Benchmarking of augmented Lagrangian and Hamiltonian formulations for multibody system dynamics

Augmented Lagrangian methods represent an efficient way to carry out the forward-dynamics simulation of mechanical systems. These algorithms introduce the constraint forces in the dynamic equations of the system through the use of a set of multipliers. While most of these formalisms were obtained using the system Lagrange’s equations as starting point, a number of them have been derived from Hamilton’s canonical equations. Besides being efficient, they are generally considered to be very robust, which makes them especially suitable for the simulation of systems with discontinuities and impacts. In this work, we have focused on the simulation of mechanical assemblies that undergo singular configurations. First, some sources of numerical difficulties in the proximity of singular configurations were identified and discussed. Afterwards, several augmented Lagrangian and Hamiltonian formulations were compared in terms of their robustness during the forward-dynamics simulation of two benchmark problems. The effect of the formulation and numerical integrator choice and parameters on the simulation performance was also assessed.

[1]  J. Cuadrado,et al.  An efficient computational method for real time multibody dynamic simulation in fully cartesian coordinates , 1991 .

[2]  J. Baumgarte.  Stabilization of constraints and integrals of motion in dynamical systems , 1972 .

[3]  M. A. Serna,et al.  A modified Lagrangian formulation for the dynamic analysis of constrained mechanical systems , 1988 .

[4]  Daniel Dopico,et al.  Determination of Holonomic and Nonholonomic Constraint Reactions in an Index-3 Augmented Lagrangian Formulation With Velocity and Acceleration Projections , 2014 .

[5]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[6]  R. Ledesma,et al.  Augmented lagrangian and mass-orthogonal projection methods for constrained multibody dynamics , 1996 .

[7]  J. G. Jalón,et al.  Multibody dynamics with redundant constraints and singular mass matrix: existence, uniqueness, and determination of solutions for accelerations and constraint forces , 2013 .

[8]  Javier Cuadrado,et al.  Intelligent Simulation of Multibody Dynamics: Space-State and Descriptor Methods in Sequential and Parallel Computing Environments , 2000 .

[9]  E. Bayo,et al.  Singularity-free augmented Lagrangian algorithms for constrained multibody dynamics , 1994, Nonlinear Dynamics.

[10]  W. Blajer.  Augmented Lagrangian Formulation: Geometrical Interpretation and Application to Systems with Singularities and Redundancy , 2002 .

[11]  József Kövecses,et al.  Use of penalty formulations in dynamic simulation and analysis of redundantly constrained multibody systems , 2013 .

[12]  Francisco González,et al.  On the effect of multirate co-simulation techniques in the efficiency and accuracy of multibody system dynamics , 2011 .

[13]  M. A. Serna,et al.  Penalty based Hamiltonian equations for the dynamic analysis of constrained mechanical systems , 1994 .

[14]  Javier García de Jalón,et al.  Kinematic and Dynamic Simulation of Multibody Systems: The Real Time Challenge , 1994 .

[15]  Daniel Dopico,et al.  Dealing with multiple contacts in a human-in-the-loop application , 2011 .

[16]  U. Lugrís,et al.  A benchmarking system for MBS simulation software: Problem standardization and performance measurement , 2006 .

[17]  F. Daerden,et al.  Forward Dynamics of Open-Loop Multibody Mechanisms Using an Efficient Recursive Algorithm Based on Canonical Momenta , 2003 .

[18]  József Kövecses,et al.  A Penalty Formulation for Dynamics Analysis of Redundant Mechanical Systems , 2009 .

[19]  J. W. Humberston.  Classical mechanics , 1980, Nature.

[20]  J. Kövecses.  Dynamics of Mechanical Systems and the Generalized Free-Body Diagram—Part I: General Formulation , 2008 .

[21]  Nathan M. Newmark,et al.  A Method of Computation for Structural Dynamics , 1959 .