Content in short: The course (5 lectures and 3 exercises) equips participants with a variety of ideas, methods and algorithms, developed for analysis and control of periodic behaviors in mechanical systems with one or several passive links such as walking/running robots and underactuated pendulums. Tools for finding and planning periodic motions and tools for their orbital stabilization are discussed and illustrated by several examples. In addition to analytical steps and computer simulations, experiments are reported and the implementation issues are discussed.

Audience: The course can be of interest for graduate students and researchers in the subjects of Robotics, Mechatronics, Control, Analysis of Human Motions, and Applied Mathematics. Lectures and exercises require only basic knowledge of mechanics and control theory as well as basic familiarity with Matlab/Simulink.

Keywords: Periodic motion planning, orbital stability/stabilization, sensitivity of cycles, the Poincare first return map, the moving Poincare section, the transverse dynamics, synchronization, virtual holonomic constraints, the compass gait biped, the cart-pendulum system, the Furuta pendulum, the spherical pendulum on the puck, the Pendubot


This course has been taught at

2009, November: Sampei Lab, Department of Mechanical and Control Engineering, Tokyo Institute of Technology, Tokyo, Japan

2009, September: Department of Theoretical Cybernetics, Faculty of Mathematics & Mechanics, St.Petersburg State University, St.Petersburg, Russia.

2009, August: Control Laboratory, Faculty of Electrical Engineering, Mathematics & Computer Science, University of Twente, The Netherlands.

2007, September: Institut de Recherche en Communications et Cybernétique de Nantes (IRCCyN), Ecole Centrale de Nantes, France

2006, August: Section for Automation, Department of Electronic Systems, Faculty of Engineering, Science & Medicine, Aalborg University, Aalborg, Denmark

2005, August: Department of Automatic Control, Lund Institute of Technology, Lund, Sweden.

2005, April: Dpto. Ingeniería de Sistemas y Automática, Escuela Superior de Ingenieros, Universidad de Sevilla,  Sevilla, Spain

We would like to acknowledge fruitful discussions and comments given by students and colleagues, especially made by (in alphabetical order): Dr. Yannick Aoustin, Prof. Javier Aracil, Prof. Carlos Canudas-de-Wit, Prof. Christine Chevallereau, Dr. Mikhail Deryabine, Prof. Thor Inge Fossen, Prof. Sergey Gusev, Prof. Alexander Fradkov, Dr. Fabio Gomez-Estern, Prof. Francisco Gordillo, Prof. Rolf Johansson, Prof. Gennady Leonov, Prof. John Perram, Dr. Anders Robertsson, Prof. Mitsuji Sampei, Dr. Roger Skjetne, Prof. Mark W. Spong, Prof. Stefano Stramigioli