Inverse kinematic analysis of the general 6R serial manipulators based on double quaternions

Qiao, S; Liao, Qizheng; Wei, Shimin; Su, Hai‐Jun

doi:10.1016/j.mechmachtheory.2009.05.013

Cited by 83 publications

(65 citation statements)

References 9 publications

(4 reference statements)

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“…Hence, This double quaternion representation is redundant as one quaternion can be deduced from the other by exchanging A i and B i and changing the sign of the dual part. Thus, either the dual quaternion (48) or (49) unambiguously represents the transformation (46). The rotation matrix M is an exact representation of M, it is not an approximation.…”

Section: B Approximating Dual Quaternions By Double Quaternionsmentioning

confidence: 99%

“…M is closer to a 4D rotation matrix as δ tends to infinity (it can be verified that det( M ) = 1 − 5/δ 2 ). This is the approach pioneered in [44] and [45] to approximate 3D homogeneous transformations by 4D rotation matrices and used, for example, in [23] in dimensional synthesis, or in [46] to solve the inverse kinematics of a 6R robot. This kind of approximation introduces a tradeoff between numerical stability and accuracy of the approximation (see [45] for details).…”

Section: B Approximating Dual Quaternions By Double Quaternionsmentioning

confidence: 99%

See 1 more Smart Citation

Approaching Dual Quaternions From Matrix Algebra

Thomas

2014

IEEE Trans. Robot.

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Abstract-Dual quaternions give a neat and succinct way to encapsulate both translations and rotations into a unified representation that can easily be concatenated and interpolated. Unfortunately, the combination of quaternions and dual numbers seem quite abstract and somewhat arbitrary when approached for the first time. Actually, the use of quaternions or dual numbers separately are already seen as a break in mainstream robot kinematics, which is based on homogeneous transformations. This paper shows how dual quaternions arise in a natural way when approximating 3D homogeneous transformations by 4D rotation matrices. This results in a seamless presentation of rigid-body transformations based on matrices and dual quaternions which permits building intuition about the use of quaternions and their generalizations.

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Section: B Approximating Dual Quaternions By Double Quaternionsmentioning

confidence: 99%

Section: B Approximating Dual Quaternions By Double Quaternionsmentioning

confidence: 99%

Approaching Dual Quaternions From Matrix Algebra

Thomas

2014

IEEE Trans. Robot.

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“…Manocha and Canny 4 proposed symbolic preprocessing and matrix computations to convert the inverse kinematics to an eigenvalue problem. In recent years, literatures [5][6][7][8] have studied the inverse kinematics of general 6R robots. However, the problem is that these methods are limited to 6R robots.…”

Section: Introductionmentioning

confidence: 99%

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

Wang

Zhang

Zhao

2017

Advances in Mechanical Engineering

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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-offreedom robot is proposed. Based on the geometry of the robot, the inverse kinematics is converted into a onedimensional 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.

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“…Generally, analytical approaches, which yield complete, accurate and fast solutions, are preferable to numerical ones that are usually used to gain the approximate solutions by convergent iteration [9]. Different from the above commonly used methods, a mixed numerical-analytical approach is proposed in [10] to approximate the IK solutions, product-of-exponentials (PoE) formulas [11][12][13], vector dot product operations [14][15][16][17][18] and double quaternions [19,20] are involved to simplify the IK solving processes.…”

Section: Introductionmentioning

confidence: 99%

Novel inverse kinematic approaches for robot manipulators with Pieper-Criterion based geometry

Liu

Zhang

Zhu

2015

Int. J. Control Autom. Syst.

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In this paper, the inverse kinematics (IK) for robot manipulators with Pieper-Criterion based geometry is investigated from a novel perspective. Different from the traditional inverse transformation method, properties on orthogonal matrix, dot product operation and block matrix are synthetically involved in the proposed schemes to help simplify the IK solving, where the IK matrix equations are transformed into pure algebraic equations without any complex calculations of the inverses for transformation matrices. In the meantime, the linear combinations of related equations in the IK solving ensure the solutions free of extraneous roots, which enhances the computational efficiency further. Moreover, the singularity problem is fully addressed for a specific robot manipulator of such kind. Finally, experimental tests are provided to verify the proposed IK schemes.

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Inverse kinematic analysis of the general 6R serial manipulators based on double quaternions

Cited by 83 publications

References 9 publications

Approaching Dual Quaternions From Matrix Algebra

Approaching Dual Quaternions From Matrix Algebra

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

Novel inverse kinematic approaches for robot manipulators with Pieper-Criterion based geometry

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