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

2016 ◽  
Vol 85 (3-4) ◽  
pp. 471-489 ◽  
Author(s):  
Mirosław Galicki
Keyword(s):  
Finite Time ◽  
Lyapunov Stability Theory ◽  
Robotic Manipulator ◽  
Task Space ◽  
Absolutely Continuous ◽  
Finite Time Convergence ◽  
Robot Trajectory ◽  
Vector Variable ◽  
Chattering Free ◽  
Task Space Control

AbstractThis 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.

scholarly journals Robust Task Space Trajectory Tracking Control of Robotic Manipulators

2016 ◽  
Vol 21 (3) ◽  
pp. 547-568 ◽  
Author(s):  
M. Galicki
Keyword(s):  
Trajectory Tracking ◽  
Lyapunov Stability Theory ◽  
Task Space ◽  
Redundant Manipulator ◽  
Trajectory Tracking Control ◽  
Finite Time Convergence ◽  
Robot Trajectory ◽  
Vector Variable ◽  
Control Schemes ◽  
Chattering Free

Abstract This work deals with the problem of the accurate 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 end-effector. Furthermore, the movement is to be accomplished in such a way as to reduce 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 propose a class of chattering-free robust 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.

scholarly journals Kinematically Optimal Robust Control of Redundant Manipulators

2017 ◽  
Vol 22 (4) ◽  
pp. 839-865
Author(s):  
M. Galicki
Keyword(s):  
Lyapunov Stability Theory ◽  
Redundant Manipulators ◽  
Task Space ◽  
Redundant Manipulator ◽  
Finite Time Convergence ◽  
Robot Trajectory ◽  
Vector Variable ◽  
Optimal Controllers ◽  
Control Schemes ◽  
Chattering Free

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.

scholarly journals Adaptive Fuzzy High-Order Super-Twisting Sliding Mode Controller for Uncertain Robotic Manipulator

2017 ◽  
Vol 26 (4) ◽  
pp. 697-715 ◽  
Author(s):  
Ankur Goel ◽  
Akhilesh Swarup
Keyword(s):  
Lyapunov Stability ◽  
Finite Time ◽  
Fuzzy Systems ◽  
Sliding Mode ◽  
Lyapunov Stability Theory ◽  
Robotic Manipulator ◽  
Sliding Mode Controller ◽  
Sliding Surface ◽  
Adaptive Fuzzy ◽  
Finite Time Convergence

AbstractThis paper presents a novel adaptive fuzzy high-order super-twisting sliding mode controller, based on the modified super-twisting control (STC), to achieve accurate trajectory tracking for a robotic manipulator with unknown structured uncertainties, parametric uncertainties, and time-varying external disturbances. Initially, a non-linear homogeneous sliding manifold is designed to achieve finite-time convergence, better robustness, and good transient characteristics. Afterwards, conventional STC is modified with the new sliding surface that eliminates the limitation of STC application only on relative degree 1 systems. Moreover, two adaptive fuzzy systems are designed to replace the STC signals for handling the chattering problem and overestimating the controller gains. These fuzzy systems are continuously adjusted by two adaptation laws that are deduced from the Lyapunov stability theory. These adaptive laws need only a sliding surface variable as an input and generate the optimal controller gains as an output. The finite-time convergence and stability of the proposed controller is analyzed by the homogeneous Lyapunov stability theory. Finally, to show the efficacy of the proposed method, the controller is simulated on a 2-degree-of-freedom planar robotic manipulator to obtain the accurate trajectory tracking. Simulation results demonstrate the superiority of the proposed control scheme in the presence of structured and unstructured uncertainties.

Super-twisting integral-sliding-mode guidance law considering autopilot dynamics

2017 ◽  
Vol 232 (9) ◽  
pp. 1787-1799 ◽  
Author(s):  
Kezi Meng ◽  
Di Zhou
Keyword(s):  
Finite Time ◽  
Disturbance Observer ◽  
Sliding Mode ◽  
Lyapunov Stability Theory ◽  
Guidance System ◽  
Integral Sliding Mode ◽  
Finite Time Stability ◽  
Guidance Law ◽  
Chattering Free ◽  
Twisting Algorithm

A new guidance law considering missile autopilot dynamics is established via integrating a smooth super-twisting algorithm with nonlinear integral sliding mode. In this guidance law, a finite-time disturbance observer is introduced to estimate mismatched and matched disturbances resulting from target maneuvers. Based on Lyapunov stability theory, the finite-time stability of the closed-loop guidance system under this law is analyzed using a finite-time bounded function. The super-twisting algorithm guarantees that the proposed guidance law is chattering-free and the disturbance observer does not depend on the prior knowledge of target acceleration. So the proposed guidance law is easy to be implemented in practice. The finite-time convergence and robustness of the proposed guidance law are demonstrated via numerical simulations accounting for missile autopilot dynamics.

