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Subsections

jacobian_dot

Syntax

ReturnMatrix jacobian_dot(const int ref=0);

Description

The manipulator Jacobian time derivative can be used to compute the end effector acceleration due to joints velocities [9]:
$\displaystyle ^i\ddot{\mbox{\boldmath$ x $}} = ^i\dot{\mbox{\boldmath$ J $}}(\mbox{\boldmath$ q $},\dot{\mbox{\boldmath$ q $}})\dot{\mbox{\boldmath$ q $}}$     (2.47)

The Jacobian time derivative expressed in the base frame is given by [9]
$\displaystyle ^0\dot{\mbox{\boldmath$ J $}}(\mbox{\boldmath$ q $},\dot{\mbox{\b...
...$ J $}}_n(\mbox{\boldmath$ q $},\dot{\mbox{\boldmath$ q $}})
\end{array}\right]$     (2.48)

with
$\displaystyle ^0\dot{\mbox{\boldmath$ J $}}_i(\mbox{\boldmath$ q $},\dot{\mbox{\boldmath$ q $}})$ $\textstyle =$ $\displaystyle \begin{array}{cc}
\left[
\begin{array}{c}
\mbox{\boldmath$ \omega...
...oldmath$ p $}}_n
\end{array}\right] & \textrm{for a revolute joint}
\end{array}$ (2.49)
$\displaystyle ^0\dot{\mbox{\boldmath$ J $}}_i(\mbox{\boldmath$ q $},\dot{\mbox{\boldmath$ q $}})$ $\textstyle =$ $\displaystyle \begin{array}{cc}
\left[
\begin{array}{c}
0 \\
0
\end{array}\right] & \textrm{for a prismatic joint}
\end{array}$ (2.50)

where $\mbox{\boldmath$ z $}_i$ and $^{i-1}\mbox{\boldmath$ p $}_n$ are expressed in the base frame and $\times$ is the vector cross product. Expressed in the $i^{th}$ frame, the Jacobian time derivative is given by


$\displaystyle ^i\dot{\mbox{\boldmath$ J $}}(\mbox{\boldmath$ q $},\dot{\mbox{\b...
...}\dot{\mbox{\boldmath$ J $}}(\mbox{\boldmath$ q $},\dot{\mbox{\boldmath$ q $}})$     (2.51)

This function returns $^i\dot{\mbox{\boldmath$ J $}}(\mbox{\boldmath$ q $},\dot{\mbox{\boldmath$ q $}})$(i=0 when not specified).

Return Value

Matrix


next up previous contents
Next: jacobian_DLS_inv Up: The Robot and mRobot Previous: jacobian   Contents
Richard Gourdeau 2004-07-06