Stable internal dynamics of a legged hopping model with locomotion speed control

  • Ambrus Zelei
  • László BencsikEmail author
  • Tamás Insperger
  • Gábor Stépán
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)


The dynamic analysis of legged locomotion typically involves issues related to multibody dynamics, underactuation, motion planning and stability. In addition to biomechanics of humans and animals, the dynamic analysis of legged locomotion is also an important issue in the control development of pedal robots. For these robots, stable internal dynamics has to be guaranteed in order to achieve reliable control.

The goal of this study is the conceptual proof of a direct eigenvalue analysis method for the internal dynamics of legged robotic locomotors. The starting point is a planar model of hopping, which provides stable periodic motion without the feedback control of the locomotion speed. In the present study, we extend the existing model with a controller whose goal is to zero the virtual constraint related to the prescribed locomotion speed. We expect that the locomotion speed can be set arbitrarily in a certain range, where the internal dynamics is stable. The stability of the internal dynamics is analyzed using a recently published method based on direct eigenvalue analysis. Although, this method is not usual in control theory, it can efficiently be applied for multibody systems.


Pedal locomotion multibody dynamics underactuated systems zero dynamics piecewise smooth dynamical systems periodic orbits eigenvalue analysis 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ambrus Zelei
    • 1
    • 2
  • László Bencsik
    • 1
    • 2
    Email author
  • Tamás Insperger
    • 2
    • 3
  • Gábor Stépán
    • 1
    • 3
  1. 1.MTA-BME Research Group on Dynamics of Machines and VehiclesBudapestHungary
  2. 2.MTA-BME Lendület Human Balancing Research GroupBudapestHungary
  3. 3.Department of Applied MechanicsBudapest University of Technology and EconomicsBudapestHungary

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