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Archive of Mechanical Engineering

The Journal of Committee on Machine Building of Polish Academy of Sciences

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Tracking Control of A Balancing Robot – A Model-Based Approach

Sterowanie Śledzące Robota Zachowującego Równowagę – Podejście Oparte Na Modelu

Tobias Zaiczek
  • Fraunhofer-Institute Integrated Circuits, Design Automation Division, Zeunerstraβe 38, 01069 Dresden, Germany
  • Email:
/ Matthias Franke
  • Fraunhofer-Institute Integrated Circuits, Design Automation Division, Zeunerstraβe 38, 01069 Dresden, Germany
  • Email:
Published Online: 2014-08-15 | DOI: https://doi.org/10.2478/meceng-2014-0019


This paper presents a control concept for a single-axle mobile robot moving on the horizontal plane. A mathematical model of the nonholonomic mechanical system is derived using Hamel's equations of motion. Subsequently, a concept for a tracking controller is described in detail. This controller keeps the mobile robot on a given reference trajectory while maintaining it in an upright position. The control objective is reached by a cascade control structure. By an appropriate input transformation, we are able to utilize an input-output linearization of a subsystem. For the remaining dynamics a linear set-point control law is presented. Finally, the performance of the implemented control law is illustrated by simulation results.


W artykule przedstawiono koncepcję sterowania ruchem jednoosiowego robota poruszajĄcego się po płaszczyźnie poziomej. Model matematyczny nieholonomicznego systemu mechanicznego wyprowadzono korzystajĄc z równań ruchu Hamela. Opisano następnie szczegółowo koncepcję sterownika śledzĄcego. Sterownik prowadzi poruszajĄcy się robot po zadanej trajektorii utrzymujĄc go jednocześnie w pozycji pionowej. Cel sterowania jest osiĄgnięty przy zastosowaniu kaskadowej struktury sterowania. Dzięki odpowiedniej transformacji danych wejściowych, w podsystemie istnieje moŻliwość linearyzacji wejście-wyjście. Dla dynamiki pozostałej części zaprezentowano prawo liniowego sterowania stałowartościowego. Ostatecznie, jakość działania zastosowanych praw sterowania zilustrowano wynikami symulacji.

Key words:: single-axle mobile robot; nonholonomic constraints; Hamel's equation; cascade control structure; input-output linearization; tracking control; nonlinear control


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About the article

Published Online: 2014-08-15

Citation Information: Archive of Mechanical Engineering, ISSN (Online) 2300-1895, DOI: https://doi.org/10.2478/meceng-2014-0019. Export Citation

© 2014 Tobias Zaiczek and Matthias Franke. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

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