Attitude stabilization of a VTOL quadrotor aircraft
TL;DR: A new quaternion-based feedback control scheme for exponential attitude stabilization of a four-rotor vertical takeoff and landing aerial robot known as a quadrotor aircraft is proposed and the model-independent PD controller, without compensation of the Coriolis and gyroscopic torques, provides asymptotic stability for the problem.
Abstract: In this paper, we propose a new quaternion-based feedback control scheme for exponential attitude stabilization of a four-rotor vertical takeoff and landing aerial robot known as a quadrotor aircraft. The proposed controller is based upon the compensation of the Coriolis and gyroscopic torques and the use of a PD/sup 2/ feedback structure, where the proportional action is in terms of the vector quaternion and the two derivative actions are in terms of the airframe angular velocity and the vector quaternion velocity. We also show that the model-independent PD controller, where the proportional action is in terms of the vector-quaternion and the derivative action is in terms of the airframe angular velocity, without compensation of the Coriolis and gyroscopic torques, provides asymptotic stability for our problem. The proposed controller as well as some other controllers have been tested experimentally on a small-scale quadrotor aircraft.
Citations
More filters
TL;DR: An observer on SO(3), termed the explicit complementary filter, that requires only accelerometer and gyro outputs; is suitable for implementation on embedded hardware; and provides good attitude estimates as well as estimating the gyro biases online.
Abstract: This paper considers the problem of obtaining good attitude estimates from measurements obtained from typical low cost inertial measurement units. The outputs of such systems are characterized by high noise levels and time varying additive biases. We formulate the filtering problem as deterministic observer kinematics posed directly on the special orthogonal group SO (3) driven by reconstructed attitude and angular velocity measurements. Lyapunov analysis results for the proposed observers are derived that ensure almost global stability of the observer error. The approach taken leads to an observer that we term the direct complementary filter. By exploiting the geometry of the special orthogonal group a related observer, termed the passive complementary filter, is derived that decouples the gyro measurements from the reconstructed attitude in the observer inputs. Both the direct and passive filters can be extended to estimate gyro bias online. The passive filter is further developed to provide a formulation in terms of the measurement error that avoids any algebraic reconstruction of the attitude. This leads to an observer on SO(3), termed the explicit complementary filter, that requires only accelerometer and gyro outputs; is suitable for implementation on embedded hardware; and provides good attitude estimates as well as estimating the gyro biases online. The performance of the observers are demonstrated with a set of experiments performed on a robotic test-bed and a radio controlled unmanned aerial vehicle.
1,581 citations
01 Dec 2010
TL;DR: New results for the tracking control of a quadrotor unmanned aerial vehicle (UAV) are provided and a nonlinear tracking controller is developed on the special Euclidean group SE(3), shown to have desirable closed loop properties that are almost global.
Abstract: 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.
827 citations
Cites background from "Attitude stabilization of a VTOL qu..."
...All of these assumptions are common [19], [4], and the presented control system can readily be extended to include linear rotor dynamics studied in [11]....
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Posted Content•
10 Mar 2010
TL;DR: In this article, a nonlinear tracking controller is developed on the special Euclidean group for each flight mode, and the closed loop is shown to have desirable closed loop properties that are almost global in each case.
Abstract: 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.
814 citations
TL;DR: To achieve predefined time-varying formations, formation protocols are presented for UAV swarm systems first, where the velocities of UAVs can be different when achieving formations, and consensus-based approaches are applied to deal with the time-Varying formation control problems.
Abstract: Formation control analysis and design problems for unmanned aerial vehicle (UAV) swarm systems to achieve time-varying formations are investigated. To achieve predefined time-varying formations, formation protocols are presented for UAV swarm systems first, where the velocities of UAVs can be different when achieving formations. Then, consensus-based approaches are applied to deal with the time-varying formation control problems for UAV swarm systems. Necessary and sufficient conditions for UAV swarm systems to achieve time-varying formations are proposed. An explicit expression of the time-varying formation center function is derived. In addition, a procedure to design the protocol for UAV swarm systems to achieve time-varying formations is given. Finally, a quadrotor formation platform, which consists of five quadrotors is introduced. Theoretical results obtained in this brief are validated on the quardrotor formation platform, and outdoor experimental results are presented.
705 citations
Additional excerpts
...controlled by PD controllers shown in [43]....
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TL;DR: In this paper, two types of nonlinear controllers for an autonomous quadrotor helicopter are presented: a feedback linearization controller and an adaptive sliding mode controller using input augmentation in order to account for the underactuated property of the helicopter, sensor noise, and uncertainty.
Abstract: This paper presents two types of nonlinear controllers for an autonomous quadrotor helicopter. One type, a feedback linearization controller involves high-order derivative terms and turns out to be quite sensitive to sensor noise as well as modeling uncertainty. The second type involves a new approach to an adaptive sliding mode controller using input augmentation in order to account for the underactuated property of the helicopter, sensor noise, and uncertainty without using control inputs of large magnitude. The sliding mode controller performs very well under noisy conditions, and adaptation can effectively estimate uncertainty such as ground effects.
