Department for Automation, Biocybernetics and Robotics

Control of rhythmic tasks with the use of a two-layered system

Research activity duration: 2008 -
Research area: Automation and Intelligent Control of Robots
Activity leader: Leon Žlajpah
Andrej Gams
Tadej Petrič


The two-layered system for control of rhythmic tasks in the first layer extracts the frequency from an arbitrary signal and in the second layer learns and imitates the waveform of the demonstrated signal.

Activity description

We address the problem of extracting the fundamental frequency of an arbitrary periodic or quasi-periodic signal for application in robotic tasks, using nonlinear oscillators. We propose to use nonlinear dynamical systems capable of extracting the frequency and the phase from an unknown periodic signal with an arbitrary waveform. The method uses a whole Fourier series representation in a feedback loop. It is capable of extracting the frequency and the phase of an unknown periodic signal in real-time, without any additional signal processing or preprocessing. Combining this method with an output dynamic system based on dynamic movement primitives, which generate the desired trajectory, allows control of different robotic tasks.


The system is computationally inexpensive, works on-line for any periodic signal, requires no  additional signal processing to determine the frequency of the input signal and can be applied in parallel to multiple dimensions. Additionally, it can adapt to changes in frequency and shape, e.g. to non-stationary signals, such as hand-generated signals and human demonstrations.


The canonical dynamical system is based on single adaptive frequency oscillators with an adaptive Fourier series in a feedback loop.  The learning process is embedded and is done in real-time. There is no need for any external optimization process.


This allows us to control of different robotic tasks. Such tasks include swinging of different pendulums, playing with toys (i.e. yo-yo or gyroscopic device Powerball), synchronizing drumming to an audio signal, human-robot cooperate rope turning or even  synchronizing human muscles actions to the robot motion or electrical neuromuscular stimulator activation.



pb_small.jpg   yoyo_small.jpg   drum_small.jpg   pend_small.jpg

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  • Petrič T., Gams A., Ijspeert A., Žlajpah L., On-line frequency adaptation and movement imitation for rhythmic robotic tasks, 2011. [More]
  • Petrič T., Curk B., Cafuta P., Žlajpah L., Modelling of the robotic Powerball : a nonholonomic, underactuated and variable structure-type system, 2010. [More]
  • Petrič T., Gams A., Žlajpah L., Robotizirani jojo : strategija vodenja z uporabo nelinearnih dinamičnih sistemov = Robotic yoyo : a control strategy based on nonlinear dynamic systems, 2010. [More] [PDF]


  • Petrič T., Gams A., Žlajpah L., Frequency extraction based on adaptive fourier series : application to robotic yo-yo, 2010. [More]
  • Petrič T., Gams A., Tomšič M., Žlajpah L., Ritmično vodenje robota z uporabo nelinearnih oscilatorjev in človeške mišične aktivnosti, 2010. [More]
  • Petrič T., Gams A., Žlajpah L., Modeling and control strategy for robotic powerball, 2009. [More]
  • Gams A., Petrič T., Žlajpah L., Controlling yo-yo and gyroscopic device with nonlinear dynamic systems, 2009. [More]
  • Petrič T., Gams A., Žlajpah L., Robotiziran jojo : strategija vodenja z nelinearnim dinamičnim sistemom = Robotic yoyo : control strategy based on nonlinear dynamic system, 2009. [More]
  • Petrič T., Gams A., Žlajpah L., Ritmično vodenje nihala z uporabo nelinearnega dinamičnega sistema, 2009. [More]