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21
Controlled Lagrangians and the stabilization of mechanical systems I: the first matching theorem
 IEEE Transactions on Automatic Control
, 2000
"... Abstract—Weextend the method of controlled Lagrangians (CL) to include potential shaping, which achieves complete statespace asymptotic stabilization of mechanical systems. The CL method deals with mechanical systems with symmetry and provides symmetrypreserving kinetic shaping and feedbackcontro ..."
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Cited by 74 (27 self)
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Abstract—Weextend the method of controlled Lagrangians (CL) to include potential shaping, which achieves complete statespace asymptotic stabilization of mechanical systems. The CL method deals with mechanical systems with symmetry and provides symmetrypreserving kinetic shaping and feedbackcontrolled dissipation for statespace stabilization in all but the symmetry variables. Potential shaping complements the kinetic shaping by breaking symmetry and stabilizing the remaining state variables. The approach also extends the method of controlled Lagrangians to include a class of mechanical systems without symmetry such as the inverted pendulum on a cart that travels along an incline. I.
A Decentralized Approach to Formation Maneuvers
 IEEE Transactions on Robotics and Automation
, 2003
"... Abstract—This paper presents a behaviorbased approach to formation maneuvers for groups of mobile robots. Complex formation maneuvers are decomposed into a sequence of maneuvers between formation patterns. The paper presents three formation control strategies. The first strategy uses relative posit ..."
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Cited by 62 (0 self)
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Abstract—This paper presents a behaviorbased approach to formation maneuvers for groups of mobile robots. Complex formation maneuvers are decomposed into a sequence of maneuvers between formation patterns. The paper presents three formation control strategies. The first strategy uses relative position information configured in a bidirectional ring topology to maintain the formation. The second strategy injects interrobot damping via passivity techniques. The third strategy accounts for actuator saturation. Hardware results demonstrate the effectiveness of the proposed control strategies. Index Terms—Behavioral methods, coordinated control, formations, mobile robots, passivity.
A Decentralized Approach To Elementary Formation Maneuvers
"... This paper presents the coupled dynamics approach to executing Elementary Formation Maneuvers (EFM) for Hilaretype mobile robots. The concept of an EFM is presented. It is then shown that each of these EFMs posses a common mathematical structure and thus may be executed by the same type of robot co ..."
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Cited by 35 (4 self)
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This paper presents the coupled dynamics approach to executing Elementary Formation Maneuvers (EFM) for Hilaretype mobile robots. The concept of an EFM is presented. It is then shown that each of these EFMs posses a common mathematical structure and thus may be executed by the same type of robot control. We present three different EFM controls in this paper. The first puts feedback on the relative motion and the global motion of each robot. The second control adds interrobot damping. And the third control uses saturated inputs on the relative motion and the global motion of each robot. We present simulation and hardware results for each of these controls. I. Introduction Cooperative robots can often be used to perform tasks that are too difficult for a single robot to perform alone. For example a group of robots can be used for moving large awkward objects [1], [2] or for moving a large number of objects [3]. In addition groups of robots can be used for terrain model acquisition [3]...
Further Passivity Results for the Attitude Control Problem
, 1998
"... In this paper we establish passivity for the system which describes the attitude motion of a rigid body in terms of minimal threedimensional kinematic parameters. In particular, we show that linear, asymptotically stabilizing controllers and control laws without angular velocity measurements follow ..."
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Cited by 11 (2 self)
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In this paper we establish passivity for the system which describes the attitude motion of a rigid body in terms of minimal threedimensional kinematic parameters. In particular, we show that linear, asymptotically stabilizing controllers and control laws without angular velocity measurements follow naturally from these passivity properties. The results of this paper extend similar results for the case of the (nonminimal) Euler parameters. Keywords Attitude control, passivity, stabilization, CayleyRodrigues parameters, Modified Rodrigues parameters. I. Introduction Recently it has been shown [1],[2],[3] that there exist linear asymptotically stabilizing control laws for the attitude motion of a rigid body using minimal, threedimensional parameterizations for the kinematics. In [1] linear control laws were derived in terms of the classical CayleyRodrigues parameters [4] and the nonstandard Modified Rodrigues parameters [1],[4] In the present paper we show that the existence of l...
PassivityBased Controllers for the Stabilization of DCtoDC Power Converters
"... Passivitybased feedback controllers are derived for the indirect stabilization of the average output voltage in PulseWidthModulation (PWM) controlled dctodc power converters of the "boost", "buckboost" and "buck" types. The controller design is carried out on the basis of well known aver ..."
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Cited by 8 (0 self)
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Passivitybased feedback controllers are derived for the indirect stabilization of the average output voltage in PulseWidthModulation (PWM) controlled dctodc power converters of the "boost", "buckboost" and "buck" types. The controller design is carried out on the basis of well known average PWM models of such circuits. These models are shown to be EulerLagrange systems corresponding to a suitable set of average EulerLagrange parameters. The proposed controllers are based on an "energy shaping plus damping injection" scheme, achievable through nonlinear dynamical feedback. The derived duty ratio synthesis policies are tested, via computer simulations, on a stochastically perturbed switched converter model. Keywords : DCtoDC Power Converters, Passivitybased control, EulerLagrange systems. This work was supported by the Consejo de Desarrollo Cient'ifico, Human'istico and Tecnol'ogico of the Universidad de Los Andes, under Research Grant I45694, and by The Commi...
