Demonstrator purpose

Proof-of-concept demonstration of interactive vehicle simulation with distributed and coupled FMUs from different software tools


  • realtime performance of a non-trivial model of a wheel loader [1]
  • different simulation tools for different parts of the system
  • include rigid multibody system, flexible bodies, driveline, control, operator hardware interface
  • handle strong coupling and dynamic contacts

Status 2014-01

  • Three coupled FMUs: driveline (Dymola), rigid multibody vehicle  (AgX Dynamics), joystick (hardware and C++)
  • stable distributed and modular co-simulation with strong coupling
  • nearly realtime performance (before code optimization and parallelization)



System splitting


Dymola part

  • Diesel engine
  • Torque converter
  • Gearbox
  • Main drive shaft

Master solver part

  • Main drive shaft – as a master constraint

AgX Dynamics part

  • Main drive shaft
  • Differential front and back
  • Differential left and right
  • Wheels
  • Terrain and rocks
  • Steering and lifting as a separate system

In extended version

  • Flexible arm by FEM elasticity (Enmesh)
  • Steering and lifting also coupled to engine via hydraulics and control unit (Matlab/Simulink)
  • Operator interface (Oryx platform)

Master solver for coupled FMUs

  • Master integrator based on SPOOK stepper [2]
  • Subsystems as FMUs
  • Master drive shaft constraint $latex 0 \equiv g_{3} = \omega_1 – \omega_2 $
  • 3-step algorithm [3]
    • get Jacobians (“trial” subsystem solve)
    • solve master constraint
    • step subsystem
  • Jacobians and Schur complement are not computed
    explicitly but indirectly (directional derivatives)
  • algorithm is modular and parallelizable


  1. Optimal control of a wheel loader in the lift-transport section of the short loading cycle, Nezhadali, Eriksson and Froberg, 7th IFAC Symposium on Advances in Automotive Control. Tokyo, Japan (2013).
  2. Regularized, stabilized, variational methods for multibodies, C. Lacoursière, In Dag Fritzson Peter Bunus and Claus Führer, editors, The 48th Scandinavian Conference on Simulation and Modeling (SIMS 2007),  Linköping University Electronic Press, December 2007.
  3. Stable co-simulation algorithms, notes by C. Lacoursiére (2013).



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