A steady state model of the contact between a deformable tire and a deformable terrain

This paper presents a lumped-parameter, planar, physical model for capturing steady-state interactions between a deformable tire and a deformable terrain. The model includes effects due to tangential and normal compliance of the terrain surface as well as radial and circumferential compliance of the tire. In addition, shear failure and dry friction limits are introduced through a distinction between regions along the circumferential direction of the tire that are in local stick or slip, respectively. The time history of interactions between individual infinitesimal patches of the tire and the terrain is then described by a hybrid dynamical system, in which changes between individual phases of motion are triggered by characteristic events. The paper further illustrates the application of a non-linear regression technique for identification of the seven model parameters and, in selected cases additional unknown kinematic variables. Specifically, the model is fit to experimental load-deflection, gross-thrust, and net-pull data demonstrating good quantitative agreement.