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Introduction to Robot Joint Control

We will learn about how we make the the robot joints move to the angles or positions that are required in order to achieve the desired end-effector motion. This is the job of the robot’s joint controller and in this lecture we will learn how this works. This journey will take us in to the realms of control theory.  

The Analytic 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.  

Velocity Ellipsoid in 3D and Manipulability

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.  

Motion in 3D

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.  

Introduction to Velocity Kinematics in 3D

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.  

Velocity Ellipse in 2D

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.  

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