A novel method for modeling skidding for systems with nonholonomic constraints

In this paper, the effect of wheel skidding on the steering motion of a simple vertical rolling disk is investigated. By modifying the nonholonomic constraints, two novel dynamic models are proposed. The first model rotates the constraints and enforces them along a plane correlated to the skid angle. It then relates the skidding in a wheel to the Lagrange multipliers associated with the kinematic constraints of that wheel. The second model relaxes the no-skidding constraint, allowing its transgression and relates the skidding to the generalized velocities of the actuated degrees of freedom of the system. To validate our model, we compare it to one in the literature and we analyze the motion of the disk on icy and snowy road conditions, where skidding can be significant.