A comparative study between the augmented Lagrangian method and the complementarity approach for modeling the contact problem

The increasing demand for real-time high-fidelity multibody dynamics simulations in several modern fields such as robotics and computer game industries has motivated many researches to propose novel approaches to model multibody systems with several contacts. The possibility of different contact conditions in a system with several contacts yields a combinatorial problem of potentially large size. Rigid contact model which is the most common model used for real-time simulations yields a non-smooth dynamic formulation. The solution of such a system can be governed using different methods. In this paper a comparison between the complementarity approaches and the augmented Lagrangian based formulations to deal with non-smooth contact models is presented via numerical examples, and the advantages and shortcomings of each method are discussed.