Research on Robust Task Space Control Uncertainty Based on Legendre Polynomial

Usually, the uncertainty bound is needed to design the control law in conventional robust control approaches. However, the proposed bound may increase the amplitude of the control signal and damage the system. To solve this problem, a robust control law is proposed in this paper. The uncertainty bound of the proposed control law is calculated by Legendre polynomials. Compared to conventional robust controllers, the proposed controller is simpler, less computational and requires less feedback. By a SCARA robot manipulator control law proposed simulation, the simulation results verify the effectiveness of the proposed control approach. Introduction In the past decades, the adaptive control and robust control of robot manipulators have been extensively studied in task space [1] and joint space [2]. Robust and adaptive control are considered important because they can overcome the uncertainty between the nominal model and the actual model due to mismatches. External disturbances, parametric uncertainties and unmodeled dynamic characteristics are the main sources of uncertainty in control engineering, and also seriously affect the performance of the controller. In the early studies of robust control methods [3], controller designs are often based on nominal models. A robust control term is then added to the control law to compensate for the uncertainty, which needs to be determined by the Lyapunov stability analysis. In these methods, uncertain boundaries need to be used to determine the stability of the system and to design the control law. Normally this boundary is the upper limit of the system state and external disturbance. Therefore, all required feedback should be available, and the upper limit of parameter uncertainty and external interference should be known in advance. In addition, the linear parameterization of the manipulator kinematics equation is necessary in most robust and adaptive control methods [4]. The controller motion equation should be modeled completely to determine the regression matrix. Most of the research in the field of robot control is based on the torque control strategy (TCS). But often TCS ignores the dynamic performance of the drive. To solve this problem, a simple and convenient voltage control strategy (voltage-based controller, VCS) was proposed. Voltage-based manipulator controller stability analysis has been studied [5]. Based on the VCS, scholars have proposed different robust control methods [6,7]. Recently, a number of adaptive control methods for regressions have been proposed [8], and the uncertainty has been estimated using the Fourier series. Based on the Lyapunov stability, some adaptive rules are deduced to adjust the Fourier series coefficients. According to [9], some other orthogonal functions, such as Legendre and Chebyshev polynomials, can be approximated to continuous time functions at arbitrary precision. In this paper, we use this idea to estimate the uncertain boundary of the Robot Task Space Control for the electrodynamic robot. Based on the above analysis, this paper presents a more simple method compared with the literature [10,11]. In this paper, the lumped uncertainty for each joint is estimated. Another 7th International Conference on Education, Management, Computer and Medicine (EMCM 2016) Copyright © 2017, the Authors. Published by Atlantis Press. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/). Advances in Computer Science Research, volume 59