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In this paper, we present a hybrid control strategy that allows for global asymptotic tracking of reference trajectories evolving on smooth manifolds, with nominal robustness. Two different versions of the hybrid controller are presented: One which allows for discontinuities of the plant input and a second one that removes the discontinuities via dynamic extension. By taking an exosystem approach, we provide a general construction of a hybrid controller that guarantees global asymptotic stability of the zero tracking error set. The proposed construction relies on the existence of proper indicators and a transport map-like function for the given manifold. We provide a construction of these functions for the case where each chart in a smooth atlas for the manifold maps its domain onto the Euclidean space. We also provide conditions for exponential convergence to the zero tracking error set. To illustrate these properties, the proposed controller is exercised on three different compact manifolds-the two-dimensional sphere, the unit-quaternion group, and the special orthogonal group of order three- A nd further applied to the problems of obstacle avoidance in the plane and global synchronization on the circle.

In this paper, we design a hybrid controller that globally exponentially stabilizes a system evolving on the n-dimensional sphere, denoted by Sn. This hybrid controller is induced by a “synergistic” collection of potential functions on Sn. We propose a particular construction of this class of functions that generates flows along geodesics of the sphere, providing convergence to the desired reference with minimal path length. We show that the proposed strategy is suitable to the exponential stabilization of a quadrotor vehicle.

In this paper, we employ a hybrid feedback control strategy to globally asymptotically stabilize a setpoint on a smooth compact manifold without boundary satisfying the following: There exists a finite maximal atlas such that the desired setpoint belongs to each chart of the atlas. The proposed hybrid controller includes a proportional-derivative (PD) action during flows and, at jumps, uses hysteresis to switch between local coordinate charts to stabilize the desired setpoint robustly with respect to exogenous disturbances. We show that the proposed controller can be used for attitude stabilization of a rigid body and we illustrate the behavior of the closed-loop system via simulation results.

This paper proposes a general framework for analyzing continuous-Time systems controlled by event-Triggered algorithms. Closed-loop systems resulting from using both static and dynamic output (or state) feedback laws that are implemented via asynchronous event-Triggered techniques are modeled as hybrid systems given in terms of hybrid inclusions and studied using recently developed tools for robust stability. Properties of the proposed models, including stability of compact sets, robustness, and Zeno behavior of solutions are addressed. The framework and results are illustrated in several event-Triggered strategies available in the literature.

In this paper, we design a hybrid controller based on the concept of centrally synergistic potential functions on the n-dimensional sphere to achieve global tracking of an attitude reference as well as exponential stabilization of the position and velocity of a vectored-thrust vehicle. The proposed hybrid attitude controller renders a partial attitude reference globally exponentially stable, and the full attitude reference globally attractive and locally exponentially stable. This controller is then combined with a position controller for the quadrotor vehicle for tracking of a given reference. Simulation results are provided so as to demonstrate the performance of the proposed controller.

Summary In this paper, we address the problem of designing a control law based on sensor measurements that provides global asymptotic stabilization to a reference trajectory defined on the SE(3)×R6. The proposed control law is a function of the angular velocity, of vector measurements characterizing the position of some given landmarks, and of their rate of change. We provide sufficient conditions for the existence of synergistic potential functions on SO(3) which are pivotal in the generation of a suitable hybrid control law. We also provide sufficient conditions on the geometry of the landmarks to solve the given problem. Finally, the proposed solution is simulated and compared with a continuous feedback control law.

In this paper, we tackle the problem of trajectory tracking for a particular class of underactuated vehicles with full torque actuation and a single force direction (thrust), which is fixed relative to a body attached frame. Additionally, we consider that thrust reversal is not available. Under some given assumptions, the control law that we propose is able to track a smooth reference position trajectory while minimizing the angular distance to a desired orientation. This objective is achieved robustly, with respect to bounded state disturbances, and globally, in the sense that it is achieved regardless of the initial state of the vehicle. The proposed controller is tested in an experimental setup, using a small scale quadrotor vehicle and a motion capture system.

In this paper, we show that the existence of centrally synergistic potential functions on the n-dimensional sphere, denoted by Sn, is a sufficient condition for the global asymptotic stabilization of a point in Sn. Additionally, if these functions decrease exponentially fast during flows and are bounded from above and from below by some polynomial function of the tracking error, then the reference point can be globally exponentially stabilized. We construct two kinds of centrally synergistic functions: the first kind consists of a finite family of potential functions on Sn while the second kind consists of an uncountable number of potential functions on Sn. While the former generates a simpler jump logic, the latter is optimal in the sense that it generates flows with minimal length.

In this paper, we devise a controller that achieves global uniform exponential stabilization of linear systems while avoiding singular input constraints, that is, the proposed controller never crosses a given input value g. We show that it is possible to solve this problem using two linear controllers and an appropriate switching logic, which leads to a hybrid controller.

In this paper, we tackle the problem of trajectory tracking for a particular class of underactuated vehicles with full torque actuation and a single force direction (thrust) that is fixed relative to a body attached frame. Additionally, we consider that thrust reversal is not available. We present the design of a hybrid controller that, under some given assumptions, is able to globally asymptotically stabilize the vehicle to a reference position trajectory while minimizing the angle to the desired attitude trajectory. This objective is achieved robustly and globally, in the sense that small perturbations do not lead to instability and it is achieved regardless of the initial state of the vehicle. The algorithm is tested in a experimental setup, using a small scale quadrotor vehicle and the VICON motion capture system.

In this paper, we address the problem of trajectory tracking for a class of underactuated vehicles with full torque actuation and only one dimensional force actuation (thrust). For this class of vehicles, the desired thrust is defined by a saturated control law that achieves global asymptotic stabilization of the position tracking error. The proposed control law also assures that the third component of the angular velocity is regulated to zero. To accomplish this task we propose a hybrid controller that is designed using backstepping techniques and recent developments on synergistic Lyapunov functions. Simulations validating the results are also provided. © 2013 AACC American Automatic Control Council.

This paper addresses the problem of trajectory tracking for a quadcopter subject to parametric uncertainties and disturbances. Using the backstepping technique and ignoring parametric uncertainties and disturbances, a nominal controller is proposed for the quadcopter. In order to ensure that the controller is adaptive to parametric uncertainties (i.e. unknown but constant mass and tensor of inertia) and external disturbances, an exponentially stable estimator is designed based on the Kalman–Bucy filter. The closed-loop system resulting from the interconnection of the plant, the controller, and the estimator is such that the backstepping error is uniformly ultimately bounded. Furthermore, simulation and experimental results are presented, validating the stability and robustness properties of the proposed control strategy. [ABSTRACT FROM AUTHOR]