Dynamic Modelling of Differential-Drive Mobile Robots using Lagrange and Newton-Euler Methodologies: A Unified Framework

This paper presents a unified dynamic modeling framework for differential-drive mobile robots (DDMR). Two formulations for mobile robot dynamics are developed; one is based on Lagrangian mechanics, and the other on Newton-Euler mechanics. Major difficulties experienced when modeling non-holonomic systems in both methods are illustrated and design procedures are outlined. It is shown that the two formulations are mathematically equivalent providing a check on their consistency. The presented work leads to an improved understanding of differentialdrive mobile robot dynamics, which will assist engineering students and researchers in the modeling and design of suitable controllers for DDMR navigation and trajectory tracking.