Energy shaping control for a class of underactuated Euler-Lagrange systems

Alin Albu-Schäer, Christian Ott Florian Petit

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

33 Scopus citations


The paper presents a new energy shaping control design for a class of underactuated Euler-Lagrange systems. Flexible joint robots, Series Elastic Actuators, and Variable Impedance Actuated Robots Albu-Schäer et al. [2008] belong for example to this class. First, classical PD control with feed-forward compensation is revisited and a novel, straight-forward and general formulation for the stability analysis is given. Lower bound conditions for the gains of this controller motivate the introduction of the new approach, which generalizes results from Albu-Schäer et al. [2007], Ch. Ott et al. [2008]. For shaping the potential energy, feedback variables based on the collocated states are introduced, which are statically equivalent to the noncollocated state variables. In this way the passivity is ensured while exactly satisfying steady state requirements formulated in terms of the noncollocated states (such as desired equilibrium configuration and desired stiffness). Using the passivity property, a Lyapunov based analysis can be easily carried out for arbitrarily low feedback gains. The controller is augmented by noncollocated feedback to shape the kinetic energy. Experimental results for a Variable stiffness Robot Grebenstein et al. [2011] validate the proposed controller.

Original languageEnglish
Title of host publicationSYROCO 2012 Preprints - 10th IFAC Symposium on Robot Control
PublisherIFAC Secretariat
Number of pages9
ISBN (Print)9783902823113
StatePublished - 2012
Externally publishedYes
Event10th IFAC Symposium on Robot Control, SYROCO 2012 - Dubrovnik, Croatia
Duration: 5 Sep 20127 Sep 2012

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
ISSN (Print)1474-6670


Conference10th IFAC Symposium on Robot Control, SYROCO 2012


  • Flexible joints
  • Impedance control
  • Underactuated systems
  • Variable impedance actuation


Dive into the research topics of 'Energy shaping control for a class of underactuated Euler-Lagrange systems'. Together they form a unique fingerprint.

Cite this