Approximate Jacobian control for robots with uncertain kinematics and dynamics. Cheah, C. C., Hirano, M., Kawamura, S., & Arimoto, S. IEEE Transactions on Robotics and Automation, 19(4):692–702, August, 2003. doi abstract bibtex Most research so far in robot control has assumed either kinematics or Jacobian matrix of the robots from joint space to Cartesian space is known exactly. Unfortunately, no physical parameters can be derived exactly. In addition, when the robot picks up objects of uncertain lengths, orientations, or gripping points, the overall kinematics from the robot's base to the tip of the object becomes uncertain and changes according to different tasks. Consequently, it is unknown whether stability of the robot could be guaranteed in the presence of uncertain kinematics. In order to overcome these drawbacks, in this paper, we propose simple feedback control laws for setpoint control without exact knowledge of kinematics, Jacobian matrix, and dynamics. Lyapunov functions are presented for stability analysis of feedback control problem with uncertain kinematics. We shall show that the end-effector's position converges to a desired position in a finite task space even when the kinematics and Jacobian matrix are uncertain. Experimental results are presented to illustrate the performance of the proposed controllers.
@article{cheah_approximate_2003,
title = {Approximate {Jacobian} control for robots with uncertain kinematics and dynamics},
volume = {19},
issn = {1042-296X},
doi = {10.1109/TRA.2003.814517},
abstract = {Most research so far in robot control has assumed either kinematics or Jacobian matrix of the robots from joint space to Cartesian space is known exactly. Unfortunately, no physical parameters can be derived exactly. In addition, when the robot picks up objects of uncertain lengths, orientations, or gripping points, the overall kinematics from the robot's base to the tip of the object becomes uncertain and changes according to different tasks. Consequently, it is unknown whether stability of the robot could be guaranteed in the presence of uncertain kinematics. In order to overcome these drawbacks, in this paper, we propose simple feedback control laws for setpoint control without exact knowledge of kinematics, Jacobian matrix, and dynamics. Lyapunov functions are presented for stability analysis of feedback control problem with uncertain kinematics. We shall show that the end-effector's position converges to a desired position in a finite task space even when the kinematics and Jacobian matrix are uncertain. Experimental results are presented to illustrate the performance of the proposed controllers.},
number = {4},
journal = {IEEE Transactions on Robotics and Automation},
author = {Cheah, C. C. and Hirano, M. and Kawamura, S. and Arimoto, S.},
month = aug,
year = {2003},
keywords = {Cartesian space, Feedback control, Jacobian matrices, Jacobian matrix, Kinematics, Lyapunov functions, Lyapunov method, Nonlinear dynamical systems, Orbital robotics, Robot control, Robotics and automation, Stability, Uncertainty, approximate Jacobian control, feedback control problem, finite task space, robot kinematics, robots, setpoint control, stability, stability analysis, uncertain dynamics, uncertain kinematics},
pages = {692--702}
}
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