Terramechanics-based wheel–terrain interaction model and its applications to off-road wheeled mobile robots

Zhenzhong Jiaa1a2, William Smitha1a2 and Huei Penga1a2 c1

a1 Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA

a2 Ground Robotics Reliability Center (GRRC), University of Michigan, Ann Arbor, MI 48109, USA


This paper presents a wheel–terrain interaction model, which enables efficient modeling of wheeled locomotion in soft soil and numerical simulations of off-road mobile robots. This modular model is derived based on wheel kinematics and terramechanics and the main focus is on describing the stress distributions along the wheel–terrain interface and the reaction forces exerted on the wheel by the soil. When the wheels are steered, the shear stresses underneath the wheel were modeled based on isotropic assumptions. The forces and torques contributed by the bulldozing effect of the side surfaces is also considered in the proposed model. Furthermore, the influence of grousers, commonly used on smaller mobile robots, was modeled by (1) averaging the normal pressures contributed by the grousers and the wheel concave portion, and (2) assuming that the shear phenomenon takes places along the grouser tips. By integrating the model with multibody system code for vehicle dynamics, simulation studies of various off-road conditions in three-dimensional environments can be conducted. The model was verified by using field experiment data, both for a single-wheel vehicle and a whole vehicle.

(Accepted June 15 2011)

(Online publication July 25 2011)


  • Wheel–terrain interaction;
  • Wheel–soil interface;
  • Terramechanics;
  • Off-road mobile robots;
  • Multibody system


c1 Corresponding author. E-mail: