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Fathi H. Ghorbel - One of the best experts on this subject based on the ideXlab platform.

  • high speed precision tracking with harmonic drive systems using Integral Manifold control design
    International Journal of Control, 2005
    Co-Authors: Prasanna S. Gandhi, Fathi H. Ghorbel
    Abstract:

    Harmonic drives are popular in precision positioning applications such as military radars, satellite cameras, and wafer alignment machines because of their unique property of near-zero backlash. However, precision positioning performance is degraded by non-linear effects of inherent kinematic error and flexibility. This paper presents new non-linear controller development along with experimental verification to compensate for kinematic error in the presence of flexibility in high-speed regulation and trajectory tracking applications. Several issues in implementation of complex theoretical controllers in experiments have been discussed. The development uses our previous algorithms to compensate only for the kinematic error ignoring flexibility effects (U.S. Patent 6,459,940). The proposed control development is based on recent results on the Integral Manifold approach and guarantees asymptotic stability. We present simulation and experimental results to further demonstrate the effectiveness of our approach...

  • Control of hysteresis and kinematic error nonlinearities in harmonic drives for high speed precision control applications
    Proceedings of the 2004 American Control Conference, 2004
    Co-Authors: Prasanna S. Gandhi, Fathi H. Ghorbel
    Abstract:

    Important nonlinear transmission attributes exhibiting coupled dynamics and deteriorating performance of harmonic drive systems include hysteresis and kinematic error. This work presents control algorithms developed to compensate for hysteresis in the presence of kinematic error (KE) for precision position tracking applications with known smooth load on the output side. A model of hysteresis with a linear flexibility part and nonlinear dissipative part represented by a differential equation is used. The model is integrated with kinematic error model to obtain a set of equations governing system dynamics. First, a singularly perturbed model of the drive is derived from this set of equations. The proposed algorithm is then developed using Integral Manifold control approach involving slow and fast control terms. A recent result by authors on compensation of kinematic error alone is employed for the same. Simulation results with the proposed algorithms establish its effectiveness.

  • Integral Manifolds of singularly perturbed systems with application to rigid-link flexible-joint multibody systems
    International Journal of Non-Linear Mechanics, 2000
    Co-Authors: Fathi H. Ghorbel, Mark W Spong
    Abstract:

    In this paper, we first review results of Integral Manifolds of singularly perturbed non-linear differential equations. We then outline the basic elements of the Integral Manifold method in the context of control system design, namely, the existence of an Integral Manifold, its attractivity, and stability of the equilibrium while the dynamics are restricted to the Manifold. Toward this end, we use the composite Lyapunov method and propose a new exponential stability result which gives, as a by-product, an explicit range of the small parameter for which exponential stability is guaranteed. The results are applied to the control problem of multibody systems with rigid links and flexible joints in which the inverse of joint stiffness plays the role of the small parameter. The proposed controller is a composite control law that consists of a fast component, as well as a slow component that was designed based on the Integral Manifold approach. We show that the proposed composite controller has the following properties: (i) it enables the exact characterization and computation of an Integral Manifold, (ii) it makes the Manifold exponentially attractive, and (iii) it forces the dynamics of the reduced flexible system on the Integral Manifold to coincide with the dynamics of the corresponding rigid system (i.e. the one obtained by making stiffness very large) implying that any control law that stabilizes the rigid system would stabilize the dynamics of the flexible system on the Manifold. We finally present a detailed stability analysis and give an explicit range of the joint stiffness, in terms of system parameters and controller gains, for which the established exponential stability is guaranteed.

