Unified Euler–Lagrange Framework for Dynamic Modeling of Wheeled Mobile Robots: Holonomic and Non-Holonomic Architectures

Abstract

This paper presents a unified Euler–Lagrange methodology for deriving the dynamic models of wheeled mobile robots (WMRs) across heterogeneous kinematic architectures. The work extends the authors’ previously developed kinematic methodology to the dynamic level, handling both holonomic platforms, where free roller motion eliminates kinematic constraints, and non-holonomic platforms, where pure-rolling conditions impose non-integrable velocity constraints. Through null-space-based reduction, constraint forces are eliminated, yielding control-affine state-space models that preserve structural properties essential for control synthesis, including inertia matrix symmetry, positive definiteness, and skew symmetry of the Coriolis matrix. The methodology is applied to four canonical architectures: differential drive, Ackermann steering, three-wheeled omnidirectional, and four-wheeled Mecanum drive. Distinct dynamic features are observed across topologies with direct implications for controller design. To confirm the correctness and practical utility of the derived models, trajectory tracking experiments are conducted in both ideal simulation and a realistic ROS2/Gazebo environment, with a model-based controller and a model-free strategy. Both successfully track the reference trajectories across all four architectures, with the model-based controller consistently achieving lower tracking errors.