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A different switching surface stabilizing an existing unstable periodic gait: an analysis based on perturbation theory

Safa, A. T ; Sharif University of Technology | 2015

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  1. Type of Document: Article
  2. DOI: 10.1007/s11071-015-2130-1
  3. Publisher: Kluwer Academic Publishers , 2015
  4. Abstract:
  5. Limit cycle walkers are known as a class of walking robots capable of presenting periodic repetitive gaits without having local controllability at all times during motion. A well-known subclass of these robots is McGeer’s passive dynamic walkers solely activated by the gravity field. The mathematics governing this style of walking is hybrid and described by a set of nonlinear differential equations along with impulses. In this paper, by applying perturbation method to a simple model of these machines, we analytically prove that for this type of nonlinear impulsive system, there exist different switching surfaces, leading to the same equilibrium points (periodic solutions) with different stabilities. Furthermore, it has been shown that the number of existing periodic solutions depends on the characteristics of the switching surface
  6. Keywords:
  7. Limit cycle walking ; Stability ; Switching surface ; Convergence of numerical methods ; Differential equations ; Impulse response ; Nonlinear equations ; Switching ; System stability ; Impulsive systems ; Limit cycle walkings ; Local controllability ; Nonlinear differential equation ; Nonlinear impulsive systems ; Passive dynamic walker ; Perturbation ; Switching surfaces ; Perturbation techniques
  8. Source: Nonlinear Dynamics ; Volume 81, Issue 4 , 2015 , Pages 2127-2140 ; 0924090X (ISSN)
  9. URL: http://link.springer.com/article/10.1007/s11071-015-2130-1