The Experts below are selected from a list of 60408 Experts worldwide ranked by ideXlab platform
Péter L. Várkonyi - One of the best experts on this subject based on the ideXlab platform.
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Lyapunov Stability of a rigid body with two frictional contacts
Nonlinear Dynamics, 2017Co-Authors: Péter L. VárkonyiAbstract:Lyapunov Stability of a mechanical system means that the dynamic response stays bounded in an arbitrarily small neighborhood of a static equilibrium configuration under small perturbations in positions and velocities. This type of Stability is highly desired in robotic applications that involve multiple unilateral contacts. Nevertheless, Lyapunov Stability analysis of such systems is extremely difficult, because even small perturbations may result in hybrid dynamics where the solution involves many non-smooth transitions between different contact states. This paper concerns Lyapunov Stability analysis of a planar rigid body with two frictional unilateral contacts under inelastic impacts, for a general class of equilibrium configurations under a constant external load. The hybrid dynamics of the system under contact transitions and impacts is formulated, and a Poincaré map at two-contact states is introduced. Using invariance relations, this Poincaré map is reduced into two semi-analytic scalar functions that entirely encode the dynamic behavior of solutions under any small initial perturbation. These two functions enable determination of Lyapunov Stability or inStability for almost any equilibrium state. The results are demonstrated via simulation examples and by plotting Stability and inStability regions in two-dimensional parameter spaces that describe the contact geometry and external load.
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Lyapunov Stability of a rigid body with two frictional contacts
Nonlinear Dynamics, 2017Co-Authors: Péter L. VárkonyiAbstract:Lyapunov Stability of a mechanical system means that the dynamic response stays bounded in an arbitrarily small neighborhood of a static equilibrium configuration under small perturbations in positions and velocities. This type of Stability is highly desired in robotic applications that involve multiple unilateral contacts. Nevertheless, Lyapunov Stability analysis of such systems is extremely difficult, because even small perturbations may result in hybrid dynamics where the solution involves many non-smooth transitions between different contact states. This paper concerns Lyapunov Stability analysis of a planar rigid body with two frictional unilateral contacts under inelastic impacts, for a general class of equilibrium configurations under a constant external load. The hybrid dynamics of the system under contact transitions and impacts is formulated, and a Poincare map at two-contact states is introduced. Using invariance relations, this Poincare map is reduced into two semi-analytic scalar functions that entirely encode the dynamic behavior of solutions under any small initial perturbation. These two functions enable determination of Lyapunov Stability or inStability for almost any equilibrium state. The results are demonstrated via simulation examples and by plotting Stability and inStability regions in two-dimensional parameter spaces that describe the contact geometry and external load.
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ICRA - On the Lyapunov Stability of quasistatic planar biped robots
2012 IEEE International Conference on Robotics and Automation, 2012Co-Authors: Péter L. Várkonyi, David Gontier, Joel W. BurdickAbstract:We investigate the local motion of a planar rigid body with unilateral constraints in the neighborhood of a two-contact frictional equilibrium configuration on a slope. A new sufficient condition of Lyapunov Stability is developed in the presence of arbitrary external forces. Additionally, we construct an example, which is stable against perturbations by infinitesimal forces, but does not possess Lyapunov Stability against infinitesimal displacements or impulses. The great difference between previous Stability criteria and ours leads to further questions about the nature of the exact Stability condition.
Georges Bastin - One of the best experts on this subject based on the ideXlab platform.
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Dissipative boundary conditions for one-dimensional quasi-linear hyperbolic systems: Lyapunov Stability for the {$C^1$}-norm
SIAM Journal on Control and Optimization, 2015Co-Authors: Jean-michel Coron, Georges BastinAbstract:This paper is concerned with boundary dissipative conditions that guarantee the exponential Stability of classical solutions of one-dimensional quasi-linear hyperbolic systems. We present a comprehensive review of the results that are available in the literature. The main result of the paper is then to supplement these previous results by showing how a new Lyapunov Stability approach can be used for the analysis of boundary conditions that are known to be dissipative for the C1-norm.
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dissipative boundary conditions for one dimensional quasi linear hyperbolic systems Lyapunov Stability for the c 1 norm
Siam Journal on Control and Optimization, 2015Co-Authors: Jean-michel Coron, Georges BastinAbstract:This paper is concerned with boundary dissipative conditions that guarantee the exponential Stability of classical solutions of one-dimensional quasi-linear hyperbolic systems. We present a comprehensive review of the results that are available in the literature. The main result of the paper is then to supplement these previous results by showing how a new Lyapunov Stability approach can be used for the analysis of boundary conditions that are known to be dissipative for the $C^1$-norm.
