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The task of stabilizing a wheeled unmanned aerial vehicle on a pipe, which is an application in oil and gas facilities for nondestructive measurements, is addressed here. After the derivation of the dynamic model of the system, a discrete-time nonlinear model predictive controller is designed over a finite horizon. The analysis of the asymptotic stability of the designed controller is carried out. Numerical tests show the performance and the robustness of the proposed solution.