Page 22: Robots! (Kinematics and Inverse Kinematics)

The concepts of transformations are very important in fields outside of graphics. For example, just as transformations are useful for moving things in the “virtual worlds” of graphics, they can be useful in figuring out how things move in the real world, for example, to do robotics. On this page, we’ll consider Inverse Kinematics, a problem that is useful in graphics (especially for animation), and is very useful in robotics, so we’ll use robots as our example.

In the real world, many objects are rigid: they don’t change size or shape. Therefore, rigid transformations (rotation and translation) that don’t change size are used a lot. That’s what we’ll focus on here. Real objects that do change size and shape generally do so in complex ways.

Modeling a character as a chain of rotational joints is an approximation for a biological system - your elbow, for example, is not a simple rotation. For a robot arm, however, it is a good model: robot arms are (usually) built of rigid pieces that have rotational joints.

Forward and Inverse Kinematics

Consider two different problems:

1. We know the angles, but we need to know where the robot is. For example, we might want to draw it, or we might want to know the position of the tip of the hand (in robot terms, its “end effector”). This is the forward kinematics problem.
2. If we know the position of the end effector (or where we want pieces to go), we need to figure out the joint angles that put the pieces in place to achieve that goal. This is the inverse kinematics problem (IK).

Here’s a little demo. It’s a 2 link robot arm. You can control the angles and see where the robot goes. That’s Forward Kinematics. You can grab the end of the robot and drag it around. The program has to compute the angles that make it go there. That’s the Inverse Kinematics problem.

As you might guess, this is really useful for a robot: you want it to get its hand to a particular place; you don’t want to tell it how to bend its elbow.

For the workbook, I want you to understand what Inverse Kinematics is.

You should know that it is a more complicated problem than forward kinematics (which we have done in this workbook). You can learn about it in a robotics class.