Health Care Engineering Systems Center, University of Illinois at Urbana-Champaign, Urbana, Illinois, United States of America.
Industrial and Enterprise Systems Engineering Dept., University of Illinois at Urbana-Champaign, Urbana, Illinois, United States of America.
PLoS One. 2019 Feb 26;14(2):e0212018. doi: 10.1371/journal.pone.0212018. eCollection 2019.
This paper describes a new implementation for calculating Jacobian and its time derivative for robot manipulators in real-time. The estimation of Jacobian is the key in the real-time implementation of kinematics and dynamics of complex planar or spatial robots with fixed as well as floating axes in which the Jacobian form changes with the structure. The proposed method is suitable for such implementations. The new method is based on matrix differential calculus. Unlike the conventional methods, which are based on screw theory, the Jacobian calculation in the proposed approach has been reduced to the inner product of two matrices. Use of the new method to derive linear and angular velocity parts of Jacobian and its time derivative is described in detail. We have demonstrated the method using a two-DOF spatial robot and a hyper-redundant spatial robot.
本文描述了一种新的实时计算机器人运动学和动力学雅可比矩阵及其时间导数的方法。雅可比矩阵的估计是在具有固定和浮动关节的复杂平面或空间机器人的运动学和动力学实时实现中的关键，其中雅可比矩阵的形式随结构而变化。所提出的方法适用于这种实现。该方法基于矩阵微分学。与基于螺旋理论的传统方法不同，所提出的方法中的雅可比矩阵计算已简化为两个矩阵的内积。详细描述了使用新方法推导出雅可比矩阵及其时间导数的线速度和角速度部分。我们已经使用两自由度空间机器人和超冗余空间机器人演示了该方法。
