Priority oriented adaptive control of kinematically redundant manipulators

Abstract

In this paper an adaptive multi-priority nonlinear control algorithm for a redundant manipulator system is developed based on the Lyapunov like approach. The method considers the parametric uncertainties in the system and defines a proper filtered error signal to achieve asymptotic stability and convergence in tracking error, both for the main task and sub-tasks according to the allocated priority. The performance of the proposed method is studied by some numerical simulations

Robust Task Space Finite-Time Chattering-Free Control of Robotic Manipulators

“…In the second approach, works [26][27][28][29][30][31][32][33][34][35][36][37] present adaptive control algorithms to compensate for parametric uncertainties in dynamic model including only the linearly parametrizable friction terms (viscous friction) and also neglecting the external (nonlinearly parametrizable) disturbances. Moreover, control laws from [26][27][28][29][30][31][32][33][34][35][36] use inverse or pseudo-inverse of either the exact or approximate Jacobian matrices. Recent study [37] estimates the pseudo-inverse by some non-singular matrix which is adaptively computed.…”

“…Based on discontinuous term (27), let us construct the Filippov mapping (a multi-valued function) : R n → 2 R n of the form (s) = s ||s|| for s = 0 and (0) = B(0, 1) otherwise, where B(0, 1) means the closed ball with centre s = 0 and radius 1. As is easy to see, is upper semi-continuous what implies, based on [6], the existence of the solution of Eq.…”

“…The control techniques offered in the first approach [16][17][18][19][20][21][22][23][24][25][43][44][45] require the full knowledge of the dynamics neglecting the external disturbances. In the second approach, works [26][27][28][29][30][31][32][33][34][35][36][37] present adaptive control algorithms to compensate for parametric uncertainties in dynamic model including only the linearly parametrizable friction terms (viscous friction) and also neglecting the external (nonlinearly parametrizable) disturbances. Moreover, control laws from [26][27][28][29][30][31][32][33][34][35][36] use inverse or pseudo-inverse of either the exact or approximate Jacobian matrices.…”

Kinematically Optimal Robust Control of Redundant Manipulators

“…The control techniques offered in Khatib [1], Hsu et al [2], Canudas et al [3], Siciliano et al [4], Galicki [5], Kelly and Moreno [6], Nakanishi et al [7], Moreno-Valenzuela and Gonzales-Hernandez [8] require the full knowledge of the robot dynamics neglecting the external disturbances. Works Tatlicioglu et al [9], Sadeghian et al [10], Sadeghian et al [11], Feng and Palaniswami [12], Zergeroglu et al [13], Braganza et al [14], Braganza et al [15], Galicki [16], Cheah et al [17], Li and Cheah [18], Li and Cheah [19], Galicki [20] present adaptive control algorithms to compensate for parametric uncertainties in dynamic model including only the linearly parametrizable friction terms (viscous friction) and also neglecting the external (non-linearly parametrizable) disturbances. Moreover, control laws from Tatlicioglu et al [9], Sadeghian et al [10], Sadeghian et al [11], Feng and Palaniswami [12], Zergeroglu et al [13], Braganza et al [14], Braganza et al [15], Galicki [16], Cheah et al [17], Li and Cheah [18], Li and Cheah [19] use pseudo-inverse of either the exact or approximate Jacobian matrices.…”

“…The first approach presented in works Khatib [1], Hsu et al [2], Canudas et al [3], Siciliano et al [4], Galicki [5], Kelly and Moreno [6], Nakanishi et al [7], Moreno-Valenzuela and Gonzales-Hernandez [8], Tatlicioglu et al [9], Sadeghian et al [10], Sadeghian et al [11], Feng and Palaniswami [12], Zergeroglu et al [13], Braganza et al [14], Braganza et al [15], Galicki [16], Cheah et al [17], Li and Cheah [18], Li and Cheah [19], Galicki [20] is based on the application of the (generalized) pseudo-inverse of the manipulator Jacobian matrix in the control formulation. The control techniques offered in Khatib [1], Hsu et al [2], Canudas et al [3], Siciliano et al [4], Galicki [5], Kelly and Moreno [6], Nakanishi et al [7], Moreno-Valenzuela and Gonzales-Hernandez [8] require the full knowledge of the robot dynamics neglecting the external disturbances.…”