Chapter 2: Spatial transformation and rigid body motion

Chapter 2: Spatial Transformations and Rigid Body Motion

📽️ Estimated Time: 5–6 hours of video lectures + 10–15 hours of study and exercises

This chapter introduces the fundamental mathematical tools for describing motion in two and three dimensions, focusing on spatial transformations essential in robotics and control systems. Through theory, visualization, and coding examples, students will gain a strong foundation in rigid body kinematics.

🔹 Motivation & Introduction

• Warm-up: Introduction to 2D motion

• Explicit vs. Implicit representations of transformations

🔹 Rotations in 2D and 3D

• Mathematical derivation of rotation matrices

• Practical use cases and applications

• Rotation chaining and composition

🔹 Angular Velocity

• Understanding angular motion in dynamic systems

🔹 Exponential Coordinates

• Representation of rotations using exponential maps

• Advantages in control and motion planning

🔹 Homogeneous Transformations

• Mathematical derivation and structure

• Use in robotics modeling

• Chaining transformations in complex systems

🔹 Twists and Screws

• Introduction to twist vectors and their role in motion

• Screw theory and physical interpretation

• Assimilation of screw motions

🔹 Wrenches

• Force and torque representation in 3D space

🔹 Hands-on Practice

• Conceptual exercises to reinforce understanding

• Programming examples to simulate and visualize motion