Testing static equilibrium for legged robots

Timothy Bretl, Sanjay Lall

Research output: Contribution to journalArticlepeer-review


Consider a legged robot at fixed foot placements. Where can the robot move its center of mass (CM) while remaining in static equilibrium? If the terrain is flat, the CM must lie above the convex hull of the robot's feet. If the terrain is not flat, this often-used approximation can be arbitrarily bad. Instead, the CM must lie above the projection of a nonlinear convex set that is defined by the properties of each foot placement. This paper presents an algorithm to compute the shape of this projection and gives a tight bound on the algorithm's running time. It also presents a method of amortizing the cost of this computation when it is only necessary to test static equilibrium at particular CM positions--that is, when it is only necessary to test the membership of points in the projection of a convex set rather than find its shape.

Original languageEnglish (US)
Pages (from-to)794-807
Number of pages14
JournalIEEE Transactions on Robotics
Issue number4
StatePublished - Aug 2008


  • Computational geometry
  • Frictional contact
  • Legged locomotion
  • Mobile robots
  • Motion planning
  • Static equilibrium

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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