Perfect position/force tracking of robots with dynamical terminal sliding mode control

According to a given performance criteria, perfect tracking is defined as the performance of zero tracking error in finite time. It is evident that robotic systems, in particular those that carry out compliant task, can benefit from this performance since perfect tracking of contact forces endows one or many constrained robot manipulators to interact dexterously with the environment. In this article, a dynamical terminal sliding mode controller that guarantees tracking in finite-time of position and force errors is proposed. The controller renders a dynamic sliding mode for all time and since the equilibrium of the dynamic sliding surface is driven by terminal attractors in the position and force controlled subspaces, robust finite-time convergence for both tracking errors arises. The controller is continuous; thus chattering is not an issue and the sliding mode condition as well the invariance property are explicitly verified. Surprisingly, the structure of the controller is similar with respect to the infinite-time tracking case, i.e., the asymptotic stability case, and the advantage becomes more evident because terminal stability properties are obtained with the same Lyapunov function of the asymptotic stability case by using more elaborate error manifolds instead of a more complicated control structure. A simulation study shows the expected perfect tracking and a discussion is presented.

[1]  Danwei Wang,et al.  Variable structure adaptive motion and force control of robot manipulators , 1994, Autom..

[2]  Kuang-Yow Lian,et al.  Sliding-mode motion/force control of constrained robots , 1998 .

[3]  Suguru Arimoto,et al.  A passivity-based adaptive sliding mode position-force control for robot manipulators , 1996 .

[4]  Chun-Yi Su,et al.  Force/motion control of constrained robots using sliding mode , 1992 .

[5]  Pushkin Kachroo,et al.  Existence of solutions to a class of nonlinear convergent chattering-free sliding mode control systems , 1999, IEEE Trans. Autom. Control..

[6]  Zhihua Qu,et al.  Robust control of robot manipulators during constrained and unconstrained motion , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[7]  Vadim I. Utkin,et al.  Adaptive simulation and control of variable-structure control systems in sliding regimes , 1996, Autom..

[8]  Suguru Arimoto,et al.  Adaptive model-based hybrid control of geometrically constrained robot arms , 1997, IEEE Trans. Robotics Autom..

[9]  G. Bartolini,et al.  Chattering avoidance by second-order sliding mode control , 1998, IEEE Trans. Autom. Control..

[10]  Danwei Wang,et al.  Vsc motion and force control of robot manipulators in the presence of environmental constraint uncertainties , 1994, J. Field Robotics.

[11]  J. Slotine,et al.  On the Adaptive Control of Robot Manipulators , 1987 .

[12]  Nikos A. Aspragathos,et al.  Sliding mode with adaptive estimation force control of robot manipulators interacting with an unknown passive environment , 1999, Robotica.

[13]  Suguru Arimoto,et al.  Model-based adaptive hybrid control for robot manipulators under holonomic constraints , 1994 .

[14]  Hariharan Krishnan,et al.  Tracking in nonlinear differential-algebraic control systems with applications to constrained robot systems , 1994, Autom..

[15]  Oussama Khatib,et al.  A unified approach for motion and force control of robot manipulators: The operational space formulation , 1987, IEEE J. Robotics Autom..

[16]  U. Ascher,et al.  Stabilization of Constrained Mechanical Systems with DAEs and Invariant Manifolds , 1995 .

[17]  D. E. Whitney,et al.  Historical Perspective and State of the Art in Robot Force Control , 1987 .

[18]  Hongnian Yu,et al.  Combined Direct and Indirect Adaptive Control of Constrained Robots , 1997 .

[19]  Vicente Parra Vega Adaptive sliding mode control for robot manipulators , 1995 .

[20]  Yunhui Liu,et al.  Adaptive and Nonadaptive Hybrid Controllers for Rheonomically Constrained Manipulators , 1998, Autom..

[21]  S. Bhat,et al.  Continuous finite-time stabilization of the translational and rotational double integrators , 1998, IEEE Trans. Autom. Control..

[22]  W. Schiehlen,et al.  A projective criterion to the coordinate partitioning method for multibody dynamics , 1994, Archive of Applied Mechanics.

[23]  Vadim I. Utkin,et al.  A control engineer's guide to sliding mode control , 1999, IEEE Trans. Control. Syst. Technol..

[24]  Romeo Ortega,et al.  Passivity-based Control of Euler-Lagrange Systems , 1998 .

[25]  Jing Yuan Adaptive control of a constrained robot - ensuring zero tracking and zero force errors , 1997, IEEE Trans. Autom. Control..

[26]  N. H. McClamroch,et al.  Feedback stabilization and tracking of constrained robots , 1988 .

[27]  Richard P. Paul,et al.  Resolved Motion Force Control of Robot Manipulator , 1982, IEEE Transactions on Systems, Man, and Cybernetics.

[28]  H. Sira-Ramírez On the dynamical sliding mode control of nonlinear systems , 1993 .

[29]  G. Hirzinger,et al.  TBG SLIDING SURFACES FOR PERFECT TRACKING OF ROBOT MANIPULATORS , 2000 .

[30]  Ag Bram de Jager,et al.  The slippery road to sliding control: conventional versus dynamical sliding mode control , 1998 .

[31]  Michail Zak,et al.  Terminal attractors in neural networks , 1989, Neural Networks.

[32]  Marco Gori,et al.  Terminal attractor algorithms: A critical analysis , 1997, Neurocomputing.

[33]  H. Khalil,et al.  Stability analysis of a continuous implementation of variable structure control , 1991 .

[34]  Yuri B. Shtessel Nonlinear output tracking in conventional and dynamic sliding manifolds , 1997, IEEE Trans. Autom. Control..

[35]  Lyubomir T. Gruyitch,et al.  Robot control for robust stability with finite reachability time in the whole , 1999 .

[36]  Zhihong Man,et al.  Multi-input uncertain linear systems with terminal sliding-mode control , 1998, Autom..

[37]  Hong Ren Wu,et al.  A robust MIMO terminal sliding mode control scheme for rigid robotic manipulators , 1994, IEEE Trans. Autom. Control..

[38]  Peilin Song,et al.  Principles for design of position and force controllers for robot manipulators , 1997, Robotics Auton. Syst..

[39]  Yu Tang,et al.  Terminal sliding mode control for rigid robots , 1998, Autom..

[40]  Xinghuo Yu,et al.  Terminal sliding mode control design for uncertain dynamic systems , 1998 .