Open AccessAnalytical method for differentiation of robot Jacobian
Author(s) -
Rhee J.Y.,
Lee B.
Publication year - 2017
Publication title -
electronics letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.375
H-Index - 146
eISSN - 1350-911X
pISSN - 0013-5194
DOI - 10.1049/el.2016.3776
Subject(s) - jacobian matrix and determinant , numerical differentiation , kinematics , acceleration , computation , trajectory , automatic differentiation , mathematics , control theory (sociology) , matrix (chemical analysis) , computer science , algorithm , mathematical analysis , artificial intelligence , control (management) , physics , classical mechanics , materials science , astronomy , composite material
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.