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A yaw angle, different from zero, introduces highly nonlinear couplings in the rotational and translational quadrotor dynamics, implying undesirable motions. This argument has motivated that the position control problem of quadrotors is studied generally regulating yaw at zero. However, zeroing yaw limits the maneuverability of underactuated quadrotors because yaw is one of the four actuated motions. In this paper, the simultaneous tracking of position and time-varying heading is proposed, based on an integral sliding mode control with a quaternion-based sliding surface. An exponential tracking with chattering-free is obtained without requiring any knowledge of the dynamic model or its parameters for implementation. Since a linear invariant orientation error manifold is enforced for all time, a time-varying gain is introduced for a well-posed finite time convergence, which is useful not only to realize the virtual position control scheme, due to underactuation, but also to guarantee a desired contact in a given point at a given desired contact time for the yaw motion. Illustrative applications are explored in a simulation study which shows the viability and versatility of position–yaw tracking in the surveillance of a field-of-view (FoV) target, aerial screw driver, and aerial grasping.

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Aiming at designing a robust controller to withstand a class of continuous, but not necessarily differentiable, disturbances, such as Hölder type, a continuous and chattering‐free sliding mode control is proposed. The key idea is a judicious synthesis of a resetting memory principle for the differintegral operators to show that a sliding mode is induced, and sustained, in finite‐time, to guarantee asymptotic tracking. The closed‐loop system achieves exact rejection of Hölder disturbances even in case of uncertain flow, but assuming certain knowledge of the input matrix. Furthermore, it is shown that our methodology generalizes continuous high‐oder sliding mode schemes by using an integral action of fractional‐order. A representative simulation study is discussed to show the feasibility of the proposal.

Exploiting algebraic and topological properties of differintegral operators as well as a proposed principle of dynamic memory resetting, a uniform continuous sliding mode controller for a general class of integer order affine non-linear systems is proposed. The controller rejects a wide class of disturbances, enforcing in finite-time a sliding regime without chattering. Such disturbance is of Hölder type that is not necessarily differentiable in the usual (integer order) sense. The control signal is uniformly continuous in contrast to the classical (integer order) discontinuous scheme that has been proposed for both fractional and integer order systems. The proposed principle of dynamic memory resetting allows demonstrating robustness as well as: (i) finite-time convergence of the sliding manifold, (ii) asymptotic convergence of tracking errors, and (iii) exact disturbance observation. The validity of the proposed scheme is discussed in a representative numerical study.

No abstract

Quadrotors are highly maneuverable light weight drones, which are prone to aerodynamic disturbances, vibrations and uncertainties. These factors stand for a problem that demands robust control laws. For position tracking, the control problem is exacerbated because the plant is underactuated in the coordinates of interest, requiring a high performance attitude tracking to resolve underactuation. In this paper, a novel fractional-order controller is proposed by considering a well-posed map that relates the position/yaw control to desired attitude references. The attitude control is continuous and enforces and sustains a sliding motion in finite-time for exponential convergence of the tracking errors to fulfill a "virtual" position controller. The resulting closed-loop system is robust against continuous disturbances that are not necessarily differentiable in the conventional sense. A numerical study based on simulations is presented to analyze the advantages of the fractional actions to design a physically realizable controller, and experiments are discussed to expose the reliability of the proposed fractional scheme implemented in an 'X' configuration quadrotor.

Dynamic models approximate physical phenomena to certain extent and ideal controllers are proposed. Nevertheless, when system specifications crave for better performance, additional robust controllers are considered. In this sense, a robust controller is proposed in this paper, which accounts for a general class of fractional-order systems, in order to compensate for matched and mismatched disturbances. The Mittag-Leffler stability of the solution of the closed-loop system is demonstrated for a class of fractional-order systems subject to non-smooth effects and control feedback. Numerical simulations are conducted to highlight the reliability of the proposed scheme.