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A Fibonacci control system with application to hyper-redundant manipulators

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Abstract

We study a model for snake-like robots based on the Fibonacci sequence. The present paper includes an investigation of the reachable workspace, a more general analysis of the control system underlying the model, its reachability and local controllability properties. In addition, we establish some fractal properties of the reachable workspace by means the theory of iterated function systems.

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Notes

  1. Notice that \(L(\mathbf u)=L(\mathbf u,\mathbf v)\) for all \(\mathbf v\in \{0,1\}^\infty \) where \(L(\mathbf u,\mathbf v):=\sum _{n=1}^\infty |x_n(\mathbf u,\mathbf v)-x_{n-1}(\mathbf u,\mathbf v)|\).

  2. Actually, we prove that such a neighborhood is indeed a polygon which is symmetric with respect to the origin.

  3. Indeed the claim immediately follows by recalling the equality \(\{L(\mathbf u)\mid \mathbf u\in \{0,1\}^\infty \}=R_\infty (q)\).

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Authors and Affiliations

  1. Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza Università di Roma, Via Scarpa 16, 00161, Rome, Italy

    Anna Chiara Lai, Paola Loreti & Pierluigi Vellucci

Authors
  1. Anna Chiara Lai
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  2. Paola Loreti
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  3. Pierluigi Vellucci
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Correspondence to Paola Loreti.

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Lai, A.C., Loreti, P. & Vellucci, P. A Fibonacci control system with application to hyper-redundant manipulators. Math. Control Signals Syst. 28, 15 (2016). https://doi.org/10.1007/s00498-016-0167-4

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