Characterization of Fixed Points of Spring-Mass Model With a Body

Karagoz O. K., Sever I., Er G. D., SARANLI U., ANKARALI M. M.

28th Signal Processing and Communications Applications Conference (SIU), ELECTR NETWORK, 5 - 07 October 2020 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Doi Number: 10.1109/siu49456.2020.9302269
  • Keywords: legged locomotion, spring-loaded inverted pendulum, body dynamics, periodic motion, fixed-point analysis, stability
  • Middle East Technical University Affiliated: Yes


The Spring Loaded Inverted Pendulum (SLIP) template has long been known to be an appropriate model for motion dynamics of legged systems. However, SLIP template does not define the stabilization of upper body which is not negligible in humanoid robotic systems, even though it effectively explains running behaviour in terms of center of mass. In this paper, fixed points of the running motion at different running speeds, heights and trunk angle conditions of a reflexive controller developed on a spring-mass model with body whose center of mass and hip joint do not overlap is investigated. After calculating fixed points of the model by numerical analysis methods, it is found that the subspace defined by fixed points consisted of a one-dimensional curve. Then, the interaction between the boundaries of the fixed points on the curve representing the steady state running behavior and the adjustable parameter of the model is observed. This observation allows us to examine which running dynamics coordinates the model parameters affect. The results obtained here can be inferred from the running dynamics of systems with body.