A Framework for Comparison of Methods for Solving Complementarity Problems That Arise in Multibody Dynamics

The simulation of multibody dynamics with physical constraints has been significant in the areas of science, engineering, computer graphics and robotics. There is a growing need for fast, accurate simulation tools in robotics applications such as manipulation planning and model-predictive control. However, the underlying dynamics model of multibody systems with contacts and friction is fundamentally nonsmooth and nonlinear, due to the intermittent unilateral contact and the stickslip transitions. The model is most commonly written as a differential complementarity problem, for which there is no closed-form solution. Therefore, one must use numerical methods to approximate the solution. This is commonly done by time discretization of the differential complementarity problem, which results in a sequence of algebraic complementarity problems. These problems also have no closed-form solution and are difficult to solve. This thesis contributes to the field of simulation of multibody dynamics systems in three primary areas: the development of new parallel solution algorithms, the development of methods to compare physical system behavior to that of simulated systems, and the development of a benchmark framework for the fair comparision of simulation algorithms. Among the simulation software packages in popular use today, there is no entirely satisfactory algorithm to compute the contact impacts with friction, and unbiased comparison and physical validation remain rare. Users with different application purposes are confused about which method to use based on the trade-off between accuracy and efficiency. Thus, we present the benchmark problems for multibody dynamics (BPMD) framework, with novel error metrics that evaluate not only the numerical error, but also the physical constraint violations to facilitate a fair comparison of common simulation models and solvers. The statistics and analytical metrics provide the robotics community, and others with a comprehensive tool to review the accuracy of possible simulation methods. To further validate the applicability of simulation methods, we conduct simulations of physical experiments and develop two analysis tools to tune model parameters and quantify errors.