# Question about robot jacobian

I try to understand jacobian for robot control. I want to precisely understand how to build that matrix. Can someone advice me course which explain how to create that matrix on a simple sample?

An other question about that matrix, I read that this matrix had to be process every step. Is it true?

## 1 Answer

Jacobian matrix is used to describe the relationship between the configuration space (space of joint angles) and the task space (space of end-effector pose) as follows:

## $$\textbf{\dot{p}} = \textbf{J(q)}\textbf{\dot{q}}$$,

where $$\textbf{J(q)}$$ is the Jacobian matrix, $$\textbf{p}$$ and $$\textbf{q}$$ are vectors represented for the end-effector pose and joint angles, respectively.

Several tutorials:

https://realitybytes.blog/2017/06/20/forward-and-inverse-kinematics-jacobians-and-differential-motion/

https://automaticaddison.com/the-ultimate-guide-to-jacobian-matrices-for-robotics/

http://www8.tfe.umu.se/courses/elektro/RobotControl/Lecture07_5EL158.pdf

You can do further searching with keywords: Denavit–Hartenberg, kinematics modeling, etc.

• "Jacobian matrix is used to describe the relationship between the configuration space (joint angles) and the task space (end-effector pose)": that's not correct as the relation needs to be intended in the differential manner, hence relating the joint velocities and the end-effector velocities. Please, amend your answer. – Ugo Pattacini Apr 22 at 18:10
• thanks, just added extra terms to make it clear. – Karim Apr 23 at 6:46