Departmental Papers (ESE)
Abstract
We present a new stability analysis for hybrid legged locomotion systems based on the “symmetric” factorization of return maps.We apply this analysis to two-degrees-of-freedom (2DoF) and threedegrees- of-freedom (3DoF) models of the spring loaded inverted pendulum (SLIP) with different leg recirculation strategies. Despite the non-integrability of the SLIP dynamics, we obtain a necessary condition for asymptotic stability (and a sufficient condition for instability) at a fixed point, formulated as an exact algebraic expression in the physical parameters. We use this expression to characterize analytically the sensory cost and stabilizing benefit of various feedback schemes previously proposed for the 2DoF SLIP model, posited as a low-dimensional representation of running.We apply the result as well to a 3DoF SLIP model that will be treated at greater length in a companion paper as a descriptive model for the robot RHex.
Document Type
Working Paper
Subject Area
GRASP, Kodlab
Date of this Version
October 2004
Keywords
legged locomotion, hybrid system, return map, spring loaded inverted pendulum, stability, time-reversal, symmetry
Date Posted: 30 June 2008
This document has been peer reviewed.
Comments
Reprinted from The International Journal of Robotics Research, Volume 23, Issue 10-11, October-November 2004, pages 979-999.
DOI: 10.1177/0278364904047389