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# Get Jacobian

Geometric Jacobian for robot configuration

• Library:
• Robotics System Toolbox / Manipulator Algorithms

## Description

The Get Jacobian block returns the geometric Jacobian relative to the base for the specified end effector at the given configuration of a `RigidBodyTree` robot model.

The Jacobian maps the joint-space velocity to the end-effector velocity relative to the base coordinate frame. The end-effector velocity equals:

`${V}_{EE}=\left[\begin{array}{c}{\omega }_{x}\\ {\omega }_{y}\\ {\omega }_{z}\\ {\nu }_{x}\\ {\nu }_{y}\\ {\nu }_{z}\end{array}\right]=J\stackrel{˙}{q}=J\left[\begin{array}{c}\begin{array}{c}{\stackrel{˙}{q}}_{1}\\ ⋮\end{array}\\ {\stackrel{˙}{q}}_{n}\end{array}\right]$`

ω is the angular velocity, υ is the linear velocity, and $\stackrel{˙}{q}$ is the joint-space velocity.

## Ports

### Input

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Robot configuration, specified as a vector of positions for all nonfixed joints in the robot model, as set by the Rigid body tree parameter. You can also generate this vector for a complex robot using the `homeConfiguration` or `randomConfiguration` functions inside a Constant or MATLAB Function block.

### Output

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Geometric jacobian of the end effector with the specified configuration, Config, returned as a 6-by-n matrix, where n is the number of degrees of freedom of the end effector. The Jacobian maps the joint-space velocity to the end-effector velocity relative to the base coordinate frame. The end-effector velocity equals:

`${V}_{EE}=\left[\begin{array}{c}{\omega }_{x}\\ {\omega }_{y}\\ {\omega }_{z}\\ {\nu }_{x}\\ {\nu }_{y}\\ {\nu }_{z}\end{array}\right]=J\stackrel{˙}{q}=J\left[\begin{array}{c}\begin{array}{c}{\stackrel{˙}{q}}_{1}\\ ⋮\end{array}\\ {\stackrel{˙}{q}}_{n}\end{array}\right]$`

ω is the angular velocity, υ is the linear velocity, and $\stackrel{˙}{q}$ is the joint-space velocity.

## Parameters

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Robot model, specified as a `RigidBodyTree` object. You can also import a robot model from an URDF (Unified Robot Description Formation) file using `importrobot`.

The default robot model, `twoJointRigidBodyTree`, is a robot with revolute joints and two degrees of freedom.

End effector for `Jacobian`, specified as a body name from the Rigid body tree robot model. To access body names from the robot model, click .

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