We address the controller design and the trajectory generation for a quadrotor maneuvering in three dimensions in a tightly constrained setting typical of indoor environments. In such settings, it is necessary to allow for significant excursions of the attitude from the hover state and small angle approximations cannot be justified for the roll and pitch. We develop an algorithm that enables the real-time generation of optimal trajectories through a sequence of 3-D positions and yaw angles, while ensuring safe passage through specified corridors and satisfying constraints on velocities, accelerations and inputs. A nonlinear controller ensures the faithful tracking of these trajectories. Experimental results illustrate the application of the method to fast motion (5–10 body lengths/second) in three-dimensional slalom courses.

Minimum snap trajectory generation and control for quadrotors

From the Publisher:
This graduate text provides an authoritative account of neural network (NN) controllers for robotics and nonlinear systems and gives the first textbook treatment of a general and streamlined design procedure for NN controllers. Stability proofs and performance guarantees are provided which illustrate the superior efficiency of the NN controllers over other design techniques when the system is unknown. New NN properties, such as robustness and passivity are introduced, and new weight tuning algorithms are presented. Neural Network Control of Robot Manipulators and Nonlinear Systems provides a welcome introduction to graduate students, and an invaluable reference to professional engineers and researchers in control systems.

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Neural Network Control of Robot Manipulators and Nonlinear Systems

Provides a summary of recent developments in control of nonholonomic systems. The published literature has grown enormously during the last six years, and it is now possible to give a tutorial presentation of many of these developments. The objective of this article is to provide a unified and accessible presentation, placing the various models, problem formulations, approaches, and results into a proper context. It is hoped that this overview will provide a good introduction to the subject for nonspecialists in the field, while perhaps providing specialists with a better perspective of the field as a whole. The paper is organized as follows: introduction to nonholonomic control systems and where they arise in applications, classification of models of nonholonomic control systems, control problem formulations, motion planning results, stabilization results, and current and future research topics.

Developments in nonholonomic control problems

This article provides a tutorial introduction to modeling, estimation, and control for multirotor aerial vehicles that includes the common four-rotor or quadrotor case.

Multirotor Aerial Vehicles: Modeling, Estimation, and Control of Quadrotor

A class of inherently nonlinear control problems has been identified, the nonlinear features arising directly from physical assumptions about constraints on the motion of a mechanical system. Models are presented for mechanical systems with nonholonomic constraints represented both by differential-algebraic equations and by reduced state equations. Control issues for this class of systems are studied and a number of fundamental results are derived. Although a single equilibrium solution cannot be asymptotically stabilized using continuous state feedback, a general procedure for constructing a piecewise analytic state feedback which achieves the desired result is suggested. >

Control and stabilization of nonholonomic dynamic systems

This paper provides new results for the tracking control of a quadrotor unmanned aerial vehicle (UAV). The UAV has four input degrees of freedom, namely the magnitudes of the four rotor thrusts, that are used to control the six translational and rotational degrees of freedom, and to achieve asymptotic tracking of four outputs, namely, three position variables for the vehicle center of mass and the direction of one vehicle body-fixed axis. A globally defined model of the quadrotor UAV rigid body dynamics is introduced as a basis for the analysis. A nonlinear tracking controller is developed on the special Euclidean group SE(3) and it is shown to have desirable closed loop properties that are almost global. Several numerical examples, including an example in which the quadrotor recovers from being initially upside down, illustrate the versatility of the controller.

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Geometric tracking control of a quadrotor UAV on SE(3)

This paper provides new results for control of complex flight maneuvers for a quadrotor unmanned aerial vehicle (UAV). The flight maneuvers are defined by a concatenation of flight modes or primitives, each of which is achieved by a nonlinear controller that solves an output tracking problem. A mathematical model of the quadrotor UAV rigid body dynamics, defined on the configuration space $\SE$, is introduced as a basis for the analysis. The quadrotor UAV has four input degrees of freedom, namely the magnitudes of the four rotor thrusts; each flight mode is defined by solving an asymptotic optimal tracking problem. Although many flight modes can be studied, we focus on three output tracking problems, namely (1) outputs given by the vehicle attitude, (2) outputs given by the three position variables for the vehicle center of mass, and (3) output given by the three velocity variables for the vehicle center of mass. A nonlinear tracking controller is developed on the special Euclidean group $\SE$ for each flight mode, and the closed loop is shown to have desirable closed loop properties that are almost global in each case. Several numerical examples, including one example in which the quadrotor recovers from being initially upside down and another example that includes switching and transitions between different flight modes, illustrate the versatility and generality of the proposed approach.

Geometric Tracking Control of a Quadrotor UAV on SE(3)

This paper provides nonlinear tracking control systems for a quadrotor unmanned aerial vehicle (UAV) that are robust to bounded uncertainties. A mathematical model of a quadrotor UAV is defined on the special Euclidean group, and nonlinear output-tracking controllers are developed to follow (i) an attitude command, and (ii) a position command for the vehicle center of mass. The controlled system has the desirable properties that the tracking errors are uniformly ultimately bounded, and the size of the ultimate bound can be reduced arbitrarily by control system parameters. Numerical examples illustrating complex maneuvers are provided.

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Nonlinear Robust Tracking Control of a Quadrotor UAV on SE(3)

The control problem of time-optimal, rest-to-rest slewing of a flexible spacecraft through a large angle is considered. The flexible spacecraft is modeled as a linear, elastic, undamped, nongyroscopic system suitable for analysis of planar rotational maneuvers. Minimum-time open-loop planar maneuvers are studied. The control histories are found to be bang-bang with multiple switches in each control variable. The optimal control history is shown to have an important time symmetry property. The switching times, final time, and costates at midmaneuver satisfy a system of nonlinear algebraic equations that can be solved using a homotopy method. An upper bound on attitude error due to control spillover is obtained. This helps to determine, a priori, the number of vibrational modes that need to be actively suppressed at the final time such that a prespecified pointing accuracy is guaranteed after the maneuver has been completed. A time-optimal slewing example is discussed to demonstrate the applicability of the results.

/pdf/planar-time-optimal-rest-to-rest-slewing-maneuvers-of-xkjfwzgl5h.pdf

Planar, time-optimal, rest-to-rest slewing maneuvers of flexible spacecraft

It is well known that three momentum wheel actuators can be used to control the attitude of a rigid spacecraft and that arbitrary reorientation maneuvers of the spacecraft can be accomplished using smooth feedback. If failure of one of the momentum wheel actuators occurs, we demonstrate that two momentum wheel actuators can be used to control the attitude of a rigid spacecraft and that arbitrary reorientation maneuvers of the spacecraft can be accomplished. Although the complete spacecraft equations are not controllable, the spacecraft equations are controllable under the restriction that the total angular momentum vector of the system is zero. The spacecraft dynamics under such a restriction cannot be asymptotically stabilized to any equilibrium attitude using a timeinvariant continuous feedback control law, but discontinuous feedback control strategies are constructed that stabilize any equilibrium attitude of the spacecraft in finite time. Consequently, reorientation of the spacecraft can be accomplished using discontinuous feedback control.

/pdf/attitude-stabilization-of-a-rigid-spacecraft-using-two-3ktpvoc0p7.pdf

N. Harris McClamroch

Papers

Geometric tracking control of a quadrotor UAV on SE(3)

Geometric Tracking Control of a Quadrotor UAV on SE(3)

Nonlinear Robust Tracking Control of a Quadrotor UAV on SE(3)

Planar, time-optimal, rest-to-rest slewing maneuvers of flexible spacecraft

Attitude stabilization of a rigid spacecraft using two momentum wheel actuators