Volumetric Contact Model of Ellipsoid-Plane Geometries

<p>Contact models of conforming surfaces are difficult to model accurately and efficiently. In multibody dynamics simulations, contact models increase system equation complexity (often dramatically so) and can also introduce nonlinearities and discontinuities into the system equations, decreasing the computational efficiency. This is particularly problematic in predictive simulations, which may determine optimal performance by running a simulation thousands of times. Contact modelling is even more complicated for large conforming surfaces, where the contact cannot be simplified to a single point. An ideal contact model must find a balance between accuracy and computational efficiency. Volumetric contact modelling is explored as a computationally efficient model conforming contacts. Volumetric contact has been used previously in robotics and biomechanics contacts, but analytical contact equations have only been derived for sphere-plane contact and 2D shapes. The model presented here improves on current work by deriving analytical volumetric contact equations for ellipsoid-plane contact which can better represent the shape of some contact surfaces. Equations for the volumetric geometrical values, normal force and damping, rolling resistance, tangential friction, and spinning friction were derived. Friction is approximated using a continuous velocity-based model of friction, and the possible limitations of this are described. This model may be useful for future use in modelling conforming contacts that can be approximated as an ellipsoid contacting a plane.</p>