Kinematics of Vehicle-Manipulator Systems

  • Pål Johan From
  • Jan Tommy Gravdahl
  • Kristin Ytterstad Pettersen
Part of the Advances in Industrial Control book series (AIC)


This chapter studies in detail the kinematics of vehicle-manipulator systems, which is the main topic of this book. Kinematically, the vehicle and the robotic manipulator are quite different in nature. While the manipulator’s motion space can be written in terms of a simple Euclidean (flat) configuration space, the vehicle’s state space is curved and defined on manifolds. We describe in detail how to find the kinematic relations of these two systems in terms of one unified theory. The formulation describes the vehicle’s state space as embedded in a manifold while it maintains the simplicity of the Euclidean space of the manipulator arm.

The kinematics of vehicle-manipulator systems is derived in detail with focus on obtaining a well-defined formulation. The chapter will give the reader a deeper understanding of the underlying spaces and in particular help to understand the difference between Euclidean and non-Euclidean spaces. This will give the reader the necessary background to model complex mechanical systems, including multibody systems with both simple Euclidean transformations and complex transformations described using matrix Lie groups.


Multibody System Configuration Space Inertial Frame Joint Position Robotic Manipulator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Duindam, V. (2006). Port-based modeling and control for efficient bipedal walking robots. Ph.D. thesis, University of Twente. Google Scholar
  2. Duindam, V., & Stramigioli, S. (2007). Lagrangian dynamics of open multibody systems with generalized holonomic and nonholonomic joints. In Proceedings of the IEEE/RSJ international conference on intelligent robots and systems, San Diego, CA, USA (pp. 3342–3347). Google Scholar
  3. Duindam, V., & Stramigioli, S. (2008). Singularity-free dynamic equations of open-chain mechanisms with general holonomic and nonholonomic joints. IEEE Transactions on Robotics, 24(3), 517–526. CrossRefGoogle Scholar
  4. Fossen, T. I. (2002). Marine control systems. Trondheim: Marine Cybernetics AS. 3rd printing. Google Scholar
  5. From, P. J. (2012a). An explicit formulation of singularity-free dynamic equations of mechanical systems in Lagrangian form—part one: single rigid bodies. Modeling, Identification and Control, 33(2), 45–60. CrossRefGoogle Scholar
  6. From, P. J. (2012b). An explicit formulation of singularity-free dynamic equations of mechanical systems in Lagrangian form—part two: multibody systems. Modeling, Identification and Control, 33(2), 61–68. CrossRefGoogle Scholar
  7. From, P. J., Duindam, V., Gravdahl, J. T., & Sastry, S. (2009). Modeling and motion planning for mechanisms on a non-inertial base. In Proceedings of international conference of robotics and automation, Kobe, Japan (pp. 3320–3326). Google Scholar
  8. From, P. J., Duindam, V., Pettersen, K. Y., Gravdahl, J. T., & Sastry, S. (2010). Singularity-free dynamic equations of vehicle-manipulator systems. Simulation Modelling Practice and Theory, 18(6), 712–731. CrossRefGoogle Scholar
  9. Murray, R. M., Li, Z., & Sastry, S. S. (1994). A mathematical introduction to robotic manipulation. Boca Raton: CRC Press. zbMATHGoogle Scholar
  10. Rossmann, W. (2002). Lie groups—an introduction through linear algebra. Oxford: Oxford Science Publications. Google Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  • Pål Johan From
    • 1
  • Jan Tommy Gravdahl
    • 2
  • Kristin Ytterstad Pettersen
    • 2
  1. 1.Department of Mathematical Sciences and TechnologyNorwegian University of Life SciencesÅsNorway
  2. 2.Department of Engineering CyberneticsNorwegian Univ. of Science & TechnologyTrondheimNorway

Personalised recommendations