kinematics of a 6-DOF Feeding and Unloading Manipulator

Zhao

Di²,

Shou

et al. 2014

KEM

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“…The forward kinematics of serial manipulators is relatively simple, and the D-H method and the screw method are commonly used. 16 Whereas the inverse kinematics of serial manipulators is more complex, the solution methods can be divided into two categories: the numerical method and the algebraic method. The numerical method is suitable for almost all manipulators, but the calculation results are influenced by the initial values.…”

Section: Introductionmentioning

confidence: 99%

An explicit solution of forward and inverse kinematics for a serial manipulator with insufficient intersection joints based on finite and instantaneous screw theory

Qi,

Zhang,

Ren

et al. 2024

International Journal of Advanced Robotic Systems

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To satisfy the requirements of large workspace, high capability, and low inertia demanded by the high precision and high stiffness aerospace equipment, serial manipulator with insufficient intersection joints is proposed in this article based on finite and instantaneous screw theory. Due to the specific topology structure with no intersecting joints at both ends, the explicit solution of forward and inverse kinematics for the serial manipulator with insufficient intersection joints proposed in this article is extremely difficult. Therefore, an analytical method based on finite and instantaneous screw theory is proposed for this serial manipulator, and the explicit kinematic solution is derived in this article. According to particular calculation principle of finite and instantaneous screw theory, the finite motion of this serial manipulator is described. Based on this description, the product of exponentials formula of the kinematics of the serial manipulator with insufficient intersection joints is established on the basic of finite and instantaneous screw theory for the first time, and a novel subproblem is arose during the decomposition of product of exponentials formula. Regarding this issue, an innovative approach to this subproblem is proposed by introducing the new Paden–Kahan subproblem with elimination, and the explicit solution for the inverse kinematics is derived. Finally, the numerical examples are simulated, and the correctness of the method proposed in this article is verified.

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“…This representation method makes the angular velocity combined with the linear velocity, force, and torque without separate calculation, which can improve the calculation efficiency and make the process expression clearer. [11][12][13] Park et al 14 established the dynamic equation of the robot by using the advantages of Lie algebra and screw theory in derivation; Huang Xinghua et al 15 used Lie group lie algebra and screw theory to describe the Newton Euler equation and Lagrange equation, and analyzed the classical two degree of freedom robot as the research object; Yang et al 16 established concise and efficient dynamic equations based on Lie group lie algebra and screw theory, and carried out dynamic analysis for heavy industrial robots with elastic joints. Applying the above dynamic modeling method to the gantry welding robot system can effectively improve the calculation efficiency of the controller and then improve the tracking effect of the controller.…”

Section: Introductionmentioning

confidence: 99%

Trajectory tracking control strategy of the gantry welding robot under the influence of uncertain factors

Sun

Wang

et al. 2022

Measurement and Control

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In this paper, aiming at the problem of high-precision trajectory tracking of the gantry welding robot system under the influence of uncertain factors, a composite adaptive fuzzy compensation controller based on the computed torque control strategy has been proposed. The controller is composed of an adaptive fuzzy feedback control strategy and a dead zone adaptive fuzzy control strategy, which realizes high-precision trajectory tracking of the gantry welding robot, improves the solving speed of the control algorithm, and its tracking errors has been reduced. Screw theory and Lie group lie algebra are used to solve the problem of high algorithm complexity of controllers in multi-degree-of-freedom robot systems due to Newton-Euler dynamics modeling. Based on the computed torque control, the adaptive fuzzy feedback control strategy is adopted to compensate for the modeling errors and external disturbances in the gantry welding robot system, and the dead zone adaptive fuzzy control strategy is designed to compensate for the nonlinear dead zone structure with unknown parameters. The Lyapunov equation is introduced to prove the stability of the controller. Finally, the controller designed in this paper is compared with the conventional controller through simulation and experiment on the gantry welding robot platform, which verifies the effectiveness and superiority of the controller.

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Algorithm for the Inverse Kinematics Calculation of 6-DOF Robots Based on Screw Theory and Paden-Kahan Sub-problems

Cited by 16 publications

References 0 publications

Kinematics of a 6-DOF Feeding and Unloading Manipulator

Kinematics of a 6-DOF Feeding and Unloading Manipulator

An explicit solution of forward and inverse kinematics for a serial manipulator with insufficient intersection joints based on finite and instantaneous screw theory

Trajectory tracking control strategy of the gantry welding robot under the influence of uncertain factors

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