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Research Papers

Performance of a Method for Formulating Geometrically Exact Complementarity Constraints in Multibody Dynamic Simulation

[+] Author and Article Information
Daniel Montrallo Flickinger

Research Assistant
CS Robotics Laboratory,
Department of Computer Science,
Rensselaer Polytechnic Institute,
Troy, NY 12180
e-mail: dmflickinger@gmail.com

Jedediyah Williams

Research Assistant
CS Robotics Laboratory,
Department of Computer Science,
Rensselaer Polytechnic Institute,
Troy, NY 12180
e-mail: jedediyah@gmail.com

Jeffrey C. Trinkle

Professor
CS Robotics Laboratory,
Department of Computer Science,
Rensselaer Polytechnic Institute,
Troy, NY 12180
e-mail: trinkle@gmail.com

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received June 20, 2013; final manuscript received March 24, 2014; published online September 12, 2014. Assoc. Editor: Dan Negrut.

J. Comput. Nonlinear Dynam 10(1), 011010 (Sep 12, 2014) (12 pages) Paper No: CND-13-1151; doi: 10.1115/1.4027314 History: Received June 20, 2013; Revised March 24, 2014

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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References

Figures

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Fig. 1

Vertex at times t1…t4 moving within the constraint half-spaces near an object, Stewart–Trinkle formulation. A large impulse acts on the vertex at t2 and the diagonal constraint is active at t3 and t4.

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Fig. 2

Vertex at times t1…t3 moving in proximity to an object, polyhedral exact geometry formulation

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Fig. 3

A particle interacting with a single edge

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Fig. 4

Particle M interacting with two edges, p1p2 and p2p3, with half-spaces represented by shaded areas

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Fig. 5

Particle M interacting with a planar polygon, the constraints are represented as dashed lines along edges 1 and 2

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Fig. 6

Trajectories of the polyhedral exact geometry and Stewart–Trinkle methods

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Fig. 7

Detailed trajectory of polyhedral exact geometry and Stewart–Trinkle methods

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Fig. 8

Problem size of the polyhedral exact geometry and Stewart–Trinkle methods, hills simulation

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Fig. 9

Solver time for the polyhedral exact geometry and Stewart–Trinkle methods, hills simulation

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Fig. 10

Trajectories of the polyhedral exact geometry and Stewart–Trinkle methods without friction

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Fig. 11

Details of the trajectories of the polyhedral exact geometry and Stewart–Trinkle methods without friction

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Fig. 12

Problem size for the polyhedral exact geometry and Stewart–Trinkle methods

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Fig. 13

Solver time for the polyhedral exact geometry and Stewart–Trinkle methods

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Fig. 14

Trajectories of the sawtooth simulation with friction, using the polyhedral exact geometry, Stewart–Trinkle, and Anitescu–Potra methods

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Fig. 15

Sawtooth simulation trajectories in proximity to the beginning of the second ballistic phase

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Fig. 16

Trajectories of the polyhedral exact geometry and Stewart–Trinkle methods

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Fig. 17

Detailed view of trajectories of the polyhedral exact geometry and Stewart–Trinkle methods

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Fig. 18

Median error in particle simulation of the polyhedral exact geometry, Stewart–Trinkle, and Anitescu–Potra methods with respect to step size

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Fig. 19

Profile view of initial configuration of slender rod simulation

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Fig. 20

Oblique view of initial configuration of slender rod simulation

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Fig. 21

Plan view of initial configuration of slender rod simulation

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Fig. 22

Median error in slender rod simulation of the polyhedral exact geometry, Stewart–Trinkle, and Anitescu–Potra methods with respect to step size

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