3: Forward and Inverse Kinematics

In order to plan a robot’s movements, we have to understand the relationship between the actuators that we can control and the robot’s resulting position in the environment. For static arms, this is rather straightforward: if we know the position/angle of each joint, we can calculate the position of its end-effectors using trigonometry. This process is known as forward kinematics. If we want to calculate the position each joint needs to be at, we need to invert this relationship. This is known as inverse kinematics. For mobile robots, this process is usually more involved, as speeds need to be integrated, which we refer to as odometry.

The goals of this chapter are:

• introduce coordinate systems and their transformations
• to introduce the forward kinematics of simple arms and mobile robots
• understand the concept of holonomy
• show how solutions for the inverse kinematics for both static and mobile robots can be derived
• provide an intuition on the relationship between inverse kinematics and path-planning

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