## Summary of Velocity Kinematics in 3D

In Robotics | No commentThis video gives summary of Velocity kinematics in 3D.

14
Jul

This video gives summary of Velocity kinematics in 3D.

14
Jul

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.

14
Jul

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.

14
Jul

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.

14
Jul

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.

14
Jul

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

14
Jul

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

14
Jul

We have a quick revision of the skew-symmetric matrix. If you’re comfortable with this topic then go straight on to the next section.

14
Jul

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.

14
Jul

A body moving in 3D space has a translational velocity and a rotational velocity. The combination is called spatial velocity and is described by a 6-element vector.

14
Jul

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 learn about rate of change of orientation and the concept of angular velocity.

14
Jul

This video gives summary of velocity Kinematics in 2D

14
Jul

We can also 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.

14
Jul

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

14
Jul

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.

14
Jul

The end-effector is not able to move equally fast in all directions, and that in fact depends on the pose of the robot. We will introduce the velocity ellipse to illustrate this.

14
Jul

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.

14
Jul

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

14
Jul

We introduce the relationship between the velocity of the robot’s joints and the velocity of the end-effector in 3D space.

14
Jul

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.