Position/Force Control of the Mobile Manipulator with Rheonomic Constraints

  • Baigeng Wang
  • Shurong LiEmail author
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 528)


In the view of the rheonomic constraints problem of the mobile manipulator, the corrected orthogonalization method is adopted to solve the problem that velocity and force are not orthogonal under rheonomic constraints. By transforming the system with the designed transformation matrix, the velocity and the force are mapped to the orthogonal spaces. Then, a position/force strategy is designed, which drives the position and force converge to zero. Furthermore, we consider the situation where there is interference in the motor and propose the desired torque control strategy and the desired motor control strategy. The robustness of the system is enhanced. By selecting the proper Lyapunov function, the effectiveness of the proposed strategy is proved. Through simulation, the validity of the above conclusions are verified.


Mobile manipulator Rheonomic constraints Position/force control Lyapunov function 


  1. 1.
    J. Chung, H. Velinsky et al., Modeling and control of a mobile manipulator. Robotica 16(16), 607–613 (1998)CrossRefGoogle Scholar
  2. 2.
    K. Watanabe, K. Sato, K. Izumi et al., Analysis and control for an omnidirectional mobile manipulator. J. Intell. Rob. Syst. 27(1–2), 3–20 (2000)CrossRefGoogle Scholar
  3. 3.
    M. Galicki, Control of mobile manipulators in a task space. IEEE Trans. Autom. Control 57(11), 2962–2967 (2012)MathSciNetCrossRefGoogle Scholar
  4. 4.
    M.H. Wu, S. Ogawa, A. Konno, Symmetry position/force hybrid control for cooperative object transportation using multiple humanoid robots. Adv. Robot. 30(2), 131–149 (2016)CrossRefGoogle Scholar
  5. 5.
    Z. Li, S.S. Ge, M. Adams et al., Robust adaptive control of uncertain force/motion constrained nonholonomic mobile manipulators. Automatica 44(3), 776–784 (2008)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Y. Jia, Robust control with decoupling performance for steering and traction of 4WS vehicles under velocity-varying motion. IEEE Trans. Control Syst. Technol. 8(3), 554–569 (2000)CrossRefGoogle Scholar
  7. 7.
    N. Chen, F. Song, G. Li et al., An adaptive sliding mode backstepping control for the mobile manipulator with nonholonomic constraints. Commun. Nonlinear Sci. Numer. Simul. 18(10), 2885–2899 (2013)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Y. Jia, Alternative proofs for improved LMI representations for the analysis and the design of continuous-time systems with polytopic type uncertainty: a predictive approach. IEEE Trans. Automat. Control 48(8), 1413–1416 (2003)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Y.H. Liu, S. Arimoto, Adaptive and Nonadaptive Hybrid Controllers for Rheonomically Constrained Manipulators (Pergamon Press, Inc., 1998)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.College of Information and Control EngineeringChina University of PetroleumQingdaoChina
  2. 2.Automation SchoolBeijing University of Posts and TelecommunicationsBeijingChina

Personalised recommendations