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.
Dynamic virtual holonomic constraints for stabilization of closed orbits in underactuated mechanical systems / Mohammadi, Alireza; Maggiore, Manfredi; Consolini, Luca. - In: AUTOMATICA. - ISSN 0005-1098. - 94(2018), pp. 112-124. [10.1016/j.automatica.2018.04.023]
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