A Kinematic Variable for Analyzing Snake Robot Dynamics

Abstract

This paper presents a modern mathematical method to analyze snake robot dynamics. The method is rooted in three facets of contemporary mathematics: Cartan’s concept of endowing all moving bodies with their own reference frames, Lie group theory with its associated algebra, and a compact notation. Building upon previous work with cranes, this paper presents a new kinematic variable for determining the equations of motion for any number of rigid bodies linked in a tree structure with revolute joints. The core equations simplify the analysis and introduce a notation for the coordinate transformation matrix that directly ports to coding. The resulting equations can be readily applied using symbolic math packages and direct numerical solvers. In addition to its primary role as a research document, this paper also serves as an expository educational resource, presenting the methodology in a semi-tutorial format. The culmination of this work yields a comprehensive 3D forward-kinematics analytical model for analyzing the multi-body dynamics of a snake robotic system.