Three-dimensional impact: energy-based modeling of tangential compliance

Impact is indispensable in robotic manipulation tasks in which objects and/or manipulators move at high speeds. Applied research using impact has been hindered by underdeveloped computational foundations for rigid body collision. This paper studies the computation of tangential impulse as two rigid bodies in the space collide at a point with both tangential compliance and friction. It extends Stronge’s spring-based planar contact structure (Stronge 2000, pp. 95–96) to three dimensions by modeling the contact point as a massless particle able to move tangentially on one body while connected to an infinitesimal region on the other body via three orthogonal springs. Slip or stick is indicated by whether the particle is still or moving. Impact analysis is carried out using normal impulse rather than time as the only independent variable, unlike in previous work on tangential compliance. This is due to the ability of updating the energies stored in the three springs. Collision is governed by a system of differential equations solvable numerically. Modularity of the impact model makes it easy to be integrated into a multibody system, with one copy at each contact, in combination with a simultaneous impact model (Jia et al. 2011) that governs normal impulses at different contacts. KEY WORDs—impact, tangential compliance, friction, tangential impulse, energy-based restitution, contact modes, sliding velocity