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Imin Kao - One of the best experts on this subject based on the ideXlab platform.
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Modeling and control of planar slippage in object manipulation using robotic soft fingers
ROBOMECH Journal, 2019Co-Authors: Amin Fakhari, Imin Kao, Mehdi KeshmiriAbstract:Slippage occurrence has an important roll in stable and robust object grasping and manipulation. However, in majority of prior research on soft finger manipulation, presence of the slippage between fingers and objects has been ignored. In this paper which is a continuation of our prior work, a revised and more general method for dynamic modeling of planar slippage is presented using the concept of Friction Limit surface. Friction Limit surface is utilized to relate contact sliding motions to contact Frictional force and moment in a planar contact. In this method, different states of planar contact are replaced with a second-order differential equation. As an example of the proposed method application, dynamic modeling and slippage analysis of object manipulation on a horizontal plane using a three-link soft finger is studied. Then, a controller is designed to reduce and remove the undesired slippage which occurs between the soft finger and object and simultaneously move the object on a predefined desired path. Numerical simulations reveal the acceptable performance of the proposed method and the designed controller.
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Development of Realistic Pressure Distribution and Friction Limit Surface for Soft-Finger Contact Interface of Robotic Hands
Journal of Intelligent & Robotic Systems, 2016Co-Authors: Amin Fakhari, Mehdi Keshmiri, Imin KaoAbstract:Various models have been presented for pressures distribution in the contact interface of a soft finger and object in the literature. These models have been proposed without considering the effect of the tangential forces which are usually exerted in the contact interface of a soft finger and object during grasping and manipulation. Having an accurate pressures distribution model across the contact interface is important for designing tactile sensors and improving the modeling of the Friction Limit surface (LS). In this paper, a new and more accurate model is proposed to describe the asymmetry of the pressure distribution in the contact interface of a hemispherical soft finger under both normal and tangential forces. This model is derived based upon observations in the previous literature stating that the contact interface would move and skew toward the direction of the tangential force. According to the proposed pressure distribution model in this study, an improved and more accurate LS is presented. The LS profile obtained by this model is compared with the corresponding results based on the previous models. The new results show that the consideration of the skewness or asymmetry in the pressure distribution (due to the tangential force) causes the LS profile to shrink compared with that constructed with symmetric pressure distribution assumption. This shrinkage, as a result of the skewness and asymmetry of the pressure distribution, makes the contact interface more vulnerable. Furthermore, this new model can also provide a more accurate tool for the analysis of grasping and manipulation involving soft contact interface.
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Modeling of Contact Mechanics and Friction Limit Surfaces for Soft Fingers in Robotics, with Experimental Results
The International Journal of Robotics Research, 1999Co-Authors: Nicholas Xydas, Imin KaoAbstract:A new theory in contact mechanics for modeling of soft fingers is proposed to define the relationship between the normal force and the radius of contact for soft fingers by considering general soft-finger materials, including linearly and nonlinearly elastic materials. The results show that the radius of contact is proportional to the normal force raised to the power of, which ranges from 0 to 1/3. This new theory subsumes the Hertzian contact model for linear elastic materials, where D 1/3. Experiments are conducted to validate the theory using artificial soft fingers made of various materials such as rubber and silicone. Results for human fingers are also compared. This theory provides a basis for numerically constructing Friction Limit surfaces. The numerical Friction Limit surface can be approximated by an ellipse, with the major and minor axes as the maximum Friction force and the maximum moment with respect to the normal axis of contact, respectively. Combining the results of the contactmechanics mo...
