A Unified Approach for Independent Manipulator Joint Acceleration Control and Observation

International Journal of Applied Mechanics and Engineering

2017

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.

Section: Task Space Control Of the Redundant Robotic Manipulatormentioning

confidence: 99%

Kinematically Optimal Robust Control of Redundant Manipulators

International Journal of Applied Mechanics and Engineering

2017

“…Although all the aforementioned observers are able to reliably reconstruct manipulator state (both joint velocity and acceleration) based on position measurement, there appears a difficulty to combine our control law and the observer from [60][61][62][63][64][65]. In order to make such combination possible, observers proposed in works [60][61][62][63][64][65] have to satisfy the so-called separation principle [68] which implies both the continuity of the controllers from [60][61][62][63][64][65] with the fully available state and asymptotic stability of the closed-loop system under the continuous state feed-back controllers. Let us observe that our control law (28) is discontinuous what prevents an application of the state observers from [60][61][62][63][64][65].…”

Section: (T)| β < |S I (T)| For |S I (T)| > 1 the Same Is Truementioning

confidence: 99%

“…In order to make such combination possible, observers proposed in works [60][61][62][63][64][65] have to satisfy the so-called separation principle [68] which implies both the continuity of the controllers from [60][61][62][63][64][65] with the fully available state and asymptotic stability of the closed-loop system under the continuous state feed-back controllers. Let us observe that our control law (28) is discontinuous what prevents an application of the state observers from [60][61][62][63][64][65]. Although the observer offered in [66] fulfils the separation principle, our controller handles unbounded uncertainties (in dynamics and disturbances) and does not require boundedness ofq andq, respectively.…”

Section: (T)| β < |S I (T)| For |S I (T)| > 1 the Same Is Truementioning

confidence: 99%

“…However, its combination with our controller requires further investigations. Application of Luenberger-style observers [60,61], high-gain observers [62,63], model-free observers [64,65] or a class of observers based on the sliding-mode algorithms [66] seems to be an efficient approach compared with both backward difference technique and direct measurement. Although all the aforementioned observers are able to reliably reconstruct manipulator state (both joint velocity and acceleration) based on position measurement, there appears a difficulty to combine our control law and the observer from [60][61][62][63][64][65].…”

Section: (T)| β < |S I (T)| For |S I (T)| > 1 the Same Is Truementioning

confidence: 99%

“…Application of Luenberger-style observers [60,61], high-gain observers [62,63], model-free observers [64,65] or a class of observers based on the sliding-mode algorithms [66] seems to be an efficient approach compared with both backward difference technique and direct measurement. Although all the aforementioned observers are able to reliably reconstruct manipulator state (both joint velocity and acceleration) based on position measurement, there appears a difficulty to combine our control law and the observer from [60][61][62][63][64][65]. In order to make such combination possible, observers proposed in works [60][61][62][63][64][65] have to satisfy the so-called separation principle [68] which implies both the continuity of the controllers from [60][61][62][63][64][65] with the fully available state and asymptotic stability of the closed-loop system under the continuous state feed-back controllers.…”

Section: (T)| β < |S I (T)| For |S I (T)| > 1 the Same Is Truementioning

confidence: 99%

See 2 more Smart Citations

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

2016

J Intell Robot Syst

This work deals with the problem of the accurate task space control subject to finite-time convergence. Kinematic and dynamic equations of a rigid robotic manipulator are assumed to be uncertain. Moreover, unbounded disturbances, i.e., such structures of the modelling functions that are generally not bounded by construction, are allowed to act on the manipulator when tracking the trajectory by the end-effector. Based on suitably defined task space non-singular terminal sliding vector variable and the Lyapunov stability theory, we derive a class of absolutely continuous (chattering-free) robust controllers based on the estimation of a Jacobian transpose matrix, which seem to be effective in counteracting uncertain both kinematics and dynamics, unbounded disturbances and (possible) kinematic and/or algorithmic singularities met on the robot trajectory. The numerical simulations carried out for a 2DOF robotic manipulator with two revolute kinematic pairs and operating in a two-dimensional task space, illustrate performance of the proposed controllers.

Constraint finite-time control of redundant manipulators

Int. J. Robust. Nonlinear Control

2016

Summary This work addresses the problem of the accurate task‐space control subject to finite‐time convergence. 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 end effector. Furthermore, the movement is to be accomplished in such a way as to optimize some performance index. Based on suitably defined task‐space non‐singular terminal sliding vector variable and the Lyapunov stability theory, we derive a class of inverse‐free robust controllers consisting of a Jacobian transpose component plus a compensating term, which seem to be effective in counteracting uncertain dynamics, unbounded disturbances and (possible) kinematic singularities met on the robot trajectory. The numerical simulations carried out for a redundant manipulator of a Selective Compliant Articulated Robot for Assembly (SCARA) type consisting of three revolute kinematic pairs and operating in a two‐dimensional task space illustrate performance of the proposed controllers. Copyright © 2016 John Wiley & Sons, Ltd.