By inverting the Jacobian matrix we can find the joint velocities required to achieve a particular end-effector velocity, so long as the Jacobian is not singular.
Search Results for: Jacobian matrix
As we did for the simple planar robots we can invert the Jacobian and perform resolved-rate motion control.
The relationship between world coordinates, image coordinates and camera spatial velocity is elegantly summed up by a single matrix equation that involves what we call the image Jacobian.
A robot manipulator may have any number of joints. We look at how the shape of the Jacobian matrix changes depending on the number of joints of the robot.
Now we introduce a variant of the Jacobian matrix that can relate our angular velocity vector back to our rates of change of the roll, pitch and yaw angles.
For a simple 2-link planar robot we introduce and derive its Jacobian matrix, and also introduce the concept of spatial velocity.
We resume our analysis of the 6-link robot Jacobian and focus on the rotational velocity part.
For a real 6-link robot our previous approach to computing the Jacobian becomes unwieldy so we will instead compute a numerical approximation to the forward kinematic function.
We extend what we have learnt to a 3-link planar robot where we can also consider the rotational velocity of the end-effector.
The Jacobian matrix provides powerful diagnostics about how well the robot’s configuration is suited to the task. Wrist singularities can be easily detected and the concept of a velocity ellipse is extended to a 3-dimensional velocity ellipsoid.