RPI-MATLAB-Simulator: A Tool for Efficient Research and Practical Teaching in Multibody Dynamics

Volume 6: 10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control

et al. 2014

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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.

A Framework for Problem Standardization and Algorithm Comparison in Multibody System

Williams

Volume 6: 10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control

et al. 2014

Self Cite

A Complementarity Based Contact Model for Geometrically Accurate Treatment of Polytopes in Simulation

Williams

Volume 6: 10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control

2014

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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.

Comparison of Multibody Dynamics Solver Performance: Synthetic Versus Realistic Data

Volume 6: 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control

2015

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In the area of robotics simulation, multibody dynamics plays an important role in designing and controlling robots, especially when the robot contacts the environment. Contacts give rise to non-penetration and friction constraints, which are nonsmooth and nonlinear. One way to simulate such systems is through the use of a discrete-time multibody dynamics model in the form of a nonlinear complementarity problem (NCP), for which, finding a solution is known to be NP-hard [1]. In situations where analytical solutions don't exist, a suite of numerical solutions accessible through a benchmarking framework is useful to fairly evaluate performance of different computer algorithms. However, many algorithm designers don't have easy access to test data from physical simulators. Under such circumstances, randomized data are used to test the performance of solution algorithms.In this paper, we present our Benchmark Problems of Multibody Dynamics (BPMD) framework and database, with the data sets from different physics engines, as a benchmarking platform. Then we compare the performance of several solvers on synthetic data and simulation data, to show the superiority of testing solution algorithms with simulation data over testing with synthetic data. We will show that algorithm tested only on synthetic data often fail to solve problem obtained from physics simulations, to demonstrate the benefit of BPMD database.