Robot Kinematics Solver Using Screw Theory
Developed a comprehensive robot kinematics library implementing forward/inverse kinematics, Jacobian computation, and trajectory planning using screw theory and the Product of Exponentials formula.
Duration
Spring 2025
Role
Developer
Institution
NTNU
Status
Completed
Technologies Used
Overview
This AIS4104 Robotics and Intelligent Systems portfolio project (Part 1) involved implementing a complete robot kinematics library from scratch using screw theory and the Product of Exponentials (PoE) formula. The implementation includes forward and inverse kinematics solvers, space and body Jacobian computation, and various trajectory generators for point-to-point and multi-point motions.
Problem Statement
Understanding and implementing robot kinematics is fundamental to robotics. This project required building a comprehensive library that can compute robot configurations, end-effector positions, and plan smooth trajectories, all based on the mathematical foundation of screw theory as presented in Modern Robotics by Lynch and Park.
Challenges & Solutions
| Challenge | Solution | Outcome |
|---|---|---|
| Gimbal Lock in Euler Angles | Implemented singularity detection and handling for ZYX Euler angle extraction from rotation matrices | Robust angle extraction even near singular configurations |
| IK Convergence | Implemented Newton-Raphson iteration with damped least squares for numerical stability | Reliable convergence to valid joint configurations |
| Trajectory Smoothness | Implemented cubic polynomial interpolation with velocity constraints | Smooth trajectories with continuous velocity profiles |