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.
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.
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.
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.