Simulation Modeling

Simulation Modelling Practice and Theory 18 (2010) 712–731

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Simulation Modelling Practice and Theory journal homepage: www.elsevier.com/locate/simpat

Singularity-free dynamic equations of vehicle–manipulator systems
Pål J. From a,*, Vincent Duindam b, Kristin Y. Pettersen a, Jan T. Gravdahl a, Shankar Sastry b a b

Department of Engineering Cybernetics, Norwegian University of Science and Technology, Norway Department of EECS, University of California, 253 Cory Hall, Berkeley, CA 94720-1770, USA

a r t i c l e

i n f o

a b s t r a c t
In this paper we derive the singularity-free dynamic equations of vehicle–manipulator systems using a minimal representation. These systems are normally modeled using Euler angles, which leads to singularities, or Euler parameters, which is not a minimal representation and thus not suited for Lagrange’s equations. We circumvent these issues by introducing quasi-coordinates which allows us to derive the dynamics using minimal and globally valid non-Euclidean configuration coordinates. This is a great advantage as the configuration space of the vehicle in general is non-Euclidean. We thus obtain a computationally efficient and singularity-free formulation of the dynamic equations with the same complexity as the conventional Lagrangian approach. The closed form formulation makes the proposed approach well suited for system analysis and model-based control. This paper focuses on the dynamic properties of vehicle–manipulator systems and we present the explicit matrices needed for implementation together with several mathematical relations that can be used to speed up the algorithms. We also show how to calculate the inertia and Coriolis matrices and present these for several different vehicle–manipulator systems in such a way that this can be implemented for simulation and control purposes without extensive knowledge of the mathematical background. By presenting the explicit

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