#### Inverting the Jacobian Matrix

lesson

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.

lesson

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.

lesson

As we did for the simple planar robots we can invert the Jacobian and perform resolved-rate motion control.

lesson

We will introduce resolved-rate motion control which is a classical Jacobian-based scheme for moving the end-effector at a specified velocity without having to compute inverse kinematics.

lesson

We extend what we have learnt to a 3-link planar robot where we can also consider the rotational velocity of the end-effector.

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We resume our analysis of the 6-link robot Jacobian and focus on the rotational velocity part.

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We will learn about the relationship, in 3D, between the velocity of the joints and the velocity of the end-effector — the velocity kinematics. This relationship is described by a Jacobian matrix which also provides information about how easily the end-effector can move in different Cartesian directions. To do this in 3D we need to […]

lesson

We will learn about the relationship, in 2D, between the velocity of the joints and the velocity of the end-effector — the velocity kinematics. This relationship is described by a Jacobian matrix which also provides information about how easily the end-effector can move in different Cartesian directions.

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We previously learnt how to derive a Jacobian which relates the velocity of a point, defined relative to one coordinate frame, to the velocity relative to a different coordinate frame. Now we extend that to the 3D case.

lesson

For a simple 2-link planar robot we introduce and derive its Jacobian matrix, and also introduce the concept of spatial velocity.

lesson

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.