Jean-michel Coron - One of the best experts on this subject based on the ideXlab platform.
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Dissipative boundary conditions for one-dimensional quasi-linear hyperbolic systems: Lyapunov Stability for the {$C^1$}-norm
SIAM Journal on Control and Optimization, 2015Co-Authors: Jean-michel Coron, Georges BastinAbstract:This paper is concerned with boundary dissipative conditions that guarantee the exponential Stability of classical solutions of one-dimensional quasi-linear hyperbolic systems. We present a comprehensive review of the results that are available in the literature. The main result of the paper is then to supplement these previous results by showing how a new Lyapunov Stability approach can be used for the analysis of boundary conditions that are known to be dissipative for the C1-norm.
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dissipative boundary conditions for one dimensional quasi linear hyperbolic systems Lyapunov Stability for the c 1 norm
Siam Journal on Control and Optimization, 2015Co-Authors: Jean-michel Coron, Georges BastinAbstract:This paper is concerned with boundary dissipative conditions that guarantee the exponential Stability of classical solutions of one-dimensional quasi-linear hyperbolic systems. We present a comprehensive review of the results that are available in the literature. The main result of the paper is then to supplement these previous results by showing how a new Lyapunov Stability approach can be used for the analysis of boundary conditions that are known to be dissipative for the $C^1$-norm.
Antonio Loria - One of the best experts on this subject based on the ideXlab platform.
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A Unified Framework for Dynamics and Lyapunov Stability of Holonomically Constrained Rigid Bodies
Journal of Advanced Computational Intelligence and Intelligent Informatics, 2005Co-Authors: Khoder Melhem, Zhaoheng Liu, Antonio LoriaAbstract:A new dynamic model for interconnected rigid bodies is proposed here. The model formulation makes it possible to treat any physical system with finite number of degrees of freedom in a unified framework. This new model is a nonminimal realization of the system dynamics since it contains more state variables than is needed. A useful discussion shows how the dimension of the state of this model can be reduced by eliminating the redundancy in the equations of motion, thus obtaining the minimal realization of the system dynamics. With this formulation, we can for the first time explicitly determine the equations of the constraints between the elements of the mechanical system corresponding to the interconnected rigid bodies in question. One of the advantages coming with this model is that we can use it to demonstrate that Lyapunov Stability and control structure for the constrained system can be deducted by projection in the submanifold of movement from appropriate Lyapunov Stability and stabilizing control of the corresponding unconstrained system. This procedure is tested by some simulations using the model of two-link planar robot.
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A unified framework for dynamics and Lyapunov Stability of holonomically constrained rigid bodies
Second IEEE International Conference on Computational Cybernetics 2004. ICCC 2004., 1Co-Authors: Khoder Melhem, Zhaoheng Liu, Antonio LoriaAbstract:A new dynamic model for interconnected rigid bodies is proposed here. The model formulation makes it possible to treat any physical system with finite number of degrees of freedom in a unified framework. This new model is a non minimal realization of the system dynamics since it contains more state variables than is needed. A useful discussion shows how the dimension of the state of this model can be reduced by eliminating the redundancy in the equations of motion, thus obtaining the minimal realization of the system dynamics. With this formulation, we can for the first time explicitly determine the equations of the constraints between different elements of the mechanical system corresponding to the interconnected rigid bodies in question. One of the advantageous coming with this model is that we can use it to demonstrate that Lyapunov Stability and control structure for the constrained system can be deducted by projection in the submanifold of movement from appropriate Lyapunov Stability and stabilizing control of the corresponding unconstrained system. This procedure is tested by some simulations using the model of two-link planar robot
Xian Fen - One of the best experts on this subject based on the ideXlab platform.
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Relations between Lyapunov Stability and ISS of nonlinear descriptor systems
Journal of Minjiang University, 2014Co-Authors: Xian FenAbstract:The problem of relations between Lyapunov Stability and input-to-state Stability( ISS) of nonlinear descriptor systems is discussed. Firstly,comparison functions are employed to analyse the Lyapunov Stability of nonlinear descriptor systems. Then we derived the result that input-to-state stable implies global asymptotic Stability for nonlinear descriptor systems. Conversely,for a general nonlinear descriptor system,global asymptotic Stability does not guarantee input-to-state stable.