  • adaptive Integral Manifold control of flexible joint robot manipulators
    International Conference on Robotics and Automation, 1992
    Co-Authors: Fathi H. Ghorbel, Mark W Spong
    Abstract:

    The authors extend the Integral Manifold approach for the control of flexible joint robot manipulators from the known parameter case to the adaptive case. The resulting adaptive law, referred to as the corrective control law, consists of a fast component to damp the fast dynamics and a slow component which is designed based on the Integral Manifold theory and which consists of a rigid based component along with additional corrective terms. The authors give a detailed derivation of the corrective control law and present tracking results. They illustrate the implementation of the control law using simulation examples and study tracking performance and robustness with respect to an allowable range of stiffness and high adaptation gains. >

  • Adaptive Integral Manifold Control of Flexible Joint Robots with Configuration Invariant Inertia
    1992 American Control Conference, 1992
    Co-Authors: Fathi H. Ghorbel, Mark W Spong
    Abstract:

    In this paper we derive a new adaptive corrective control law for a class of flexible joint robot manipulators with configuration-invariant inertia matrices. The control law consists of a fast controller to damp the elastic oscillations of the joints and a slow (corrective) controller designed based on the theory of Integral Manifolds for singularly perturbed nonlinear systems. We derive the first parameter update law that takes into consideration joint flexibility. We present detailed stability analysis using the composite Lyapunov function method.

Mark W Spong - One of the best experts on this subject based on the ideXlab platform.

  • Integral Manifolds of singularly perturbed systems with application to rigid-link flexible-joint multibody systems
    International Journal of Non-Linear Mechanics, 2000
    Co-Authors: Fathi H. Ghorbel, Mark W Spong
    Abstract:

    In this paper, we first review results of Integral Manifolds of singularly perturbed non-linear differential equations. We then outline the basic elements of the Integral Manifold method in the context of control system design, namely, the existence of an Integral Manifold, its attractivity, and stability of the equilibrium while the dynamics are restricted to the Manifold. Toward this end, we use the composite Lyapunov method and propose a new exponential stability result which gives, as a by-product, an explicit range of the small parameter for which exponential stability is guaranteed. The results are applied to the control problem of multibody systems with rigid links and flexible joints in which the inverse of joint stiffness plays the role of the small parameter. The proposed controller is a composite control law that consists of a fast component, as well as a slow component that was designed based on the Integral Manifold approach. We show that the proposed composite controller has the following properties: (i) it enables the exact characterization and computation of an Integral Manifold, (ii) it makes the Manifold exponentially attractive, and (iii) it forces the dynamics of the reduced flexible system on the Integral Manifold to coincide with the dynamics of the corresponding rigid system (i.e. the one obtained by making stiffness very large) implying that any control law that stabilizes the rigid system would stabilize the dynamics of the flexible system on the Manifold. We finally present a detailed stability analysis and give an explicit range of the joint stiffness, in terms of system parameters and controller gains, for which the established exponential stability is guaranteed.

  • adaptive Integral Manifold control of flexible joint robot manipulators
    International Conference on Robotics and Automation, 1992
    Co-Authors: Fathi H. Ghorbel, Mark W Spong
    Abstract:

    The authors extend the Integral Manifold approach for the control of flexible joint robot manipulators from the known parameter case to the adaptive case. The resulting adaptive law, referred to as the corrective control law, consists of a fast component to damp the fast dynamics and a slow component which is designed based on the Integral Manifold theory and which consists of a rigid based component along with additional corrective terms. The authors give a detailed derivation of the corrective control law and present tracking results. They illustrate the implementation of the control law using simulation examples and study tracking performance and robustness with respect to an allowable range of stiffness and high adaptation gains. >

  • Adaptive Integral Manifold Control of Flexible Joint Robots with Configuration Invariant Inertia
    1992 American Control Conference, 1992
    Co-Authors: Fathi H. Ghorbel, Mark W Spong
    Abstract:

    In this paper we derive a new adaptive corrective control law for a class of flexible joint robot manipulators with configuration-invariant inertia matrices. The control law consists of a fast controller to damp the elastic oscillations of the joints and a slow (corrective) controller designed based on the theory of Integral Manifolds for singularly perturbed nonlinear systems. We derive the first parameter update law that takes into consideration joint flexibility. We present detailed stability analysis using the composite Lyapunov function method.

