Abstract：Based on the hopping characteristics of kangaroos,a spring-mass model of hopping kangaroo robot is deve-loped.The dynamic equation is established using Lagrange method and linear approximation.The radial motion and horizontal motion during stance phase are analysed.According to gait stability conditions,the apex return map function,existence of fixed point and stability of fixed point of hopping kangaroo robot are studied.The range of each parameter which satisfies gait stability during kangaroo robot hopping process and the explicit relational expression of parameters are obtained.Finally,the linear approximation analysis is proved by example to be effective and the relation among parameters when kangaroo robot hops stably is obtained.
[1] Dawson T J,Taylor C R.Energetic cost of locomotion in kangaroos[J].Nature,1973,246(5431):313-314. [2] Ghigliazza R M,Altendoffer R,Holmes P,et al.A simple stabilized running model[J].SIAM J.Appl.Dynamical Systens,2003(2):187-218 [3] Schwind W J,Koditschek D E.Approximating the stance map of a2-DOF monoped runner[J].Journal of Nonlinear Sciences,2000,10(5):533-568. [4] Geyer H,Seyfarth A,Blickhan R.Spring-mass running:simple approximate solution and application to gait stability[J].Journal of Theoretical Biology,2005,232(3):315-328. [5] Full R J,Farley C T.Musculoskeletal dynamics in rhythmic systems-a comparative approach to legged locomotion[A].Biomechanics and Neural Control of Movement[M].New York,USA:Springer-Verlag,1999.192-205. [6] Farley C T,Blickhan R,Saito J,et al.Hopping frequency in humans:a test of how springs set stride frequency in bouncing gaits[J].Journal of Applied Physiology,1991,71:2127-2132. [7] Geyer H,Blickhan R,Seyfarth A.Natural dynamics of spring-like running:emergence of self-stability[A].5th International Conference on Climbing and Walking Robots[C].Suffolk,England:Professional Engineering Publishing Ltd,2002.87-92. [8] Raibert M H,Hodgins J K.Animation of dynamic legged locomotion[J].Computer Graphics,1991,25(4):349-358. [9] Farley C T,Glasheen J,McMabon T A.Running springs:speed and animal size[J].The Journal of Experimental Biology,1993,185(1):71-86.
