Experimental Studies of Contact Space Model for Multi-surface Collisions in Articulated Rigid-Body Systems

Modeling simultaneous contact and collisions at multiple surfaces in articulated rigid-body systems is computationally challenging because joint and contact constraints must be enforced together. Previously, we have proposed an efficient method to treat multi-surface collisions in the contact space coordinates which represent the relative motion at the contact surfaces [12]. The inertial dynamics of the multi-surface collision is then equivalent to a simultaneous collision between two rigid bodies whose inertia equals the effective inertia of the respective articulated bodies in the contact space. In this paper, we present an experimental study of this model on planar and spatial systems of passive jointed pendulums. Across several frictionless/frictional, single/multi-surface collision events, the model accurately predicted post-collision joint positions and velocities. Furthermore, joint velocity predictions in the dynamically consistent null space were significantly more accurate than those in the contact space. This indicates that the contact space model accurately describes inertial dynamics of multisurface collisions in articulated rigid-body systems, but a better empirical restitution model can further improve prediction accuracy.