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Geometric Tracking Control of a Quadrotor UAV on SE(3)
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.
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09 May 2011
TL;DR: An algorithm is developed 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.
Abstract: 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.
1,875 citations
TL;DR: In this article, a tutorial for modeling, estimation, and control for multi-rotor aerial vehicles that includes the common four-rotors or quadrotors case is presented.
Abstract: This article provides a tutorial introduction to modeling, estimation, and control for multirotor aerial vehicles that includes the common four-rotor or quadrotor case.
1,241 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
01 Apr 2016
TL;DR: This work presents a method of jointly optimizing polynomial path segments in an unconstrained quadratic program that is numerically stable for high-order polynomials and large numbers of segments, and is easily formulated for efficient sparse computation.
Abstract: We explore the challenges of planning trajectories for quadrotors through cluttered indoor environments. We extend the existing work on polynomial trajectory generation by presenting a method of jointly optimizing polynomial path segments in an unconstrained quadratic program that is numerically stable for high-order polynomials and large numbers of segments, and is easily formulated for efficient sparse computation. We also present a technique for automatically selecting the amount of time allocated to each segment, and hence the quadrotor speeds along the path, as a function of a single parameter determining aggressiveness, subject to actuator constraints. The use of polynomial trajectories, coupled with the differentially flat representation of the quadrotor, eliminates the need for computationally intensive sampling and simulation in the high dimensional state space of the vehicle during motion planning. Our approach generates high-quality trajecrtories much faster than purely sampling-based optimal kinodynamic planning methods, but sacrifices the guarantee of asymptotic convergence to the global optimum that those methods provide. We demonstrate the performance of our algorithm by efficiently generating trajectories through challenging indoor spaces and successfully traversing them at speeds up to 8 m/s. A demonstration of our algorithm and flight performance is available at: http://groups.csail.mit.edu/rrg/quad_polynomial_trajectory_planning.
578 citations
01 Jan 2016
TL;DR: This chapter presents a modular Micro Aerial Vehicle (MAV) simulation framework, which enables a quick start to perform research on MAVs, and is a good starting point to tackle higher level tasks, such as collision avoidance, path planning, and vision based problems, like Simultaneous Localization and Mapping (SLAM), on MAV.
Abstract: In this chapter we present a modular Micro Aerial Vehicle (MAV) simulation framework, which enables a quick start to perform research on MAVs. After reading this chapter, the reader will have a ready to use MAV simulator, including control and state estimation. The simulator was designed in a modular way, such that different controllers and state estimators can be used interchangeably, while incorporating new MAVs is reduced to a few steps. The provided controllers can be adapted to a custom vehicle by only changing a parameter file. Different controllers and state estimators can be compared with the provided evaluation framework. The simulation framework is a good starting point to tackle higher level tasks, such as collision avoidance, path planning, and vision based problems, like Simultaneous Localization and Mapping (SLAM), on MAVs. All components were designed to be analogous to its real world counterparts. This allows the usage of the same controllers and state estimators, including their parameters, in the simulation as on the real MAV.
421 citations
References
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Book•
01 Jan 2003TL;DR: In this paper, the authors propose energy-based methods for stabilizing nonholonomic systems using non-holonomic control theory based on geometric properties of the system's properties. But they do not discuss the energy-independent methods of stabilisation.
Abstract: Introduction.- Mathematical Preliminaries.- Basic Concepts in Geometric Mechanics.- Introduction to Aspects of Geometric Control Theory.- Nonholonomic Mechanics.- Control of Mechanical and Nonholonomic Systems.- Optimal Control.- Stability of Nonholonomic Systems.- Energy-Based Methods for Stabilization.- References.- Index.
1,328 citations
20 Aug 2007
TL;DR: In this paper, a theoretical development is presented, and validated through both thrust test stand measurements and vehicle flight tests using the Stanford Testbed of Autonomous Rotorcraft for Multi-Agent Control (STARMAC) quadrotor helicopter.
Abstract: Quadrotor helicopters are emerging as a popular platform for unmanned aerial vehicle (UAV) research, due to the simplicity of their construction and maintenance, their ability to hover, and their vertical take o and landing (VTOL) capability. Current designs have often considered only nominal operating conditions for vehicle control design. This work seeks to address issues that arise when deviating significantly from the hover flight regime. Aided by well established research for helicopter flight control, three separate aerodynamic eects are investigated as they pertain to quadrotor flight, due to vehicular velocity, angle of attack, and airframe design. They cause moments that aect attitude control, and thrust variation that aects altitude control. Where possible, a theoretical development is first presented, and is then validated through both thrust test stand measurements and vehicle flight tests using the Stanford Testbed of Autonomous Rotorcraft for Multi-Agent Control (STARMAC) quadrotor helicopter. The results enabled improved controller performance.
1,074 citations
Book•
01 Dec 1996TL;DR: In this paper, the authors present a generalization of the Hamilton-Jacobi theory for systems on Lie groups and homogenous spaces, including linear and polynomial control systems with quadratic costs.
Abstract: Introduction Acknowledgments Part I. Reachable Sets and Controllability: 1. Basic formalism and typical problems 2. Orbits of families of vector fields 3. Reachable sets of Lie-determined systems 4. Control affine systems 5. Linear and polynomial control systems 6. Systems on Lie groups and homogenous spaces Part II. Optimal Control Theory: 7. Linear systems with quadratic costs 8. The Riccati equation and quadratic systems 9. Singular linear quadratic problems 10. Time-optimal problems and Fuller's phenomenon 11. The maximum principle 12. Optimal problems on Lie groups 13. Symmetry, integrability and the Hamilton-Jacobi theory 14. Integrable Hamiltonian systems on Lie groups: the elastic problem, its non-Euclidean analogues and the rolling-sphere problem References Index.
1,066 citations
18 Apr 2005
TL;DR: The results of two nonlinear control techniques applied to an autonomous micro helicopter called Quadrotor are presented, a backstepping and a sliding-mode techniques.
Abstract: The latest technological progress in sensors, actuators and energy storage devices enables the developments of miniature VTOL systems. In this paper we present the results of two nonlinear control techniques applied to an autonomous micro helicopter called Quadrotor. A backstepping and a sliding-mode techniques. We performed various simulations in open and closed loop and implemented several experiments on the test-bench to validate the control laws. Finally, we discuss the results of each approach. These developments are part of the OS4 project in our lab.
1,010 citations
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.
982 citations