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Control of Underactuated Mechanical Systems with two Degrees of Freedom and Symmetry
"... In this paper, we consider a special class of underactuated mechanical systems with two degrees of freedom and symmetry. By symmetry, we mean the inertia matrix of the system is independent of the unactuated degree of freedom. We show that there exists a natural global change of coordinates obtained ..."
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Cited by 68 (9 self)
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In this paper, we consider a special class of underactuated mechanical systems with two degrees of freedom and symmetry. By symmetry, we mean the inertia matrix of the system is independent of the unactuated degree of freedom. We show that there exists a natural global change of coordinates obtained from the Lagrangian of the system that transforms the system into a partially linear cascade nonlinear system that is strict feedback. The nonlinear part of this system is nona#ne in control and this highly complicates control design for the system. We provide conditions under which this nonlinear subsystem can be globally stabilized and give globally stabilizing control laws for it. The strict feedback structure of the system in new coordinates allows us to obtain a globally stabilizing control law for the composite system using standard backstepping. We apply our result to global asymptotic stabilization of the Acrobot.
Adaptive position tracking of vtol uavs
 in Proc. 48th IEEE Conf. Decision Control and 28th Chin. Control Conf
, 2009
"... Abstract—An adaptive positiontracking control scheme is proposed for vertical takeoff and landing (VTOL) unmanned airborne vehicles (UAVs) for a set of bounded external disturbances. The control design is achieved in three main steps. The first step is devoted to the design of an a priori bounde ..."
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Cited by 16 (4 self)
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Abstract—An adaptive positiontracking control scheme is proposed for vertical takeoff and landing (VTOL) unmanned airborne vehicles (UAVs) for a set of bounded external disturbances. The control design is achieved in three main steps. The first step is devoted to the design of an a priori bounded linear acceleration driving the translational dynamics toward the desired trajectory. In the second step, we extract the required a priori bounded thrust and the desired attitude, in terms of unit quaternion, from the desired acceleration derived in the first step. In the last step, we design the required torque for the rotational dynamics, allowing the system’s attitude to be driven toward the desired attitude obtained at the second step. Two control laws for the system control torque are rigorously designed. The first control law ensures that the positiontracking objective is satisfied for any initial conditions, whereas the second ensures that the tracking objective is satisfied for a set of initial conditions, which is dependant on the control gains. The latter case is included, since it is less complicated than the former control law and may be advantageous from a practical point of view. Finally, simulation results are provided to illustrate the effectiveness of the proposed control strategy. Index Terms—Adaptive control, unmanned airborne vehicle (UAV), vertical takeoff and landing (VTOL). I.
Homogeneous stabilization of the extended chained form system
 Proceedings of the 15th IFAC World Congres on Automatic Control
, 2002
"... Abstract: A controller is presented for point stabilization of the extended chained form system. The extended chained form system can not be stabilized by means of continuous purestate feedback. Moreover, it can not be exponentially stabilized by smooth feedback, since the linearization around equi ..."
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Abstract: A controller is presented for point stabilization of the extended chained form system. The extended chained form system can not be stabilized by means of continuous purestate feedback. Moreover, it can not be exponentially stabilized by smooth feedback, since the linearization around equilibrium points is uncontrollable. In this paper, a controller is given that ρexponentially stabilizes the system. The controller is derived by using a combined averaging technique for homogeneous systems and a backstepping approach. The controller is illustrated in a benchmark example by application to the V/STOL aircraft without gravity.
Nonlinear and Cooperative Control of Multiple Hovercraft with Input Constraints
"... In this paper, we introduce an approach for distributed nonlinear control of multiple hovercrafttype underactuated vehicles with bounded and unidirectional inputs. First, a bounded nonlinear controller is given for stabilization and tracking of a single vehicle, using cascade backstepping according ..."
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In this paper, we introduce an approach for distributed nonlinear control of multiple hovercrafttype underactuated vehicles with bounded and unidirectional inputs. First, a bounded nonlinear controller is given for stabilization and tracking of a single vehicle, using cascade backstepping according to the method in OlfatiSaber (2002). Then, this controller is combined with a distributed gradientbased control for multivehicle formation stabilization using formation potential functions introduced in OlfatiSaber and Murray (2002). The vehicles are used in the Caltech MultiVehicle Wireless Testbed (MVWT). We provide simulation results for stabilization and tracking of a single vehicle and stabilization of a sixvehicle formation, and demonstrate that in all cases the control bounds are satisfied. Based on the simulation results, the obtained controllers demonstrate rather aggressive behaviors as the inputs are close to the control bounds initially.
