Fast algorithms to test robust static equilibrium for legged robots

A. Del Prete, S. Tonneau, N. Mansard

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Maintaining equilibrium is of primary importance for legged systems. It is not surprising then that static equilibrium is at the core of most control/planning algorithms for legged robots. Being able to check whether a system is in static equilibrium is thus important, and doing it efficiently is crucial. While this is straightforward for a system in contact with a flat ground only, it is not the case for arbitrary contact geometries. In this paper we propose two new techniques to test static equilibrium and we show that they are computationally faster than all other existing methods. Moreover, we address the issue of robustness to errors in the contact-force tracking, which could lead to slippage or rotation at the contacts. We extend all the discussed techniques to test for robust static equilibrium, that is the ability to maintain equilibrium while avoiding to lose contacts despite bounded force-tracking errors. Accounting for robustness does not affect the computation time of the equilibrium tests, while it qualitatively improves the contact postures generated by our reachability-based multicontact planner.
Original languageEnglish
Title of host publication2016 IEEE International Conference on Robotics and Automation (ICRA)
Number of pages7
Publication statusPublished - 1 May 2016
Event2016 IEEE International Conference on Robotics and Automation - Stockholm, Sweden
Duration: 16 May 201621 May 2016


Conference2016 IEEE International Conference on Robotics and Automation
Abbreviated titleICRA 2016
Internet address


  • legged locomotion
  • robust control
  • robust static equilibrium
  • legged robots
  • legged systems
  • robustness
  • contact-force tracking
  • slippage
  • contacts rotation
  • bounded force-tracking errors
  • equilibrium tests
  • contact postures
  • reachability-based multicontact planner
  • Robustness
  • Robots
  • Friction
  • IP networks
  • Force
  • Approximation algorithms
  • Face


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