Nonlinear Dynamics

, Volume 70, Issue 3, pp 2089–2094

Stability of quadruped robots’ trajectories subjected to discrete perturbations

Original Paper

DOI: 10.1007/s11071-012-0600-2

Cite this article as:
Pinto, C.M.A. Nonlinear Dyn (2012) 70: 2089. doi:10.1007/s11071-012-0600-2


In this paper, we study the stability of a mathematical model for trajectory generation of a qua-druped robot. We consider that each movement is composed of two types of primitives: rhythmic and discrete. The discrete primitive is inserted as a perturbation of the purely rhythmic movement. The two primitives are modeled by nonlinear dynamical systems. We adapt the theory developed by Golubitsky et al. in (Physica D 115: 56–72, 1998; Buono and Golubitsky in J. Math. Biol. 42:291–326, 2001) for quadrupeds gaits. We conclude that if the discrete part is inserted in all limbs, with equal values, and as an offset of the rhythmic part, the obtained gait is stable and has the same spatial and spatiotemporal symmetry groups as the purely rhythmic gait, differing only on the value of the offset.


Quadruped locomotion Modular trajectory Symmetry Central pattern generators H/K theorem 

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Centro de Matemática da Universidade do PortoPortoPortugal
  2. 2.Instituto Superior de Engenharia do PortoPortoPortugal

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