Variable Structure Tracking Control of Robot Manipulator in Task Space in the Presences of Structure and Unstructured Uncertainties in Dynamics and Kinematics

Abstract

In most of the researches which has been conducted until now on the robot manipulator tracking control, it has been presumed which the kinematic of robot manipulator or Jacobian Matrix of robot from the joint space to the task space is quite known. However, none of the physical parameters in robot manipulator equations can be calculated by high accuracy. In addition, when the robot manipulator moves something, uncertainties occur in length, direction and point of contact of end-effector. Hence, uncertainties occur on the kinematic of robot manipulator either, and due to the different functions of the robot manipulator, its kinematic is changed as well. Therefore, ensuring stability of the closed-loop system in the presence of uncertainties in the dynamics and kinematics of robot manipulator is quite challenging. In this paper, for overcoming on these uncertainties, we present our simple robust control for tracking the position of robot manipulator in the presence of uncertainties in the dynamics kinematics and Jacobian Matrix of the robot manipulator. The proving of the stability shows the closed-loop system has Global asymptotic stability. Then, to overcome the practical problems of proposed control, amendments will be provided. The closed loop system with improved control has limited uniform stability. Since in many of the operations has been performed by the robot manipulator, transient error plays an important role. Due to this reason, the modified control structure is a changed in a way which could improve the transient error. Finally, for displaying the function of the final controller, a case study is implemented on a two-link elbow robot. Mathematical proof and simulation results confirm the good performance of the proposed control.

Keywords

References

[1] Hollerbach JM (1980) A recursive lagrangian formulation of manipulator dynamics and a comparative study of dynamics formulation complexity. IEEE Trans On Sys; Man and Cyb. 10(2): 123–135.
[2] Luh JYS, Walker MH, Paul RP (1980) On–line computational scheme for mechanical manipulator. Jour Dyn Sys Meas Cont. 102(5): 69–76.
[3] Takegaki M , Arimoto S (1981) A new feedback method for dynamic control of  manipulators. Jour Dyn Sys Meas Cont. 102(3): 119–125.
[4] Arimoto S, Miyazaki F (1985) Asymptotic stability of feedback control for robot manipulators. Proc IFAC Symp Rob Cont Spa.: 447–452.
[5] Arimoto S (1996) Control theory of nonlinear mechanical systems; A passivity based and circuit theoretic approach. 1th edn, Oxford, U.K.
[6] Shafiei SE, Soltanpour MR (2009) Robust neural network control of electrically driven robot manipulator using backstepping  approach. Inter Jour of Adv Rob Sys. 6(4): 285–292.
[7] Shafiei SE, Soltanpour MR (2011) Neural network sliding–model–PID controller design for electrically driven robot manipulators. Inter Jour of Inno Comp Infor and Cont. 5(12): 3949–3960.
[8] Fateh MM, Soltanpour MR (2009) Robust task-space control of robot manipulators under imperfect transformation of control space. Inter Jour of Inno Comp Infor and Cont. 5(12): 3949–3960.
[9] Soltanpour MR, Siahi M. (2009) Robust control of robot manipulator in task space. App and Comp Math. 8(2): 227–238.
[10] Soltanpour MR, Shafiei SE (2009) Robust backstepping control of robot manipulator in task space with uncertainties in kinematics and dynamics. Inter Jour of elec and elec eng. 96(8): 75–80.
[11] Soltanpour MR, Shafiei SE (2010) Robust adaptive control of manipulators in the task space by dynamical partitioning approach. Inter. Jour of  elec and elec eng. 101(5): 73–78.
[12] Soltanpour MR, Shafiei SE (2010) Design and stability analysis of a robust impedance control system for a robot manipulator. Stud in Info and Cont. 19(1): 5–16.
[13] Soltanpour MR, Fateh MM (2009) Sliding mode robust control of robot manipulator in the task space by support of feedback linearization and backStepping control. Worl App Sci Jour. 6(1): 70–76.
[14] Soltanpour MR, Fateh MM (2009) Adaptive robust tracking control of robot manipulators in the task–space under uncertainties. Aus Jour  of Bas and App Sci. 3(1): 308–322.
[15] Dixon WE (2004) Adaptive regulation of amplitude limited robot manipulators with uncertain kinematics and dynamics. Proc of Amer Cont Conf.: 3844–3939.
[16] Cheah CC, Hirano M, Kawamura S, Arimoto S (2003) Approximate Jacobian control for robots with uncertain kinematics and dynamics. IEEE Trans Of Rob Auto.  19(4): 692–702.
[17] Cheah CC, Kawamura S, Arimoto S (1999) Feedback control for robotic manipulator with an uncertain Jacobian matrix. Jour of Rob Sys. 16(2): 119–134.
[18] Cheah CC, Kawamura S, Arimoto S (2003) Stability of hybrid position and force control for robotic manipulator with uncertain kinematics and dynamics. Automatica 39(5): 847–855.
[19] Cheah CC, Han H, Kawamura S, Arimoto S (1998) Grasping and position control of multi-fingered robot hands with uncertain jacobian matrices.Proc IEEE Inter Conf of  Rob Auto Belgium: 2403–2408.
[20] Cheah CC, Liu C, Slotine JJE (2006) Adaptive Jacobian tracking control of robots with uncertainties in kinematic, Dynamic and Actuator Models. IEEE Trans on Auto Cont. 51(6): 323-335.
[21] Cheah CC, Liu C, Slotine JJE (2005) Adaptive Jacobian tracking control of robots based on visual task–space information. Proc IEEE Inter Conf of Rob Auto Amer: 3509–3514.
[22] Cheah CC, Liu C, Slotine JJE (2004) Approximate Jacobian adaptive control for robot manipulators. Proc IEEE Inter Conf of Rob Auto Amer: 3075–3080.
[23] Qu Z, Dawson D (1996) Robust tracking control of robot manipulators, 1th edn,  IEEE Press, New York.
[24] Spong MW, Hutchinson S, Vidyasagar M (2006) Robot modeling and control, 1th edn, Wiley, New York.
Journal of Solid and Fluid Mechanics
Volume 1, Issue 1 - Serial Number 1
September and October 2011
Pages 81-88

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