Seminář Collocated virtual holonomic constraints in the underactuated walking design with the multi-step hybrid stability


prof. RNDr. Sergej Čelikovský, CSc. (UTIA AV ČR, Praha)

Datum akce: 
Středa, 6. Prosinec 2017 - 13:00 - 15:30

This seminar will present the concept of the so-called collocated virtual holonomic constraints and its application in the underactuated hybrid stable multi-step walking design. To demonstrate this approach, the so-called four link will be considered in detail and the analysis of the hybrid stability of its pre-designed walking-like trajectory and its feedback tracking controller will be presented. The four link is a planar mechanical chain having four degrees of freedom and three actuators placed between its links. In such a way it resembles a pair of legs with knees. The proof of hybrid stability is based on computing the appropriate Poincaré map linear approximation and showing numerically that its eigenvalues are inside the unit circle  of complex plane. Unlike the frequent approach in robotic walking showing the stable path following, nature of our designed trajectory enables to prove its tracking including the time dependence. The tested trajectory and the feedback controller were obtained via combination of the design for the so-called Acrobot and suitable selected collocated holonomic constraints enforced by feedback imposed in knees actuators. Finally, the simulations and animation will be presented. They demonstrate the hybrid stability of 150 steps of  the four link having lengths and masses corresponding to the existing laboratory model built in ÚTIA AV ČR.


  1. Introduction. Mechanical systems. Virtual holonomic constraints (VHCs).
  2. Input output exact feedback linearization and realization of the collocated VHCs.
  3. Hybrid invariance of the flat collocated VHCs.
  4. Application to the four link mechanical chain walking.
  5. Analysis of the hybrid walking stability.
  6. Simulations of the multi-step hybrid stable four link walking.
  7. Laboratory model of the underactuated walking robot.
  8. Conclusions and discussion.

Prof. Sergej Čelikovský: 1984 MSc. in Applied Mathematics, Optimal Control Department, Moscow State University;  1988 PhD. in Technical Cybernetics, Czechoslovak Academy of Sciences. Visiting researcher at University of Twente, Enschede 1996; Department of Mechanical and Automation Engineering, Chinese University of Hong Kong 1998; and CINVESTAV del I.P.N., Mexico 1998-2000. Currently, researcher fellow and head of the Department of Control Theory, Institute of Information Theory and Automation, Czech Academy of Sciences. Full Professor at the Department of Control Engineering, Czech Technical University in Prague. His research interests include nonlinear systems, exact feedback linearization, stabilization, chaotic systems, observers and output feedback control, underactuated mechanical systems and walking robots. Co-author of one book and two book chapters, 57 papers in the journals reported in WoS, over 100 papers in the international  conference proceeding.

Místo konání: 

Ústav automatizace a měřicí techniky
Technická 12
616 00 Brno
(Zasedací místnost ÚAMT SD3.102)
Kde nás najdete


Na seminář je nutné se předem registrovat. Přihlášky na seminář zasílejte prostřednictvím níže uvedeného formuláře. Registrace bude uzavřena 5.12.2017 v 12:00

pozvanka_07_1712.pdf40.68 KB

Registrace na tuto akci již byla ukončena.