  • ICRA - Adaptive Integral Manifold control of flexible joint robot manipulators
    Proceedings 1992 IEEE International Conference on Robotics and Automation, 1
    Co-Authors: Fathi H. Ghorbel, Mark W Spong
    Abstract:

    The authors extend the Integral Manifold approach for the control of flexible joint robot manipulators from the known parameter case to the adaptive case. The resulting adaptive law, referred to as the corrective control law, consists of a fast component to damp the fast dynamics and a slow component which is designed based on the Integral Manifold theory and which consists of a rigid based component along with additional corrective terms. The authors give a detailed derivation of the corrective control law and present tracking results. They illustrate the implementation of the control law using simulation examples and study tracking performance and robustness with respect to an allowable range of stiffness and high adaptation gains. >

Petar V. Kokotovic - One of the best experts on this subject based on the ideXlab platform.

Rajni V. Patel - One of the best experts on this subject based on the ideXlab platform.

  • an Integral Manifold approach for tip position tracking of flexible multi link manipulators
    International Conference on Robotics and Automation, 1997
    Co-Authors: Mehrdad Moallem, Khashayar Khorasani, Rajni V. Patel
    Abstract:

    In this paper, a nonlinear control strategy for tip position trajectory tracking of a class of structurally flexible multilink manipulators is developed. Using the concept of Integral Manifolds and singular perturbation theory, the full-order flexible system is decomposed into corrected slow and fast subsystems. The tip-position vector is similarly partitioned into corrected slow and fast outputs. To ensure an asymptotic tracking capability, the corrected slow subsystem is augmented by a dynamical controller in such a way that the resulting closed-loop zero dynamics are linear and asymptotically stable. The tracking problem is then redefined as tracking the slow output and stabilizing the corrected fast subsystem by using dynamic output feedback. Consequently, it is possible to show that the tip position tracking errors converge to a residual set of O(/spl epsiv//sup 2/), where /spl epsiv/ is the singular perturbation parameter. A major advantage of the proposed strategy is that the only measurements required are the tip positions, joint positions, and joint velocities. Experimental results for a single-link arm are also presented and compared with the case when the slow control is designed based on the rigid-body model of the manipulator.

  • tip position tracking of flexible multi link manipulators an Integral Manifold approach
    International Conference on Robotics and Automation, 1996
    Co-Authors: Mehrdad Moallem, K. Khorasani, Rajni V. Patel
    Abstract:

    In this paper a nonlinear control strategy for tip position trajectory tracking of a class of structurally flexible multi-link manipulators is developed. Using the concept of Integral Manifolds and singular perturbation theory, the full-order flexible system is decomposed into corrected slow and fast subsystems. The tip position vector is similarly partitioned into corrected slow and fast outputs. To ensure an asymptotic tracking capability, the corrected slow subsystem is augmented by a dynamical controller in such a way that the resulting closed-loop zero-dynamics are linear and asymptotically stable. The tracking problem is then re-defined as tracking the slow output and stabilizing the corrected fast subsystem by using dynamic output feedback. A major advantage of the proposed strategy is that the only measurements required are the tip positions, joint positions, and joint velocities.

  • ICRA - Tip position tracking of flexible multi-link manipulators: An Integral Manifold approach
    Proceedings of IEEE International Conference on Robotics and Automation, 1
    Co-Authors: Mehrdad Moallem, K. Khorasani, Rajni V. Patel
    Abstract:

    In this paper a nonlinear control strategy for tip position trajectory tracking of a class of structurally flexible multi-link manipulators is developed. Using the concept of Integral Manifolds and singular perturbation theory, the full-order flexible system is decomposed into corrected slow and fast subsystems. The tip position vector is similarly partitioned into corrected slow and fast outputs. To ensure an asymptotic tracking capability, the corrected slow subsystem is augmented by a dynamical controller in such a way that the resulting closed-loop zero-dynamics are linear and asymptotically stable. The tracking problem is then re-defined as tracking the slow output and stabilizing the corrected fast subsystem by using dynamic output feedback. A major advantage of the proposed strategy is that the only measurements required are the tip positions, joint positions, and joint velocities.

H.c. Tseng - One of the best experts on this subject based on the ideXlab platform.