The modeling and control of complex multi-rigid-body systems remain challenging due to the systems’ pronounced coupling and nonlinearity. In this paper, we propose a novel extended hierarchical modeling method for complex multi-rigid body systems, obtain an analytical model of system dynamics, and introduce a constraint-following control method to address the challenges of system modeling and control. In this approach, constraints are categorized into two levels: structural constraints constitute the first level, and motion constraints form the second level. Within the second level constraints, arbitrary initial conditions can lead to trajectory divergence. Consequently, we propose the asymptotic convergence criterion to address this issue. Subsequently, the analytical dynamic equation and trajectory tracking control force for the mobile robot are derived simultaneously. Numerical simulations of the mobile robots are performed to demonstrate the efficacy and accuracy of this methodology.