Every robot, from a small wheeled rover to an industrial arm, is described with the same mathematical tools. Before you wire a motor or write a control loop, you need a language for saying where something is, which way it is pointing, and what forces make it move. This module builds that language.
You'll start with linear algebra, seeing matrices as transformations of space rather than grids of numbers. Then you'll apply that idea to coordinate frames, rotation matrices, and homogeneous transformations, the tools robots use to relate a camera, a gripper, and the world to each other. You'll also meet the common ways to represent orientation, including Euler angles and quaternions.
The module closes with the physics side: Newton's laws and how forces produce motion. These ideas return later in Control Systems and Kinematics & Dynamics, so it's worth taking the time to get comfortable with them here.
A visual introduction to linear transformations in two dimensions and how matrices describe them. This is the foundation for rotations, frames, and every transformation you'll use in robotics.
How to describe the position and orientation of a rigid body, what a rotation matrix is, and how homogeneous transformations combine rotation and translation into a single 4×4 matrix.
Chaining transformations between frames and solving transform equations, then comparing ways to represent orientation: rotation matrices, Euler angles, and quaternions, with the strengths and singularities of each.
The physics behind robot motion: how forces change an object's movement, what inertial frames are, and how F = ma connects the forces your actuators apply to the motion you get.