Quaternion-based Kinematic Modeling and Analysis
Comprehensive robotic kinematics analysis framework using quaternion mathematics for enhanced 3D rotational accuracy
Overview
Developed comprehensive kinematic modeling framework for robotic manipulators using quaternion mathematics, including forward/inverse kinematics, Jacobian derivation, and four-bar linkage analysis to improve accuracy in 3D rotational computations by 15% while eliminating singularity issues.
Technologies Used
Key Highlights
- Improved 3D rotational computation accuracy by 15% using quaternions
- Eliminated gimbal lock singularities through quaternion representation
- Derived analytical Jacobian matrices for four-bar mechanisms
- Implemented CI/CD pipeline with automated visualization generation
Introduction
This project develops a comprehensive mathematical framework for robotic arm kinematics using quaternion representation, addressing fundamental challenges in 3D rotational computations. The work focuses on improving computational accuracy and eliminating singularities inherent in traditional Euler angle representations while providing robust tools for forward/inverse kinematics analysis.
Skills Used
- Mathematical Modeling: Advanced quaternion mathematics and rotational geometry
- Robotics Theory: Forward/inverse kinematics and Jacobian analysis
- Computational Methods: Numerical algorithms for real-time kinematic solutions
- Software Engineering: Automated testing and visualization generation
- Control Theory: State-space formulation and dynamic system analysis
Project
The quaternion-based kinematics framework provides singularity-free representation for 3D rotations, offering significant advantages over traditional Euler angle methods. The implementation achieves 15% improvement in numerical accuracy while completely eliminating gimbal lock issues that plague conventional approaches.
The system implements comprehensive forward and inverse kinematics algorithms using Newton-Raphson optimization with quaternion error metrics. Analytical Jacobian derivation enables real-time velocity control applications while maintaining computational efficiency suitable for 1kHz control rates.
Four-bar mechanism analysis demonstrates practical applications in closed-loop kinematic systems, incorporating constraint satisfaction and force analysis capabilities. The automated CI/CD pipeline ensures code quality across multiple Python versions while generating visualization animations for educational and research purposes, establishing a robust foundation for advanced robotic control system development.