Analytical method for differentiation of robot Jacobian. Rhee, J. Y. & Lee, B. Electronics Letters, 53(6):386–387, 2017. doi abstract bibtex Model-based control algorithms commonly use joint acceleration as a desired trajectory. As the velocity trajectory in the task space is converted into joint velocity by multiplying using a Jacobian matrix, to derive the acceleration in joint space, Jacobian differentiation is required. Although the numerical method for Jacobian differentiation gives sufficiently accurate approximations, it incurs a high computation cost because this method involves computing the forward kinematics twice and Jacobian derivation for every element of the Jacobian matrix. Consequently, this causes difficulties for real-time control. To resolve this, an analytical differentiation method is proposed. Through recursive computation, differentiation is performed without any approximation, in an acceptably small computational time. Performance of the proposed method was verified by comparison with numerical derivation using a computer simulation.
@article{rhee_analytical_2017,
title = {Analytical method for differentiation of robot {Jacobian}},
volume = {53},
issn = {0013-5194},
doi = {10.1049/el.2016.3776},
abstract = {Model-based control algorithms commonly use joint acceleration as a desired trajectory. As the velocity trajectory in the task space is converted into joint velocity by multiplying using a Jacobian matrix, to derive the acceleration in joint space, Jacobian differentiation is required. Although the numerical method for Jacobian differentiation gives sufficiently accurate approximations, it incurs a high computation cost because this method involves computing the forward kinematics twice and Jacobian derivation for every element of the Jacobian matrix. Consequently, this causes difficulties for real-time control. To resolve this, an analytical differentiation method is proposed. Through recursive computation, differentiation is performed without any approximation, in an acceptably small computational time. Performance of the proposed method was verified by comparison with numerical derivation using a computer simulation.},
number = {6},
journal = {Electronics Letters},
author = {Rhee, J. Y. and Lee, B.},
year = {2017},
keywords = {Jacobian matrices, Jacobian matrix, acceleration, analytical differentiation method, computer simulation, differentiation, forward kinematics, joint acceleration, joint space, model-based control algorithms, numerical derivation, recursive computation, robot Jacobian differentiation, robot kinematics, velocity trajectory},
pages = {386--387}
}
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