Inverse Kinematics Solution for Robotic Systems

In this documentation, we explore the inverse kinematics solution for a two-degree-of-freedom robotic system. Specifically, we employ Lagrangian energy methods to formulate the robot's kinematic equations, enabling the calculation of joint angles from torque inputs to achieve inverse kinematics resolution. It's important to note that inverse kinematics represents a fundamental challenge in robotics, as it involves converting end-effector positions into corresponding joint angles - a non-trivial transformation requiring sophisticated mathematical modeling. Our implementation includes numerical methods for solving the derived equations, potentially involving iterative algorithms like Newton-Raphson or gradient descent for practical computation. We will provide detailed, step-by-step explanations of the algorithm's implementation process, including mathematical derivations and corresponding code structure. Additionally, we will examine practical application scenarios and discuss integration methods for real-world robotic applications, with potential code examples demonstrating torque-to-angle conversion functions and trajectory planning modules. This documentation aims to provide comprehensive understanding of both theoretical foundations and practical implementation aspects.