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ORIGINAL PAPER
Kinematically Optimal Robust Control of Redundant Manipulators
M. Galicki 1
 
 
 
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Faculty of the Mechanical Engineering University of Zielona Góra ul. Prof. Z. Szafrana 4, 65-516, Zielona Góra, POLAND
 
 
Online publication date: 2017-12-09
 
 
Publication date: 2017-12-20
 
 
International Journal of Applied Mechanics and Engineering 2017;22(4):839-865
DOI: https://doi.org/10.1515/ijame-2017-0055
 
 
Article (PDF)
References (73)
 
KEYWORDS
redundant robotic manipulator
task space trajectory tracking
robust optimal finite-time control
Lyapunov stability
 
ABSTRACT
This work deals with the problem of the robust optimal task space trajectory tracking subject to finite-time convergence. Kinematic and dynamic equations of a redundant manipulator are assumed to be uncertain. Moreover, globally unbounded disturbances are allowed to act on the manipulator when tracking the trajectory by the endeffector. Furthermore, the movement is to be accomplished in such a way as to minimize both the manipulator torques and their oscillations thus eliminating the potential robot vibrations. Based on suitably defined task space non-singular terminal sliding vector variable and the Lyapunov stability theory, we derive a class of chattering-free robust kinematically optimal controllers, based on the estimation of transpose Jacobian, which seem to be effective in counteracting both uncertain kinematics and dynamics, unbounded disturbances and (possible) kinematic and/or algorithmic singularities met on the robot trajectory. The numerical simulations carried out for a redundant manipulator of a SCARA type consisting of the three revolute kinematic pairs and operating in a two-dimensional task space, illustrate performance of the proposed controllers as well as comparisons with other well known control schemes.
 
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