Original Paper

Nonlinear Dynamics

, Volume 70, Issue 3, pp 2089-2094

First online:

Stability of quadruped robots’ trajectories subjected to discrete perturbations

  • Carla M. A. PintoAffiliated withCentro de Matemática da Universidade do PortoInstituto Superior de Engenharia do Porto Email author 

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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