Abstract
To tackle the frictional contact problem of multi-rigid-body with redundant constraints, efficient numerical resolution methods and stabilization algorithm are proposed. Firstly, based on time-stepping method and linear programming theories, a mixed nonlinear complementary model describing frictional contact problem is built. In order to solve the model effectively, the least square method for solving redundant constraints and linearization method are used to change the mixed nonlinear complementary problem into a linear complementary problem that can be easily solved. And then, a direct stabilization algorithm is given to stabilize resolution process of contact forces in advance, which effectively eliminates the drift problem for both equality and inequality constraints. At last, the validity of the numerical resolution methods and stabilization algorithm are verified through a numerical example.
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References
Glocker, C., Pfeiffer, F.: Complementarity Problems in Multibody Systems with Planar Friction. Archive of Applied Mechanics 63(7), 452–463 (1993)
Trinkle, J.C., Zeng, D.C.: Prediction of the Quasistatic Planar Motion of a Contacted Rigid Body. IEEE Transactions Robotics Automation 11, 229–246 (1995)
Pang, J.S., Trinkle, J.C.: Complementarity Formulation and Existence of Solutions of Dynamic Multi-rigid-body Contact Problem with Coulomb Friction. Mathematical Programming 73(2), 199–266 (1996)
Stewart, D.E.: Convergence of a Time-stepping Scheme for Rigid-body Dynamics and Resolution of Painleve’s Problem. Archive for Rational Mechanics and Analysis 145(3), 215–260 (1998)
Stewart, D.E., Trinkle, J.C.: An Implicit Time-stepping Scheme for Rigid Body Dynamics with Inelastic Coulomb Friction. In: Proceeding of the 2000 IEEE International Conference on Robotics & Automation, vol. 1, pp. 162–169. IEEE Press, San Francisco (2000)
Berard, S., Egan, K., Trinkle, J.C.: Contact Modes and Complementary Cones. In: Proceeding of the 2004 IEEE International Conference on Robotics & Automation, vol. 5, pp. 5280–5286. IEEE Press, New Orieans (2004)
Forg, M., Pfeiffer, F., Ulbrich, H.: Simulation of Unilateral Constrained Systems with Many Bodies. Multibody System Dynamics 14(2), 137–154 (2005)
Zhao, W.J., Pan, Z.K.: Least Square Algorithms and Constraint Stabilization for Euler-Lagrange Equations of Multi-body System Dynamics. Acta Mechanica Sinica 34(2), 594–602 (2002)
Glocker, C., Studer, C.: Formulation and Preparation for Numerical Evaluation of Linear Complementarity Systems in Dynamics. Multibody system Dynamics 13(4), 447–463 (2005)
Hairer, E., Wanner, G.: Solving ordinary differential equations II: Stiff and differential-algebraic problems, 2nd edn. Springer, Heidelberg (1996)
Burgermeister, B., Arnold, M., Esterl, B.: DAE Time Integration for Real-time Applications in Multi-body Dynamics. Journal of Applied Mathematics and Mechanics 86, 759–771 (2006)
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Gao, H., Zhang, Z., Liu, J., Lu, G., Shi, J. (2009). Numerical Methods for Frictional Contact of Multi-rigid-body with Redundant Constraints. In: Xie, M., Xiong, Y., Xiong, C., Liu, H., Hu, Z. (eds) Intelligent Robotics and Applications. ICIRA 2009. Lecture Notes in Computer Science(), vol 5928. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10817-4_57
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DOI: https://doi.org/10.1007/978-3-642-10817-4_57
Publisher Name: Springer, Berlin, Heidelberg
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