637 citations
Cites methods from "Attitude stabilization of a VTOL qu..."
...To deal with this system, many modeling approaches have been presented [1,2] and various control methods proposed [3-17]....
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...A quaternion-based feedback controller for attitude stabilization was shown in [10]....
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References
More filters
Book•
01 Jan 1989
TL;DR: This self-contained introduction to practical robot kinematics and dynamics includes a comprehensive treatment of robot control, providing background material on terminology and linear transformations and examples illustrating all aspects of the theory and problems.
Abstract: From the Publisher:
This self-contained introduction to practical robot kinematics and dynamics includes a comprehensive treatment of robot control. Provides background material on terminology and linear transformations, followed by coverage of kinematics and inverse kinematics, dynamics, manipulator control, robust control, force control, use of feedback in nonlinear systems, and adaptive control. Each topic is supported by examples of specific applications. Derivations and proofs are included in many cases. Includes many worked examples, examples illustrating all aspects of the theory, and problems.
3,736 citations
"Attitude stabilization of a VTOL qu..." refers methods in this paper
...This drawback can be avoided by using the four-parameter description of the orientation called the quaternion representation [6]‐[9], [17], which is based upon the fact that any rotation of a rigid body can by described by a single rotation about a fixed axis [ 15 ]....
[...]
...The rotation matrix is related to the quaternion through the Rodriguez formula [5], [ 15 ], and an algorithm for the quaternion extraction is presented in [9]....
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TL;DR: In this paper, the first comprehensive presentation of data, theory, and practice in attitude analysis is presented, including orthographic globe projections to eliminate confusion in vector drawings and a presentation of new geometrical procedures for mission analysis and attitude accuracy studies which can eliminate many complex simulations.
Abstract: This classic book is the first comprehensive presentation of data, theory, and practice in attitude analysis. It was written by 33 senior technical staff members in the Spacecraft Attitude Department of the Computer Sciences Corporation and incorporates their experience in supporting more than 30 space missions. Because of the extensive cross-references, complete index, and 13 technical appendices, this book can be either a self teaching text, or a reference handbook. Among its unique features are orthographic globe projections to eliminate confusion in vector drawings; discussions of common data anomalies, data validation, attitude hardware, and associated mathematical models; and a presentation of new geometrical procedures for mission analysis and attitude accuracy studies which can eliminate many complex simulations.
2,124 citations
"Attitude stabilization of a VTOL qu..." refers result in this paper
...As shown in [ 18 ], this can be achieved as follows:...
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Book•
01 Jan 1986
TL;DR: In this article, the effect of internal energy dissipation on the Directional Stability of Spinning Bodies was investigated in the context of gyroscope-based spin stabilization in Orbit and dual-stabilization in Orbit.
Abstract: Introduction Rotational Kinematics Attitude Motion Equations Attitude Dynamics of a Rigid Body Effect of Internal Energy Dissipation on the Directional Stability of Spinning Bodies Directional Stability of Multispin Vehicles Effect of Internal Energy Dissipation on the Directional Stability of Gyrostats Spacecraft Torques Gravitational Stabilization Spin Stabilization in Orbit Dual-Stabilization in Orbit: Gyrostats and Bias Momentum Satellites Appendixes References Index.
1,499 citations
TL;DR: In this article, a general framework for the analysis of the attitude tracking control problem for a rigid body is presented and a large family of globally stable control laws are obtained by using the globally nonsingular unit quaternion representation in a Lyapunov function candidate whose form is motivated by the consideration of the total energy of the rigid body.
Abstract: A general framework for the analysis of the attitude tracking control problem for a rigid body is presented. A large family of globally stable control laws is obtained by using the globally nonsingular unit quaternion representation in a Lyapunov function candidate whose form is motivated by the consideration of the total energy of the rigid body. The controllers share the common structure of a proportional-derivative feedback plus some feedforward which can be zero (the model-independent case), the Coriolis torque compensation, or an adaptive compensation. These controller structures are compared in terms of the requirement on the a priori model information, guaranteed transient performance, and robustness. The global stability of the Luh-Walker-Paul robot end-effector controller is also analyzed in this framework. >
1,000 citations
Book•
01 Jan 1986
TL;DR: This text provides information necessary to analyze the performance of an existing helicopter or to participate in the design of a new helicopter, including the derivation of the theory behind the various methods of analysis, appropriate experimental data to correlate and supplement the theory, and charts that permit rapid analysis.
Abstract: This text provides, for both students and practicing helicopter aerodynamicists, the information necessary to analyze the performance of an existing helicopter or to participate in the design of a new helicopter. The information includes the derivation of the theory behind the various methods of analysis, appropriate experimental data to correlate and supplement the theory, and charts that permit rapid analysis. A special attempt is made to relate helicopter aerodynamics to airplane aerodynamics for those making the transition. The first six chapters give various aspects of helicopter performance. Chapters 7, 8 and 9 cover stability and control. The last chapter presents the tradeoff considerations that the engineer must face during the preliminary design phase to ensure both good performance and good flying qualities.
632 citations