Dynamic virtual holonomic constraints for stabilization of closed orbits in underactuated mechanical systems

• Autores: Alireza Mohammadi, Manfredi Maggiore, Luca Consolini
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Nº. 94, 2018, págs. 112-124
• Idioma: inglés
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• Resumen

  • This article investigates the problem of enforcing a virtual holonomic constraint (VHC) on a mechanical system with degree of underactuation one while simultaneously stabilizing a closed orbit on the constraint manifold. This problem, which to date is open, arises when designing controllers to induce complex repetitive motions in robots. In this paper, we propose a solution which relies on the parameterization of the VHC by the output of a double integrator. While the original control inputs are used to enforce the VHC, the control input of the double-integrator is designed to asymptotically stabilize the closed orbit and make the state of the double-integrator converge to zero. The proposed design is applied to the problem of making a PVTOL aircraft follow a circle on the vertical plane with a desired speed profile, while guaranteeing that the aircraft does not roll over for suitable initial conditions.