The validation of a semi-recursive vehicle dynamics model for a real-time simulation

Abstract Semi-recursive formulations and their various versions have made it possible to describe complex nonlinear systems such as vehicles precisely while still solving the relevant equations of motion in real time. An optimal combination of an efficient multibody formulation and a fast numerical time integration scheme are needed to accurately simulate complex systems in real time. This paper introduces a double-step semi-recursive multibody formulation and analyzes its performance with high-order numerical time-integration algorithms for real-time simulation. The Runge-Kutta, Gill, Runge-Kutta-Fehlberg, Adams-Bashforth-Moulton, and adaptive time step Runge-Kutta numerical methods are explained and compared. Results are verified against a commercial multibody software solution. A 15-degree-of-freedom sedan vehicle model serves as a benchmark to verify the theoretical results. The results highlight the differences between the numerical algorithms and suggest appropriate approaches for a nonlinear vehicle dynamics model, particularly for cases where simulation times are long.

[1]  J. G. Jalón,et al.  An Efficient Dynamic Formulation for Solving Rigid and Flexible Multibody Systems Based on Semirecursive Method and Implicit Integration , 2016 .

[2]  D. Del Vecchio,et al.  Development of a Scaled Vehicle With Longitudinal Dynamics of an HMMWV for an ITS Testbed , 2008, IEEE/ASME Transactions on Mechatronics.

[3]  Javier García de Jalón,et al.  Iterative Refinement of Accelerations in Real-Time Vehicle Dynamics , 2018 .

[4]  Andrew S. Whittaker,et al.  Cross-platform implementation, verification and validation of advanced mathematical models of elastomeric seismic isolation bearings , 2018, Engineering Structures.

[5]  Javier García de Jalón,et al.  Real-Time Dynamic Simulations of Large Road Vehicles Using Dense, Sparse, and Parallelization Techniques , 2015 .

[6]  Javier García de Jalón,et al.  Comparison of Semirecursive and Subsystem Synthesis Algorithms for the Efficient Simulation of Multibody Systems , 2017 .

[7]  Javier Cuadrado,et al.  A Computational Benchmark for 2D Gait Analysis Problems , 2015 .

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

[9]  Javier Cuadrado,et al.  Index-3 divide-and-conquer algorithm for efficient multibody system dynamics simulations: theory and parallel implementation , 2018, Nonlinear Dynamics.

[10]  J. Dormand,et al.  High order embedded Runge-Kutta formulae , 1981 .

[11]  Hans B. Pacejka,et al.  Tire and Vehicle Dynamics , 1982 .

[12]  Andrés F. Hidalgo,et al.  Efficient Solution of Maggi’s Equations , 2011 .

[13]  Reinhold von Schwerin.  MultiBody System SIMulation - Numerical Methods, Algorithms, and Software , 1999, Lecture Notes in Computational Science and Engineering.

[14]  Alfonso Callejo,et al.  Efficient and accurate modeling of rigid rods , 2016, Multibody System Dynamics.

[15]  Aki Mikkola,et al.  An Efficient High-Order Time-Step Algorithm With Proportional-Integral Control Strategy for Semirecursive Vehicle Dynamics , 2019, IEEE Access.

[16]  Javier Cuadrado,et al.  A collaborative benchmarking framework for multibody system dynamics , 2010, Engineering with Computers.

[17]  W. Jerkovsky.  The Structure of Multibody Dynamics Equations , 1978 .

[18]  J. Dormand,et al.  A family of embedded Runge-Kutta formulae , 1980 .

[19]  K. Gustafsson,et al.  API stepsize control for the numerical solution of ordinary differential equations , 1988 .

[20]  S. M. Yang,et al.  A generalized recursive formulation for constrained flexible multibody dynamics , 2001 .

[21]  J. G. Jalón,et al.  A Fast and Simple Semi-Recursive Formulation for Multi-Rigid-Body Systems , 2005 .

[22]  Daniel Dopico,et al.  A Combined Penalty and Recursive Real-Time Formulation for Multibody Dynamics , 2004 .

[23]  Marek Teichmann,et al.  Multibody system dynamics interface modelling for stable multirate co-simulation of multiphysics systems , 2018, Mechanism and Machine Theory.

[24]  Antoni Aguilar-Mogas,et al.  Implementation of an algorithm based on the Runge‐Kutta‐Fehlberg technique and the potential energy as a reaction coordinate to locate intrinsic reaction paths , 2010, J. Comput. Chem..

[25]  Qiang Tian,et al.  A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints , 2018 .

[26]  John C. Butcher,et al.  Estimating local truncation errors for Runge-Kutta methods , 1993 .

[27]  Peter Betsch,et al.  Validation of flexible multibody dynamics beam formulations using benchmark problems , 2015 .

[28]  Payman Jalali,et al.  Computationally efficient approach for simulation of multibody and hydraulic dynamics , 2018 .

[29]  F. Potra.  Runge-Kutta Integrators for Multibody Dynamics , 1995 .

[30]  Daniel Dopico,et al.  An Efficient Unified Method for the Combined Simulation of Multibody and Hydraulic Dynamics: Comparison with Simplified and Co-Integration Approaches , 2011 .

[31]  J. Verner.  Explicit Runge–Kutta Methods with Estimates of the Local Truncation Error , 1978 .

[32]  Asko Rouvinen,et al.  Real-time analysis of mobile machines using sparse matrix technique , 2016 .

[33]  T. E. Simos,et al.  A family of trigonometrically fitted partitioned Runge-Kutta symplectic methods , 2009, Appl. Math. Comput..

[34]  Yusuf Gurefe,et al.  Multiplicative Adams Bashforth–Moulton methods , 2011, Numerical Algorithms.

[35]  Jacinto Javier Ibáñez,et al.  Adams-Bashforth and Adams-Moulton methods for solving differential Riccati equations , 2010, Comput. Math. Appl..

[36]  Robert G. Sargent,et al.  Verification and validation of simulation models , 2009, IEEE Engineering Management Review.

[37]  Werner Schiehlen,et al.  History of Benchmark Problems in Multibody Dynamics , 2014 .

[38]  Mohsen Zayernouri,et al.  Fractional Adams-Bashforth/Moulton methods: An application to the fractional Keller-Segel chemotaxis system , 2016, J. Comput. Phys..

[39]  Georg Rill,et al.  Numerical methods in vehicle system dynamics: state of the art and current developments , 2011 .

[40]  Caishan Liu,et al.  The effect of non-spherical aspect of a dimer on the dynamic behaviors , 2018, Nonlinear Dynamics.

[41]  Development and validation of a numerical model for the simulation of high-velocity impacts on advanced composite armor systems , 2018 .