Introduction to Robotics: Kinematics and Trajectory Planning

Robotic arms are transforming industries from manufacturing to healthcare, but programming their movement requires a solid grasp of how they navigate physical space. Understanding the underlying mathematics of motion is the essential first step to building, controlling, or simulating any robotic system. This course guides you through the foundational physics, geometry, and mathematics behind robotic manipulation. You will transition from understanding simple coordinate frames to calculating complex multi-joint movements and planning precise, smooth paths. What you'll learn: - Understand spatial descriptions, rotation matrices, and homogeneous transformations to describe objects in 3D space. - Calculate forward kinematics to determine the exact position of a robot's end-effector based on joint angles. - Solve inverse kinematics problems to find the required joint configurations for reaching a target destination. - Plan smooth robotic trajectories using polynomial paths and modern motion-profile algorithms. - Explore how these mathematical foundations map to modern industry tools and robotics middleware frameworks. The course begins with core definitions and spatial coordinate systems before progressing step-by-step through kinematic equations and practical trajectory planning scenarios. You will read detailed explanations, analyze mathematical derivations, and work through conceptual exercises to reinforce your learning. This course is designed for aspiring robotics engineers, students, and hobbyists who want a clear, beginner-friendly introduction to robot mechanics with no prior robotics experience required. Begin your journey into the mechanics of robotics and start mastering the math behind autonomous movement today.