Foundations of Robotics: Robot Modeling and Kinematics

Understanding how robots move and interact with their environment requires a solid foundation in mathematical modeling. This comprehensive written course guides you through the essential principles of spatial representations, kinematics, and dynamic foundations. You will transition from a curious beginner to someone who can confidently formulate kinematic equations for robotic arms and understand how modern robot description formats represent physical mechanisms. What you'll learn: - Understand foundational spatial representations, including rotation matrices, Euler angles, and homogeneous transformations. - Apply Denavit-Hartenberg parameters to model the forward kinematics of multi-joint robotic arms. - Formulate inverse kinematics solutions to determine required joint angles for desired spatial positions. - Explore differential kinematics, velocity relationships, and the role of the Jacobian matrix. - Read and write robot description configurations using modern URDF standards. - Practice modeling concepts using Python-based symbolic math and matrix computations. The course begins with core geometric and algebraic foundations before moving systematically through forward kinematics, inverse kinematics, and modern robot description formats. You will reinforce your learning through clear written explanations, step-by-step mathematical derivations, and practical code snippets. This course is designed for beginners in robotics, engineering students, and software developers looking to build a strong theoretical foundation in robot kinematics without any prior modeling experience. Start reading today to master the mathematical core of modern robotic systems.