A Comprehensive Comparison of Spatial, Screw, Geometric, and Quaternion Approaches in Snake Robot Kinematics

This study investigates the application of Spatial Operator Algebra (SOA), Screw Theory, Geometric Algebra, and Quaternions in the kinematic analysis and control of a robotic snake. Given the complex, multi-segmented nature of robotic snakes, selecting an optimal mathematical framework for motion planning and control poses significant challenges. We systematically compare these four mathematical frameworks to evaluate their efficacy in handling the intricate locomotion and body configurations of a robotic snake. Our criteria for comparison include computational efficiency, ease of integration with existing control systems, and the ability to handle complex, non-linear motions characteristic of serpentine locomotion. Preliminary results indicate that while each framework has its strengths, certain methods offer distinct advantages in specific aspects of robotic snake control. This paper aims to provide a foundation for selecting the most suitable kinematic framework for robotic snakes, contributing to more efficient, flexible, and responsive designs.