Modeling, analysis and simulation of multibody systems with contact and friction

Dynamic simulation of multibody systems plays an important role in a wide range of fields, from robotics to computer animation, and from digital prototyping to virtual reality. While there is a significant body of research on dynamic simulation of bilateral systems, much less progress has been made in the development of simulation tools for unilateral systems, especially when friction is involved. This is partly because of the mathematical inconsistencies introduced by the use of classical rigid body dynamic models combined with empirical friction laws such as Coulomb's law.; The focus of this thesis is to develop the theoretical framework and supporting tools for computer simulation and analysis of constrained multibody systems. We analyze the difficulties associated with the uniqueness and existence when using classical approaches to simulate unilateral systems. By introducing a family of compliant contact models for dynamic simulation, we are able to gain insight into the inconsistencies of the rigid body models and completely overcome these difficulties. We formulate the compliant contact models as complementarity problems and prove that a compliant contact model with coupled normal and tangential springs and dampers distributed around the contact point guarantees a unique solution for contact forces. Experimental investigation for the single point contact case shows the consistency between the compliant contact models and the rigid body model.; Whenever possible, it is preferable to use rigid body models for dynamic simulation because such simulators are invariably more efficient. We present examples of interactive simulation environments for virtual prototyping and design customization of one-of-a-kind mechanisms, where in fact rigid body models are adequate for simulation. However, it is important to be able to reconcile the rigid body dynamic models with compliant contact models when rigid body models becomes inadequate. We use singular perturbation theory to model the fast time scale dynamics corresponding to the compliant contacts and the slow time scale dynamics corresponding to the rigid body dynamics. We derive necessary conditions for the stability of rigid body solutions. Based on these conditions, we are able to create a simulation algorithm that integrates the computationally expensive, but accurate compliant contact model with the less expensive but possibly flawed rigid body model for dynamic simulation.; The dynamic models and simulation algorithms developed in this thesis can be used in many applications. We address the application of the above ideas to two types of robot manipulation systems, including whole arm manipulation and multi-robot cooperative manipulation.