On Global Output Feedback Regulation of EulerLagrange Systems with Bounded Inputs
"... In this short paper we identify a class of EulerLagrange systems with bounded inputs that can be globally asymptotically stabilized via dynamic output feedback. In particular we prove that if the system is fully actuated and the forces due to the potential field can be "dominated" by the constrained ..."
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Cited by 5 (0 self)
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In this short paper we identify a class of EulerLagrange systems with bounded inputs that can be globally asymptotically stabilized via dynamic output feedback. In particular we prove that if the system is fully actuated and the forces due to the potential field can be "dominated" by the constrained control signals then global output feedback regulation is still possible incorporating some suitable saturation functions in the controller. I. Introduction It is well known that in EulerLagrange (EL) systems the number and stability properties of the equilibria are univocally defined by its potential energy and dissipation functions, see e.g., [1]. This fundamental feature is at the core of passivity based control of EL systems, which hinges upon the (physically appealing principles) of shaping the systems energy and injection of the required damping. These ideas though well known in mechanics, were first introduced in control in the seminal paper [2] and rigorously articulated in [...
A BehaviorBased Approach to Multiple Spacecraft Formation Flying
, 2000
"... of a dissertation submitted by Jonathan R. T. Lawton This dissertation has been read by each member of the following graduate committee and by majority vote has been found to be satisfactory. ..."
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Cited by 4 (1 self)
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of a dissertation submitted by Jonathan R. T. Lawton This dissertation has been read by each member of the following graduate committee and by majority vote has been found to be satisfactory.
Creating Artificial Damping By Means Of Damping Injection
 in Proceedings of the ASME Dynamic Systems and Control Division
, 1996
"... This paper presents a way to design a "physical controller" for a robot which has to interact with the environment. Such systems need artificial damping in order to achieve proper interactive performances. A method of creating extra damping without the need to measure velocities will be presented. ..."
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Cited by 2 (2 self)
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This paper presents a way to design a "physical controller" for a robot which has to interact with the environment. Such systems need artificial damping in order to achieve proper interactive performances. A method of creating extra damping without the need to measure velocities will be presented. 1 Introduction Most of the tasks that robotic manipulators have to perform are subjected to interaction with the environment. Interaction is characterized by the exchange of energy between the robot and the environment which can be viewed as two interactive subsystems. It is known in physics and well represented in the bondgraph methodology (Paynter 1960) that this energetic interaction is characterized by a bidirectional signal exchange, and therefore both subsystems influence the other's behavior. For this reason it seems a must to design the control of the robot considering explicitly that it is an interactive system (Colgate and Hogan 1987). This means controlling the relation between ...
A Passivity Approach to Attitude Stabilization Using Nonredundant Kinematic Parameterizations
 in Proceedings of the 34th Conference on Decision and Control
, 1995
"... In a recent paper we showed that there exist linear controllers which globally asymptotically stabilize the attitude motion of a rigid body using a nonredundant, threedimensional set of kinematic parameters. In this paper we show, using the inherent passivity properties of the system, that these re ..."
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Cited by 2 (2 self)
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In a recent paper we showed that there exist linear controllers which globally asymptotically stabilize the attitude motion of a rigid body using a nonredundant, threedimensional set of kinematic parameters. In this paper we show, using the inherent passivity properties of the system, that these results can be extended to stabilizing control laws without any angular velocity measurements. A numerical example demonstrates the theoretical results. 1. Introduction In a recent paper [14] we have shown that there exist linear globally asymptotically stabilizing control laws for the attitude motion of a rigid body using minimal, threedimensional parameterizations for the kinematics. In particular, in [14] we derived linear control laws in terms of the classical CayleyRodrigues parameters [4, 11] and the newly developed Modified Rodrigues parameters [7, 10, 11, 13, 14]. The approach in [14] uses a Lyapunov function which is the sum of a quadratic term in the angular velocities and a log...
A Passivation Approach to Power Systems Stabilization
, 1998
"... In this paper we address the problem of supression of low frequency oscillations in power systems. These oscillations appear in strongly interconnected networks because of load and topology changes, and they may cause loss of synchronism and generator tripping. We propose the utilisation of passivat ..."
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Cited by 2 (1 self)
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In this paper we address the problem of supression of low frequency oscillations in power systems. These oscillations appear in strongly interconnected networks because of load and topology changes, and they may cause loss of synchronism and generator tripping. We propose the utilisation of passivation techniques to design power system stabilizers for the synchronous generators. The generator to be controlled is described by a standard lagrange model, with three forcing terms: the mechanical torque coming from the turbine, the terminal voltage of the network and the field voltage, which is our control variable. In view of the significant differences between the mechanical and the electrical time scales, the first signal can be treated as a constant disturbance. The terminal voltage may be viewed as the output of an operator, defined by the remaining part of the network, which is in feedback interconnection with the generator. Our basic assumption is that the network is always absor...