A Generalized, Optimal Complexity, Parallel Algorithm For Modeling Nonholonomic Constraints in Multi-rigid Body System Dynamics

Rudranarayan Mukherjee , Paweł Malczyk

Abstract

We present a new algorithm for serial or parallel implementation based simulations of the dynamics of multi-rigid body systems subject to nonholonomic and holonomic constraints in generalized topologies i.e. serial chain, tree or kinematically closed loop topologies. The algorithm presents an elegant approach for eliminating the nonholonomic constraints explicitly from the equations of motion and implicitly expressing them in terms of nonlinear coupling in the operational inertias of the bodies subject to these constraints. The resulting equations are in the same form as those of a body subject to kinematic joint constraints. This enables the nonholohomic constraints to be seamlessly treated in either a (i) recursive or (ii) hierarchic assembly-disassembly process for solving the equations of motion of generalized multirigid body systems in serial or parallel implementations respectively. The algorithm is non-iterative and although the nonholonomic constraints are imposed at the acceleration level, constraint satisfaction is excellent as demonstrated by the two numerical test cases implemented to verify the algorithm. The algorithm achieves time-optimal logarithmic complexity and linear complexity in solving the equations of motion in parallel and serial implementations respectively. The methodology is based on the use of mixed set of variables i.e. relative and absolute coordinates. It employs a hierarchic assembly disassembly process and uses distinct set of formulae for handling holonomic and non-holonomic constraints. The formalism of projecting equations of motion into the complementary spaces of motion enabled and constraints imposed by kinematic joints is fundamental to the approach presented here.
Author Rudranarayan Mukherjee
Rudranarayan Mukherjee,,
-
, Paweł Malczyk (FPAE / IAAM)
Paweł Malczyk,,
- The Institute of Aeronautics and Applied Mechanics
Pages155-156
Publication size in sheets0.3
Book Terze Zdravko (eds.): Proceedings of the 2013 ECCOMAS Thematic Conference on Multibody Dynamics, 2013, University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, ISBN 978-953-7738-21-1, [978-953-7738-22-8], 507 p.
Keywords in EnglishSystem dynamics , Algorithms , Modeling
Languageen angielski
Score (nominal)15
ScoreMinisterial score = 10.0, 04-09-2019, BookChapterMatConfByIndicator
Ministerial score (2013-2016) = 15.0, 04-09-2019, BookChapterMatConfByIndicator
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