Robust global exponential stabilization on the n-dimensional sphere with applications to trajectory tracking for quadrotors

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

Hybrid Control for Robust and Global Tracking on Smooth Manifolds

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

Hybrid Planning and Control for Multiple Fixed-Wing Aircraft under Input Constraints

This paper presents a novel hybrid control protocol for de-conflicting multiple vehicles with constraints on control inputs. We consider turning rate and linear speed constraints to represent fixed-wing or car-like vehicles. A set of state-feedback controllers along with a state-dependent switching logic are synthesized in a hybrid system to generate collision-free trajectories that converge to the desired destinations of the vehicles. The switching law is designed so that the safety can be guaranteed while no Zeno behavior can occur. A novel temporary goal assignment technique is also designed to guarantee convergence. We analyze the individual modes for safety and the closed-loop hybrid system for convergence. The theoretical developments are demonstrated via simulation results.Comment: Best Student Paper Finalist, AIAA-SciTech GNC Conference, 201

Analysis and design of event-Triggered control algorithms using hybrid systems tools

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

Analysis and design of event-Triggered control algorithms using hybrid systems tools

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