Foundation of Robotics from Math to Control - Course (1) : Kinematics

This lesson provides a foundational overview of vectors and coordinate frames, essential tools for understanding and modeling robotic motion. Students will explore basic vector operations, learn how to define and use reference frames, and get a first intuitive exposure to 3D rotations.

This lesson introduces matrices as fundamental tools for representing and manipulating data and transformations in robotics. Students will review matrix operations, properties, and key concepts such as the determinant, inverse, and multiplication rules, all of which are essential for describing robotic motion mathematically.

Practical examples about vectors and matrices

Optional extra readings about linear algebra from the book: Linear Algebra and Its Applications - Lay, David; Lay, Steven; McDonald, Judi: 9780321989925 - AbeBooks. (n.d.).

You may look at chapters 1, 2 and 3.

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.

In this lesson, students will explore 3D rotation matrices and how they describe orientation and motion in space. The concept of angular velocity and its representation using skew-symmetric matrices will be introduced. Finally, exponential coordinates and Rodrigues’ formula will be used to connect rotations with axis-angle representations.

Practical exercises on rotation.

This lesson introduces homogeneous transformations to represent combined rotation and translation in 3D space. Students will learn how to use twists to describe rigid body motion and how to switch between reference frames. The connection between twists, screw theory, and exponential coordinates is also covered, along with practical examples.

Practical exercises on homogeneous transformation.

This lesson introduces the concept of wrenches to describe forces and torques together in a unified 6D representation. Students will explore how wrenches behave, how to change their reference frames, and how they are measured in practice.

Optional extra readings from the book: Lynch, K. M., & Park, F. C. (2017). Modern Robotics: Mechanics, Planning, and Control. Cambridge Univeristy Press.

This lesson introduces the fundamental concepts necessary to describe robotic motion using forward kinematics. Students will learn about configuration space, degrees of freedom, robot structure, and how joint constraints define a robot’s mobility. These concepts form the basis for computing the pose of a robot’s end-effector.

This lesson introduces the Denavit–Hartenberg (D-H) convention, a systematic method for assigning coordinate frames to robotic manipulators. Students will learn how to extract and use the four D-H parameters to compute the transformation between joints, and how to handle special geometric cases in 3D configurations.

Practice exercise: derive FK in both base and body frames

This optional reading provides a structured discussion and consolidation of concepts already introduced in class regarding the Denavit-Hartenberg (D-H) convention. It revisits how D-H parameters define transformations between adjacent links in a manipulator, and how the convention relates to the Product of Exponentials (PoE) formulation. The reading is ideal for reinforcing and comparing both approaches to forward kinematics.

It is driven from the book: Lynch, K. M., & Park, F. C. (2017). Modern Robotics: Mechanics, Planning, and Control. Cambridge Univeristy Press.