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IROS - Modeling of contact mechanics with experimental results for soft fingers
Proceedings. 1998 IEEE RSJ International Conference on Intelligent Robots and Systems. Innovations in Theory Practice and Applications (Cat. No.98CH36, 1Co-Authors: Nicholas Xydas, Imin KaoAbstract:A new theory in contact mechanics for modeling of soft fingers is proposed to define the relationship between normal force and area of contact for soft fingers by considering the soft finger materials as nonlinearly elastic. The results show that the radius of contact is proportional to the normal force raised to the power of /spl gamma/ which ranges from 0 to 1/3. This new theory subsumes the Hertzian contact model for linear elastic materials where /spl gamma/=/3. Experiments are conducted to validate the theory using artificial soft fingers made of various materials such as rubber and silicone. This theory provides basis for constructing Friction Limit surface numerically. Combining the results of the contact mechanics model with the contact Friction model the normalized Friction Limit surface is derived for anthropomorphic soft fingers.
Hermann Grabert - One of the best experts on this subject based on the ideXlab platform.
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Quantum Brownian Motion With Large Friction
Chaos (Woodbury N.Y.), 2005Co-Authors: Joachim Ankerhold, Hermann Grabert, Philip PechukasAbstract:Quantum Brownian motion in the strong Friction Limit is studied based on the exact path integral formulation of dissipative systems. In this Limit the time-nonlocal reduced dynamics can be cast into an effective equation of motion, the quantum Smoluchowski equation. For strongly condensed phase environments it plays a similar role as master equations in the weak coupling range. Applications for chemical, mesoscopic, and soft matter systems are discussed and reveal the substantial role of quantum fluctuations.
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Strong Friction Limit in quantum mechanics: the quantum Smoluchowski equation.
Physical review letters, 2001Co-Authors: Joachim Ankerhold, Philip Pechukas, Hermann GrabertAbstract:For a quantum system coupled to a heat bath environment the strong Friction Limit is studied starting from the exact path integral formulation. Generalizing the classical Smoluchowski Limit to low temperatures, a time evolution equation for the position distribution is derived and the strong role of quantum fluctuations in this Limit is revealed.
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Quantum Smoluchowski equation
Annalen der Physik, 2000Co-Authors: Philip Pechukas, Joachim Ankerhold, Hermann GrabertAbstract:The strong Friction Limit of the Caldeira-Leggett model for quantum Brownian motion is analyzed. In this Smoluchowski Limit the density operator of the Brownian particle is essentially diagonal in coordinate, and the diagonal element satisfies the classical Smoluchowski equation. This result cannot be obtained from the master equations that have been proposed for quantum Brownian motion, whether or not these equations are of Lindblad form.
Pierrehenri Chavanis - One of the best experts on this subject based on the ideXlab platform.
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initial value problem for the linearized mean field kramers equation with long range interactions
arXiv: Statistical Mechanics, 2013Co-Authors: Pierrehenri ChavanisAbstract:We solve the initial value problem for the linearized mean field Kramers equation describing Brownian particles with long-range interactions in the $N\rightarrow +\infty$ Limit. We show that the dielectric function can be expressed in terms of incomplete Gamma functions. The dielectric functions associated with the linearized Vlasov equation and with the linearized mean field Smoluchowski equation are recovered as special cases corresponding to the no Friction Limit or to the strong Friction Limit respectively. Although the stability of the Maxwell-Boltzmann distribution is independent on the Friction parameter, the evolution of the perturbation depends on it in a non-trivial manner. For illustration, we apply our results to self-gravitating systems, plasmas, and to the attractive and repulsive BMF models.
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General properties of nonlinear mean field Fokker‐Planck equations
AIP Conference Proceedings, 2007Co-Authors: Pierrehenri ChavanisAbstract:Recently, several authors have tried to extend the usual concepts of thermodynamics and kinetic theory in order to deal with distributions that can be non-Boltzmannian. For dissipative systems described by the canonical ensemble, this leads to the notion of nonlinear Fokker-Planck equation (T.D. Frank, Non Linear Fokker-Planck Equations, Springer, Berlin, 2005). In this paper, we review general properties of nonlinear mean field Fokker-Planck equations, consider the passage from the generalized Kramers to the generalized Smoluchowski equation in the strong Friction Limit, and provide explicit examples for Boltzmann, Tsallis and Fermi-Dirac entropies.