Commande par retour d’état pour des engins volants de type VTOL: résultats et perspectives
, 2009
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Path Following for the PVTOL: A Set Stabilization Approach
"... Abstract—This article proposes a path following controller that regulates the center of mass of the planar vertical takeoff and landing aircraft (PVTOL) to the unit circle and makes the aircraft traverse the circle in a desired direction. A static feedback controller is designed using the ideas of ..."
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Abstract—This article proposes a path following controller that regulates the center of mass of the planar vertical takeoff and landing aircraft (PVTOL) to the unit circle and makes the aircraft traverse the circle in a desired direction. A static feedback controller is designed using the ideas of transverse feedback linearization, finite time stabilization and virtual constraints. No time parameterization is given to the desired motion on the unit circle. Instead, our approach relies on the nested stabilization of two sets on which the dynamics of the PVTOL exhibit desirable behavior.
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"... le Institut Supérieur de l’Aéronautique et de l’Espace (ISAE) Henry de PLINVAL mercredi 15 janvier 2014 Commande référencée vision pour drones à décollages et atterrissages verticaux ..."
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le Institut Supérieur de l’Aéronautique et de l’Espace (ISAE) Henry de PLINVAL mercredi 15 janvier 2014 Commande référencée vision pour drones à décollages et atterrissages verticaux
CONTROL ALGORITHMS FOR GROUPS OF KINEMATIC UNICYCLE AND SKIDSTEERING MOBILE ROBOTS WITH RESTRICTED INPUTS
"... Abstract. The paper presents analytical and practical studies concerning the control problems of a group of Wheeled Mobile Robots (WMRs) subject to physical constraints. Firstly, controllers for achieving trajectory tracking for kinematic unicyclelike and skidsteering mobile robots with restricted ..."
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Abstract. The paper presents analytical and practical studies concerning the control problems of a group of Wheeled Mobile Robots (WMRs) subject to physical constraints. Firstly, controllers for achieving trajectory tracking for kinematic unicyclelike and skidsteering mobile robots with restricted control inputs are established. Next, the underlying tracking controllers are applied for group control under the condition of actuator constraints. In particular we are developing control strategies for establishing rigid and convoylike formations for vehicles with bounded inputs. The group control approach is based on the concepts of virtual robot and virtual formation. The proposed controllers employ smooth bounded functions that can easily be realized. The performance of the resulting controllers are demonstrated by means of numerical and simulation results.
OUTPUTFEEDBACK GLOBAL STABILIZATION OF UNCOUPLED PVTOL AIRCRAFT WITH BOUNDED INPUTS
"... An outputfeedback scheme for the global stabilization of uncoupled PVTOL aircraft with bounded inputs is proposed. The control objective is achieved avoiding input saturation and through the exclusive consideration of system positions in the feedback. To cope with the lack of velocity measurements, ..."
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An outputfeedback scheme for the global stabilization of uncoupled PVTOL aircraft with bounded inputs is proposed. The control objective is achieved avoiding input saturation and through the exclusive consideration of system positions in the feedback. To cope with the lack of velocity measurements, the proposed algorithm involves a finitetime observer. With respect to previous approaches, the developed finitetimeobserverbased scheme guarantees the global stabilization objective disregarding velocity measurements in a bounded input context. Simulation results corroborate the analytical developments. Key words Global stabilization, output feedback, PVTOL aircraft, bounded inputs, finitetime observers 1
Cascade Normal Forms for Underactuated Mechanical Systems
"... In this paper, we introduce cascade normal forms for underactuated mechanical systems that are convenient for control design. These normal forms are partially linear which results from a wellknown fact that underactuated systems can be partially linearized using a change of control [12]. The diffic ..."
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In this paper, we introduce cascade normal forms for underactuated mechanical systems that are convenient for control design. These normal forms are partially linear which results from a wellknown fact that underactuated systems can be partially linearized using a change of control [12]. The difficulty arises when the new control appears both in the linear and nonlinear subsystems. We introduce a method for decoupling these two subsystems by applying a change of coordinates that transforms the dynamics of the system into a cascade normal form with the property that control of the overall system reduces to control of its nonlinear subsystem. Under a symmetry condition on the inertia matrix of the system, this transformation can be obtained explicitly from the Lagrangian. This eventually leads to classification of underactuated systems. We provide several applications and two detailed examples of complex underactuated systems, namely, the Acrobot and the Rotating Pendulum. 1