Robust adaptive attitude manoeuvre control with finite-time convergence for a flexible spacecraft

2016 ◽  
Vol 40 (2) ◽  
pp. 425-435 ◽  
Author(s):  
Chenxing Zhong ◽  
Liping Wu ◽  
Jian Guo ◽  
Yu Guo ◽  
Zhiyong Chen
Keyword(s):  
Finite Time ◽  
Sliding Mode ◽  
Coupling Effect ◽  
Lyapunov Stability Theory ◽  
Flexible Spacecraft ◽  
Practical Case ◽  
External Disturbances ◽  
Terminal Sliding Mode ◽  
Chattering Free ◽  
Robust Adaptive

This paper investigates a finite-time attitude manoeuvre control problem for a flexible spacecraft subject to bounded external disturbances. A robust discontinuous finite-time controller with terminal sliding mode control is designed to solve this problem provided that the disturbances and the coupling effect of flexible modes are bounded with a known boundary. The controller is further enhanced by an adaptive scheme to deal with the more practical case that the boundary is unknown. The enhanced version is continuous and chattering-free. The results are rigorously proved using the Lyapunov stability theory. The effectiveness and robustness of the proposed controllers are demonstrated by numerical simulation.

Task space control of mobile manipulators

Robotica ◽  
2010 ◽  
Vol 29 (2) ◽  
pp. 221-232 ◽  
Author(s):  
Mirosław Galicki
Keyword(s):  
State Constraints ◽  
Lyapunov Stability Theory ◽  
Mobile Manipulator ◽  
Mobile Manipulators ◽  
Minimal Energy ◽  
Task Space ◽  
End Effector ◽  
Task Space Control ◽  
Simulation Results ◽  
Penalty Function Approach

SUMMARYThis study offers the solution of the end-effector trajectory tracking problem subject to state constraints, suitably transformed into control-dependent ones, for mobile manipulators. Based on the Lyapunov stability theory, a class of controllers fulfilling the above constraints and generating the mobile manipulator trajectory with (instantaneous) minimal energy, is proposed. The problem of manipulability enforcement is solved here based on an exterior penalty function approach which results in continuous mobile manipulator controls even near boundaries of state constraints. The numerical simulation results carried out for a mobile manipulator consisting of a non-holonomic unicycle and a holonomic manipulator of two revolute kinematic pairs, operating in a two-dimensional task space, illustrate the performance of the proposed controllers.

Adaptive path-constrained control of a robotic manipulator in a task space

Robotica ◽  
2006 ◽  
Vol 25 (1) ◽  
pp. 103-112 ◽  
Author(s):  
Mirosław Galicki
Keyword(s):  
Degrees Of Freedom ◽  
Path Following ◽  
Lyapunov Stability Theory ◽  
Robotic Manipulator ◽  
Task Space ◽  
End Effector ◽  
State Dependent ◽  
Control Scheme ◽  
Robot Task ◽  
Three Degrees Of Freedom

This study addresses the problem of adaptive controlling of both a nonredundant and a redundant robotic manipulator with state-dependent constraints. The task of the robot is to follow a prescribed geometric path given in the task space, by the end-effector. The aforementioned robot task has been solved on the basis of the Lyapunov stability theory, which is used to derive the control scheme. A new adaptive Jacobian controller is proposed in the paper for the path following of the robot, with both uncertain kinematics and dynamics. The numerical simulation results carried out for a planar redundant three-DOF (three degrees of freedom) manipulator whose end-effector follows a prescribed geometric path given in a two-dimensional (2D) task space, illustrate the trajectory performance of the proposed control scheme.

Sign in / Sign up

Export Citation Format

Share Document