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Chapman-Enskog derivation of the generalized Smoluchowski equation
Physica A: Statistical Mechanics and its Applications, 2004Co-Authors: Pierrehenri Chavanis, Philippe Laurençot, Mohammed LemouAbstract:We use the Chapman-Enskog method to derive the Smoluchowski equation from the Kramers equation in a high Friction Limit. We consider two main extensions of this problem: we take into account a uniform rotation of the background medium and we consider a generalized class of Kramers equations associated with generalized free energy functionals. We mention applications of these results to systems with long-range interactions (self-gravitating systems, 2D vortices, bacterial populations,...). In that case, the Smoluchowski equation is non-local. In the Limit of short-range interactions, it reduces to a generalized form of the Cahn-Hilliard equation. These equations are associated with an effective generalized thermodynamical formalism.
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On the analogy between self-gravitating Brownian particles and bacterial populations
Nonlocal Elliptic and Parabolic Problems, 2004Co-Authors: Pierrehenri Chavanis, Carole Rosier, Magali Ribot, Clément SireAbstract:We develop the analogy between self-gravitating Brownian particles and bacterial populations. In the high Friction Limit, the self-gravitating Brownian gas is described by the Smoluchowski-Poisson system. These equations can develop a self-similar collapse leading to a finite time singularity. Coincidentally, the Smoluchowski-Poisson system corresponds to a simplified version of the Keller-Segel model of bacterial populations. In this biological context, it describes the chemotactic aggregation of the bacterial colonies. We extend these classical models by introducing a small-scale regularization. In the gravitational context, we consider a gas of self-gravitating Brownian fermions and in the biological context we consider finite size effects. In that case, the collapse stops when the system feels the influence of the small-scale regularization. A phenomenon of ''explosion'', reverse to the collapse, is also possible.
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Anomalous diffusion and collapse of self-gravitating Langevin particles in D dimensions
Physical Review E : Statistical Nonlinear and Soft Matter Physics, 2004Co-Authors: Pierrehenri Chavanis, Clément SireAbstract:We address the generalized thermodynamics and the collapse of a system of self-gravitating Langevin particles exhibiting anomalous diffusion in a space of dimension D. The equilibrium states correspond to polytropic distributions. The index n of the polytrope is related to the exponent of anomalous diffusion. We consider a high-Friction Limit and reduce the problem to the study of the nonlinear Smoluchowski-Poisson system. We show that the associated Lyapunov functional is the Tsallis free energy. We discuss in detail the equilibrium phase diagram of self-gravitating polytropes as a function of D and n and determine their stability by using turning points arguments and analytical methods. When no equilibrium state exists, we investigate self-similar solutions describing the collapse. These results can be relevant for astrophysical systems, two-dimensional vortices and for the chemotaxis of bacterial populations. Above all, this model constitutes a prototypical dynamical model of systems with long-range interactions which possesses a rich structure and which can be studied in great detail.
Clément Sire - One of the best experts on this subject based on the ideXlab platform.
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Anomalous diffusion and collapse of self-gravitating Langevin particles in D dimensions
Physical Review E : Statistical Nonlinear and Soft Matter Physics, 2004Co-Authors: Pierrehenri Chavanis, Clément SireAbstract:We address the generalized thermodynamics and the collapse of a system of self-gravitating Langevin particles exhibiting anomalous diffusion in a space of dimension D. The equilibrium states correspond to polytropic distributions. The index n of the polytrope is related to the exponent of anomalous diffusion. We consider a high-Friction Limit and reduce the problem to the study of the nonlinear Smoluchowski-Poisson system. We show that the associated Lyapunov functional is the Tsallis free energy. We discuss in detail the equilibrium phase diagram of self-gravitating polytropes as a function of D and n and determine their stability by using turning points arguments and analytical methods. When no equilibrium state exists, we investigate self-similar solutions describing the collapse. These results can be relevant for astrophysical systems, two-dimensional vortices and for the chemotaxis of bacterial populations. Above all, this model constitutes a prototypical dynamical model of systems with long-range interactions which possesses a rich structure and which can be studied in great detail.
