This paper presents a trajectory tracking control for the position and heading angle of a quadrotor helicopter. The control design is based on the backstepping approach and proves the asymptotic stability of the tracking problem. We use a beneficial quaternion-based attitude parametrization, which is composed of two rotations. The first describes the orientation of the thrust vector independently from the second, which describes the quadrotor's heading. As a result, the translational dynamics and the yaw dynamics decouple from each other, which augments the control design. In addition, this decoupling allows an analytical derivation of all control signals within the backstepping procedure with reasonable expense. Experimental results show the practical use of the suggested control design.
This paper presents an adaptive backstepping controller for the position trajectory tracking of a quadrotor. The design adopts and modifies the L1 adaptive control approach for nonlinear reference systems to fit into the backstepping design and to decouple the nominal controller from the adaptation. The controller compensates for all model uncertainties and all bounded disturbances within a particular frequency range. A stability criterion and verifiable bounds on the system signals are derived. Simulations and experimental tests demonstrate the powerful properties of the presented controller.Zusammenfassung: Dieser Beitrag stellt eine adaptive Backsteppingregelung für die Positionsfolge eines Quadrokopters vor. Der Entwurf greift den Ansatz der L1-adaptiven Regelung für nichtlineare Referenzmodelle auf, passt ihn an das Backsteppingschema an und modifiziert ihn dahingehend, so dass der nominale Regler von der Adaption entkoppelt. Der resultierende Regler ist in der Lage alle Modellunsicherheiten und alle begrenzten Stö-rungen innerhalb einer gewissen Frequenz zu kompensieren. Es werden ein Stabilitätskriterium sowie verifizierbare Schranken für die Systemsignale hergeleitet. Simulationen und Experimente zeigen die starken Eigenschaften des vorgestellten Reglers.
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