We present a contact model for rigid-body simulation that considers the local geometry at points of contact between convex polyhedra in order to improve physical fidelity and stability of simulation. This model formulates contact constraints as sets of complementarity problems in a novel way, avoiding or correcting the pitfalls of previous models. We begin by providing insight into the special considerations of collision detection needed to prevent interpenetration of bodies during time-stepping simulation. Then, three fundamental complementarity based contact constraints are presented which provide the foundation for our model. We then provide general formulations for 2D and 3D which accurately represent the complete set of physically feasible contact interactions in six unique configurations. Finally, experimental results are presented which demonstrate the improved accuracy of our model compared to four others.
The underlying dynamic model of multibody systems takes the form of a differential Complementarity Problem (dCP), which is nonsmooth and thus challenging to integrate. The dCP is typically solved by discretizing it in time, thus converting the simulation problem into the problem of solving a sequence of complementarity problems (CPs). Because the CPs are difficult to solve, many modelling options that affect the dCPs and CPs have been tested, and some reformulation and relaxation options affecting the properties of the CPs and solvers have been studied in the hopes to find the “best” simulation method. One challenge within the existing literature is that there is no standard set of benchmark simulations.
In this paper, we propose a framework of Benchmark Problems for Multibody Dynamics (BPMD) to support the fair testing of various simulation algorithms. We designed and constructed a BPMD database and collected an initial set of solution algorithms for testing. The data stored for each simulation problem is sufficient to construct the CPs corresponding to several different simulation design decisions. Once the CPs are constructed from the data, there are several solver options including the PATH solver, nonsmooth Newton methods, fixed-point iteration methods for nonlinear problems, and Lemke’s algorithm for linear problems. Additionally, a user-friendly interface is provided to add customized models and solvers.
As an example benchmark comparison, we use data from physical planar grasping experiments. Using the input from a physical experiment to drive the simulation, uncertain model parameters such as friction coefficients are determined. This is repeated for different simulation methods and the parameter estimation error serves as a measure of the suitability of each method to predict the observed physical behavior.
Contemporary problem formulation methods used in the dynamic simulation of rigid bodies suffer from problems in accuracy, performance, and robustness. Significant allowances for parameter tuning, coupled with careful implementation of a broad-phase collision detection scheme are required to make dynamic simulation useful for practical applications. A constraint formulation method is presented herein that is more robust, and not dependent on broad-phase collision detection or system tuning for its behavior. Several uncomplicated benchmark examples are presented to give an analysis and make a comparison of the new polyhedral exact geometry (PEG) method with the well-known Stewart–Trinkle method. The behavior and performance for the two methods are discussed. This includes specific cases where contemporary methods fail to match theorized and observed system states in simulation, and how they are ameliorated by the new method presented here. The goal of this work is to complete the groundwork for further research into high performance simulation.
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