This paper aims to demonstrate the necessity of simulation-based multibody dynamic modeling for determining the driving stability of logistics transport robots, including those with complex-shaped tires and suspension structures. Specifically, we generate a 3D dynamic model of a mobile robot using RecurDyn software and propose a new lumped parameter tire model for the lug-type tire to calculate contact forces between the tire and ground. The tire model is validated through tire compression tests, resulting in good agreement between the model and test results. We perform various driving simulations using the dynamic model, and calculate roll and pitch stability based on the dynamic behavior and tire forces of the robot. We present stability indicators for different driving conditions as a 3D map, providing criteria for stable driving. The proposed models and methods have the potential to improve the performance and stability of multi-terrain mobile robots in various industries.