Modeling the contact between a rolling sphere and a compliant ground plane

In this paper a complete 3D contact model is presented. This model has nonlinearity in determining both normal and friction forces. A new nonlinear normal force model is introduced and the differences between this new model and previous ones are described. Also, the characteristics of this model are discussed and compared with the classical models and empirical results. For calculating the friction force, a new nonlinear model which is able to calculate pre-sliding displacement and viscous friction is presented. It is shown that this model allows us to keep track of all the energy in the system and therefore, supports an energy audit. Also, the rolling motion of a sphere on a compliant ground plane is simulated, and the results are presented. Rolling motion is an integral part of simulating the general 3D motion of a robot's foot while in contact with the ground.