Contact tracking algorithms in case of the omni-directional wheel rolling on the horizontal surface

Abstract

An omni-wheel is defined as a wheel having rollers along its rim. Vehicles with omni-wheels are able to maneuver in any direction. For modeling the dynamics of omni-wheels we use general formalisms, previously developed by the authors for the multibody dynamics description in the framework of the object-oriented dynamical modeling language Modelica. Such an omni-wheel model, which is a class component, can be built into a vehicle model of any type. The axes of the rollers are usually set along the rim of the wheel either (a) parallel to the mid-plane of the wheel or (b) at some angle to this plane. Case (a) is the simplest one and the floor–roller contact tracking algorithm provides the fastest dynamical model. The more flexible case (b) consumes longer computation time. At the same time the suggested implementation of the case (b) turns out to be more efficient as compared with the approach based on the general formulas of contact problems. As an example, here these algorithms are combined with the simplest and fastest point-contact model, which runs regularly in the process of motion simulation. The proposed algorithms demonstrate the reliability and a nonimpact method of transferring contact point from one roller to another in the process of rolling the wheel. The implementation of these algorithms is described and computational experiments for numerical verification of the model are presented.