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On the analogy between self-gravitating Brownian particles and bacterial populations
Nonlocal Elliptic and Parabolic Problems, 2004Co-Authors: Pierrehenri Chavanis, Carole Rosier, Magali Ribot, Clément SireAbstract:We develop the analogy between self-gravitating Brownian particles and bacterial populations. In the high Friction Limit, the self-gravitating Brownian gas is described by the Smoluchowski-Poisson system. These equations can develop a self-similar collapse leading to a finite time singularity. Coincidentally, the Smoluchowski-Poisson system corresponds to a simplified version of the Keller-Segel model of bacterial populations. In this biological context, it describes the chemotactic aggregation of the bacterial colonies. We extend these classical models by introducing a small-scale regularization. In the gravitational context, we consider a gas of self-gravitating Brownian fermions and in the biological context we consider finite size effects. In that case, the collapse stops when the system feels the influence of the small-scale regularization. A phenomenon of ''explosion'', reverse to the collapse, is also possible.
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Thermodynamics of self-gravitating systems
Physical Review E : Statistical Nonlinear and Soft Matter Physics, 2002Co-Authors: Pierrehenri Chavanis, Carole Rosier, Clément SireAbstract:We study the thermodynamics and the collapse of a self-gravitating gas of Brownian particles. We consider a high-Friction Limit in order to simplify the problem. This results in the Smoluchowski-Poisson system. Below a critical energy or below a critical temperature, there is no equilibrium state and the system develops a self-similar collapse leading to a finite time singularity. In the microcanonical ensemble, this corresponds to a "gravothermal catastrophe" and in the canonical ensemble to an "isothermal collapse." Self-similar solutions are investigated analytically and numerically.
Philippe Laurençot - One of the best experts on this subject based on the ideXlab platform.
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Non-isothermal Smoluchowski–Poisson equations as a singular Limit of the Navier–Stokes–Fourier–Poisson system
Journal de Mathématiques Pures et Appliquées, 2007Co-Authors: Eduard Feireisl, Philippe LaurençotAbstract:Abstract The convergence of weak solutions to the compressible Navier–Stokes–Fourier–Poisson system with a Friction term is studied in the high Friction Limit, the pressure law including that corresponding to Fermi–Dirac particles. The Limit is shown to be a weak solution of a non-isothermal Smoluchowski–Poisson system with a time-dependent and spatially homogeneous temperature determined by the conservation of the total energy.
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Non-isothermal Smoluchowski-Poisson equations as a singular Limit of the Navier-Stokes-Fourier-Poisson system
Journal de Mathématiques Pures et Appliquées, 2007Co-Authors: Eduard Feireisl, Philippe LaurençotAbstract:The convergence of weak solutions to the compressible Navier-Stokes -Fourier-Poisson system with a Friction term is studied in the high Friction Limit, the pressure law including that corresponding to Fermi-Dirac particles. The Limit is shown to be a weak solution of a non-isothermal Smoluchowski-Poisson system with a time-dependent and spatially homogeneous temperature determined by the conservation of the total energy.
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Chapman-Enskog derivation of the generalized Smoluchowski equation
Physica A: Statistical Mechanics and its Applications, 2004Co-Authors: Pierrehenri Chavanis, Philippe Laurençot, Mohammed LemouAbstract:We use the Chapman-Enskog method to derive the Smoluchowski equation from the Kramers equation in a high Friction Limit. We consider two main extensions of this problem: we take into account a uniform rotation of the background medium and we consider a generalized class of Kramers equations associated with generalized free energy functionals. We mention applications of these results to systems with long-range interactions (self-gravitating systems, 2D vortices, bacterial populations,...). In that case, the Smoluchowski equation is non-local. In the Limit of short-range interactions, it reduces to a generalized form of the Cahn-Hilliard equation. These equations are associated with an effective generalized thermodynamical formalism.
