Jacobian Matrix

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Su Jian-bo - One of the best experts on this subject based on the ideXlab platform.

  • The estimation of image Jacobian Matrix with time-delay compensation for uncalibrated visual servoing
    Control theory & applications, 2009
    Co-Authors: Su Jian-bo
    Abstract:

    A novel online estimation of image Jacobian Matrix with time-delay compensation for uncalibrated visual servoing is proposed.The traditional methods didn't consider the time-delay which causes larger estimation error.In order to compensate the time-delay,local fitting Jacobian Matrix with time-delay compensation based on polynomial fitting is employed to obtain more accurate Jacobian estimation and image precompensation.Simulations and experiments of uncalibrated mobile robot and uncalibrated visual sensors show that this method improves the system dynamic performance and reduces the steady-state error,demonstrating the feasibility and validity of the time-delay compensation.

Anthony A Maciejewski - One of the best experts on this subject based on the ideXlab platform.

  • optimal fault tolerant Jacobian Matrix generators for redundant manipulators
    International Conference on Robotics and Automation, 2011
    Co-Authors: Hamid Abdi, Saeid Nahavandi, Anthony A Maciejewski
    Abstract:

    The design of locally optimal fault-tolerant manipulators has been previously addressed via adding constraints on the bases of a desired null space to the design constraints of the manipulators. Then by algebraic or numeric solution of the design equations, the optimal Jacobian Matrix is obtained. In this study, an optimal fault-tolerant Jacobian Matrix generator is introduced from geometric properties instead of the null space properties. The proposed generator provides equally fault-tolerant Jacobian matrices in R3 that are optimally fault-tolerant for one or two locked joint failures. It is shown that the proposed optimal Jacobian matrices are directly obtained via regular pyramids. The geometric approach and zonotopes are used as a novel tool for determining relative manipulability in the context of fault-tolerant robotics and for bringing geometric insight into the design of optimal fault-tolerant manipulators.

  • ICRA - Optimal fault-tolerant Jacobian Matrix generators for redundant manipulators
    2011 IEEE International Conference on Robotics and Automation, 2011
    Co-Authors: Hamid Abdi, Saeid Nahavandi, Anthony A Maciejewski
    Abstract:

    The design of locally optimal fault-tolerant manipulators has been previously addressed via adding constraints on the bases of a desired null space to the design constraints of the manipulators. Then by algebraic or numeric solution of the design equations, the optimal Jacobian Matrix is obtained. In this study, an optimal fault-tolerant Jacobian Matrix generator is introduced from geometric properties instead of the null space properties. The proposed generator provides equally fault-tolerant Jacobian matrices in R3 that are optimally fault-tolerant for one or two locked joint failures. It is shown that the proposed optimal Jacobian matrices are directly obtained via regular pyramids. The geometric approach and zonotopes are used as a novel tool for determining relative manipulability in the context of fault-tolerant robotics and for bringing geometric insight into the design of optimal fault-tolerant manipulators.

Suguru Arimoto - One of the best experts on this subject based on the ideXlab platform.

  • pid control of robotic manipulator with uncertain Jacobian Matrix
    International Conference on Robotics and Automation, 1999
    Co-Authors: Chien Chern Cheah, Suguru Arimoto, Sadao Kawamura, K. Lee
    Abstract:

    Most research so far on robot control assumes that the kinematics and Jacobian Matrix of the manipulator from joint space to task space are known exactly. This assumption leads to several open problems in the literature of robot control and limits the potential research and applications of robots. In this paper, we present an approximate Jacobian PID control law for set-point control of robot with uncertain kinematics from joint space to task space. Simulation results are presented to illustrate the results.

  • Feedback control for robotic manipulator with an uncertain Jacobian Matrix
    Journal of Robotic Systems, 1999
    Co-Authors: Chien Chern Cheah, Sadao Kawamura, Suguru Arimoto
    Abstract:

    In most applications of robots, a desired path for the end-effector is usually specified in task space such as Cartesian space. One way to move the robot along this path is to solve the inverse kinematics problem to generate the desired angles in joint space. However, it is a very time consuming task to solve the inverse kinematics problem. Furthermore, in the presence of uncertainty in kinematics, it is impossible to derive the desired joint angle from the desired end-effector path and the Jacobian Matrix of the mapping from joint space to task space. In this article, a feedback control law using an uncertain Jacobian Matrix is proposed for setpoint control of robots. Sufficient conditions for the bound of the estimated Jacobian Matrix and stability conditions for the feedback gains are presented to guarantee the stability and passivity of the robots. A gravity regressor with an uncertain Jacobian Matrix is also proposed for gravitational force compensation when the gravitational force is uncertain. Simulation results are presented to illustrate the performance of the proposed controllers. ©1999 John Wiley & Sons, Inc.

  • Asymptotic stability of robot control with approximate Jacobian Matrix and its application to visual servoing
    Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), 1
    Co-Authors: Chien Chern Cheah, K. Lee, Sadao Kawamura, Suguru Arimoto
    Abstract:

    In order to describe a task for the robot manipulator, a desired path for the end effector is usually specified in task space such as Cartesian space. In the presence of uncertainty in kinematics, it is impossible to derive the desired joint angle from the desired end effector path by solving the inverse kinematics problem. In addition, the Jacobian Matrix of the mapping from joint space to task space could not be exactly derived. We present feedback control laws for setpoint control of a robot with uncertain kinematics and Jacobian Matrix from joint space to task space. Sufficient conditions for the bound of the estimated Jacobian Matrix and stability conditions for the feedback gains are presented to guarantee the stability of the robot's motion. Simulation results are presented to illustrate the performance of the proposed controllers.

