Robotics 1

Homogeneous Transformation Matrix

Homogeneous Transformation Matrix

This video shows how the rotation matrix and the displacement vector can be combined to form the Homogeneous Transformation Matrix. These matrices can be combined by multiplication the same way rotation matrices can, allowing us to find the position of the end-effector in the base frame. In this video, we complete calculating the Homogeneous Transformation Matrix in our Python code and test the results with the manipulator we built on our board.

To complete this lab activity, make a video that includes the following in one video:

Undergraduates:

(1) You saying your name

(2) Your 2-degree-of-freedom SCARA manipulator built on your board with the marker as its end-effector, moving to a position

(3) Your Python code correctly using the homogeneous transformation matrix to predict the position of the marker

Graduates:

(1) You saying your name

(2) Your Python code calculating the homogeneous transformation matrix from a Denavit-Hartenberg parameter table for one of the other examples in the Examples video (other than Cartesian)

(3) You explaining how you can tell that your result is correct by comparing the H0_3 matrix to the kinematic diagram

Undergraduates:

(1) You saying your name

(2) Your 2-degree-of-freedom SCARA manipulator built on your board with the marker as its end-effector, moving to a position

(3) Your Python code correctly using the homogeneous transformation matrix to predict the position of the marker

Graduates:

(1) You saying your name

(2) Your Python code calculating the homogeneous transformation matrix from a Denavit-Hartenberg parameter table for one of the other examples in the Examples video (other than Cartesian)

(3) You explaining how you can tell that your result is correct by comparing the H0_3 matrix to the kinematic diagram

In this video, we learn how to find a Denavit-Hartenberg parameter table, and then use the parameter table to find the Homogeneous Transformation Matrix.

Note: Graduate students did this 'blue' video last time. They can skip the blue video this time.

In this video, I give a number of examples of how to find the Denavit-Hartenberg parameter table for the standard manipulator types.

In this video, I show how to compute the Homogeneous Transformation Matrix from a Denavit-Hartenberg parameter table using Python.