Liu et al. / J Zhejiang Univ-Sci C (Comput & Electron) 2010 11(12):956-966 956 Saturated output feedback tracking control for robot manipulators via fuzzy self-tuning * Hua-shan LIU †1,2 , Shi-qiang ZHU †‡1 , Zhang-wei CHEN 1 ( 1 State Key Lab of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China) ( 2 College of Information Science and Technology, Donghua University, Shanghai 201620, China) † E-mail: watson683@163.com; sqzhu@zju.edu.cn Received Dec. 18, 2009; Revision accepted Apr. 12, 2010; Crosschecked Nov. 12, 2010 Abstract: This paper concerns the problem of output feedback tracking (OFT) control with bounded torque inputs of robot manipulators, and proposes a novel saturated OFT controller based on fuzzy self-tuning proportional and derivative (PD) gains. First, aiming to accomplish the whole closed-loop control with only position measurements, a linear filter is involved to generate a pseudo velocity error signal. Second, different from previous strategies, the arctangent function with error-gain is applied to ensure the boundedness of the torque control input, and an explicit system stability proof is made by using the theory of singularly perturbed systems. Moreover, a fuzzy self-tuning PD regulator, which guarantees the continuous stability of the overall closed-loop system, is added to obtain an adaptive performance in tackling the disturbances during tracking control. Simulation showed that the proposed controller gains more satisfactory tracking results than the others, with a better dynamic response performance and stronger anti-disturbance capability. Key words: Robot, Tracking systems, Bounded torque input, Fuzzy control, Output feedback doi:10.1631/jzus.C0910772 Document code: A CLC number: TP24 1 Introduction Recently, the issue of trajectory tracking control with bounded torque inputs has aroused increasing interest in robot motion control research, especially the output feedback tracking (OFT) control without velocity measurements (Loria and Nijmeijer, 1998; Santibanez and Kelly, 2001; Moreno-Valenzuela et al., 2008a). The first saturated OFT controller was proposed by Loria and Nijmeijer (1998), where the hyperbolic tangent function was invoked in the control law to ensure the boundedness of the torque input to each joint actuator of robot, while a nonlinear filter con- taining only the position error variable was applied to create a pseudo velocity error signal. The semi-global stability of the system was achieved by using suffi- ciently large observer gains, although the stability analysis was expressed in a rather complicated man- ner. This scheme exerted an important effect on sub- sequent research. Santibanez and Kelly (2001) made a supplementary development to this scheme by con- sidering the viscous friction in the robot joints, and proved that the global asymptotic stability can be assured if a large enough viscous friction damping is present. Moreno-Valenzuela et al. (2008a; 2008b) introduced the stability theory of singularly perturbed systems to make an explicit stability proof of the OFT controller and proposed a general expression of a class of saturated OFT controllers. Motivated by this, and based on the theory of singularly perturbed sys- tems, Liu and Zhu (2009) designed a more general- ized saturated OFT controller with a broader rela- tionship between the variable matrix and the error- gain matrix, and applied a linear filter to generate the ‡ Corresponding author * Project (No. 2008C21106) supported by the Science and Technology Foundation of Zhejiang Province, China © Zhejiang University and Springer-Verlag Berlin Heidelberg 2010 Journal of Zhejiang University-SCIENCE C (Computers & Electronics) ISSN 1869-1951 (Print); ISSN 1869-196X (Online) www.zju.edu.cn/jzus; www.springerlink.com E-mail: jzus@zju.edu.cn