Hamid Abdi - One of the best experts on this subject based on the ideXlab platform.

  • optimal fault tolerant Jacobian Matrix generators for redundant manipulators
    International Conference on Robotics and Automation, 2011
    Co-Authors: Hamid Abdi, Saeid Nahavandi, Anthony A Maciejewski
    Abstract:

    The design of locally optimal fault-tolerant manipulators has been previously addressed via adding constraints on the bases of a desired null space to the design constraints of the manipulators. Then by algebraic or numeric solution of the design equations, the optimal Jacobian Matrix is obtained. In this study, an optimal fault-tolerant Jacobian Matrix generator is introduced from geometric properties instead of the null space properties. The proposed generator provides equally fault-tolerant Jacobian matrices in R3 that are optimally fault-tolerant for one or two locked joint failures. It is shown that the proposed optimal Jacobian matrices are directly obtained via regular pyramids. The geometric approach and zonotopes are used as a novel tool for determining relative manipulability in the context of fault-tolerant robotics and for bringing geometric insight into the design of optimal fault-tolerant manipulators.

  • ICRA - Optimal fault-tolerant Jacobian Matrix generators for redundant manipulators
    2011 IEEE International Conference on Robotics and Automation, 2011
    Co-Authors: Hamid Abdi, Saeid Nahavandi, Anthony A Maciejewski
    Abstract:

    The design of locally optimal fault-tolerant manipulators has been previously addressed via adding constraints on the bases of a desired null space to the design constraints of the manipulators. Then by algebraic or numeric solution of the design equations, the optimal Jacobian Matrix is obtained. In this study, an optimal fault-tolerant Jacobian Matrix generator is introduced from geometric properties instead of the null space properties. The proposed generator provides equally fault-tolerant Jacobian matrices in R3 that are optimally fault-tolerant for one or two locked joint failures. It is shown that the proposed optimal Jacobian matrices are directly obtained via regular pyramids. The geometric approach and zonotopes are used as a novel tool for determining relative manipulability in the context of fault-tolerant robotics and for bringing geometric insight into the design of optimal fault-tolerant manipulators.

Chien Chern Cheah - One of the best experts on this subject based on the ideXlab platform.

  • pid control of robotic manipulator with uncertain Jacobian Matrix
    International Conference on Robotics and Automation, 1999
    Co-Authors: Chien Chern Cheah, Suguru Arimoto, Sadao Kawamura, K. Lee
    Abstract:

    Most research so far on robot control assumes that the kinematics and Jacobian Matrix of the manipulator from joint space to task space are known exactly. This assumption leads to several open problems in the literature of robot control and limits the potential research and applications of robots. In this paper, we present an approximate Jacobian PID control law for set-point control of robot with uncertain kinematics from joint space to task space. Simulation results are presented to illustrate the results.

  • Feedback control for robotic manipulator with an uncertain Jacobian Matrix
    Journal of Robotic Systems, 1999
    Co-Authors: Chien Chern Cheah, Sadao Kawamura, Suguru Arimoto
    Abstract:

    In most applications of robots, a desired path for the end-effector is usually specified in task space such as Cartesian space. One way to move the robot along this path is to solve the inverse kinematics problem to generate the desired angles in joint space. However, it is a very time consuming task to solve the inverse kinematics problem. Furthermore, in the presence of uncertainty in kinematics, it is impossible to derive the desired joint angle from the desired end-effector path and the Jacobian Matrix of the mapping from joint space to task space. In this article, a feedback control law using an uncertain Jacobian Matrix is proposed for setpoint control of robots. Sufficient conditions for the bound of the estimated Jacobian Matrix and stability conditions for the feedback gains are presented to guarantee the stability and passivity of the robots. A gravity regressor with an uncertain Jacobian Matrix is also proposed for gravitational force compensation when the gravitational force is uncertain. Simulation results are presented to illustrate the performance of the proposed controllers. ©1999 John Wiley & Sons, Inc.

  • Asymptotic stability of robot control with approximate Jacobian Matrix and its application to visual servoing
    Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), 1
    Co-Authors: Chien Chern Cheah, K. Lee, Sadao Kawamura, Suguru Arimoto
    Abstract:

    In order to describe a task for the robot manipulator, a desired path for the end effector is usually specified in task space such as Cartesian space. In the presence of uncertainty in kinematics, it is impossible to derive the desired joint angle from the desired end effector path by solving the inverse kinematics problem. In addition, the Jacobian Matrix of the mapping from joint space to task space could not be exactly derived. We present feedback control laws for setpoint control of a robot with uncertain kinematics and Jacobian Matrix from joint space to task space. Sufficient conditions for the bound of the estimated Jacobian Matrix and stability conditions for the feedback gains are presented to guarantee the stability of the robot's motion. Simulation results are presented to illustrate the performance of the proposed controllers.

  • Approximate Jacobian robot control with adaptive Jacobian Matrix
    42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), 1
    Co-Authors: Chien Chern Cheah
    Abstract:

    In this paper, we present approximate Jacobian feedback control laws for setpoint control of robot with uncertain kinematics from joint space to task space. An adaptive law is proposed to update the approximate Jacobian Matrix to improve the performance. Sufficient conditions for the feedback gains are presented to guarantee the stability of the robot's motion. Simulation results are presented to illustrate the performance of the proposed adaptive controllers.