Bounds on the largest singular value of the manipulator Jacobian

Sagli, J.R.; Egeland, Olav

doi:10.1109/70.210799

Cited by 3 publications

(5 citation statements)

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“…This algorithm is computational expensive because of 2 min . Several algorithms were proposed [5,6] to use an estimatê 2 min instead of computing 2 min . It has been discovered that the accuracy of 2 min deteriorates when the two smallest eigenvalues of J T J cross over.…”

Section: Simulation and Experimentsmentioning

confidence: 99%

“…The Jacobian matrix J(q) plays an important rule in robot kinematics. It relates Cartesian velocities ẋ R 6 of the end-effector to joint velocity q R 6 of the robot bẏ…”

Section: Introductionmentioning

confidence: 99%

“…The accuracy of DLSI can be improved by estimating the singular values of the Jacobian matrix. [5][6][7] Chiaverini et al 8 applied DLSI to a six-joint robot and proposed the weighted DLSI to distribute the total error in user-defined directions. The closed-loop inverse kinematics (CLIK) algorithm 9,10 also uses DLSI to resolve the joint rates or joint accelerations.…”

Section: Introductionmentioning

confidence: 99%

“…For a six-joint robot, J(q) is a square matrix and a function of joint coordinate vector q R 6 . In many industrial applications, it is often desired to operate a robot such that the end-effector moves along specific curves or lines in Cartesian space.…”

Section: Introductionmentioning

confidence: 99%

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Local SVD inverse of robot Jacobians

Yuan¹

2001

Robotica

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SUMMARYThis study presents a fast inverse kinematics algorithm for a class of robots, including PUMA and SCARA. It decomposes a robot Jacobian into a product of sub-matrices to locate singularities. Singular value decomposition (SVD) is applied to each singular sub-matrix to find a local leastsquares inverse. Perfect inverses are derived for all non-singular sub-matrices. The proposed algorithm is extremely fast. A total inverse requires 54 flops for PUMA and 43 for SCARA. Simulation and experiment are conducted to test the accuracy and real-time speed of the algorithm.

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Section: Simulation and Experimentsmentioning

confidence: 99%

“…The Jacobian matrix J(q) plays an important rule in robot kinematics. It relates Cartesian velocities ẋ R 6 of the end-effector to joint velocity q R 6 of the robot bẏ…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Local SVD inverse of robot Jacobians

Yuan¹

2001

Robotica

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“…A suitable criterion is used to compute varying damping and weighting factors. In this respect, to know good estimates of the smallest singular value, which gives a measure of closeness to singularity [15]- [16], is recognized to yield considerable performance enhancements. A recently proposed estimation algorithm of the two smallest singular values is utilized [17] which is originated from the numerical filtering method proposed in [ 181.…”

Section: Introductionmentioning

confidence: 99%

Review of the damped least-squares inverse kinematics with experiments on an industrial robot manipulator

Chiaverini

Siciliano

Egeland³

1994

IEEE Trans. Contr. Syst. Technol.

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278

146

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The goal of this paper is to present experimental results on the implementation of the damped least-squares method for the six-joint ABB IRb2000 industrial robot manipulator. A number of inverse kinematics schemes are reviewed which allow robot control through kinematic singularities. The basic schemes adopts a damped least-squares inverse of the manipulator Jacobian with a varying damping factor acting in the neighbor-hood of singularities. The effect of a weighted damped least-squares solution is investigated to provide user-defined accuracy capabilities along prescribed end-effector space directions. An on-line estimation algorithm is employed to measure closeness to singular configurations. A feedback correction error term is introduced to ensure algorithm tracking convergence and its effect on the joint velocity solution is discussed

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Inverse Kinematics without matrix inversion

Pechev

2008

2008 IEEE International Conference on Robotics and Automation

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-This paper presents a new singularity robust and computationally efficient method for solving the inverse kinematics (IK) problem. In this method, the transformation from Cartesian space to joint space is performed in a feedback loop and as a result the new feedback inverse kinematics (FIK) law operates as a filter and does not require matrix manipulations (inversion, singular value decomposition or a computation of a damping factor). While the computational demand is greatly reduced, the performance is comparable to the one delivered by the damped least squares (DLS) law. The new algorithm is capable of escaping and avoiding kinematic singularities and in this respect it outperforms pseudo-inverse based formulations.

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Bounds on the largest singular value of the manipulator Jacobian

Cited by 3 publications

References 4 publications

Local SVD inverse of robot Jacobians

Local SVD inverse of robot Jacobians

Review of the damped least-squares inverse kinematics with experiments on an industrial robot manipulator

Inverse Kinematics without matrix inversion

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