Sliding Mode Control Based on Synthesis of Approximating State Feedback for Robotic Manipulator

Abstract

In this paper, three paradigms are used to deal with a robot manipulator control problem. These paradigms are feedback linearization method, approximating control by Taylor truncation, and sliding mode approach. Robotic manipulator is highly nonlinear, highly time-varying, and highly coupled. In robotic manipulator there are many uncertainties such as dynamic parameters (eg., inertia and payload conditions), dynamical effects (e.g., complex nonlinear frictions), and unmodeled dynamics. The classical linear controllers have many difficulties in treating these behaviors. To overcome this problem, sliding mode control (SMC) has been widely used as one of the precise and robust algorithms. Application of traditional SMC in nonlinear system uses exact feedback linearization. Geometric differential theory is used to develop exact linearization transformation of nonlinear dynamical system, by using nonlinear cancellation and state variable transformation. Hence, the controller can be synthesized by using the standard sliding mode for linear system. The main weak point of the exact linearization is that its implementation is difficult. This study presents a synthesis SMC based on approximating state feedback for robotic manipulator control system. This approximating state feedback is derived from exact feedback linearization. Based on approximating state feedback, sliding mode controller is derived. The closed loop stability is evaluated by using the Lyapunov like theory.Keywords: Robotic manipulator, exact feedback linearization, approximating state feedback, sliding mode, Lyapunov like theory I. IntroductionRobots are ideal candidates for material handling operations, manufacturing, and measuring devices because of their capacity to pick up, move, and release an object, to manipulate both objects and tools and their capacity to explore the three dimensional space.Nowadays, robotic manipulator is extensively used in the industrial field. The desire of a high-speed or a high-precision performance for this kind of mechanical systems has led to research into improved control systems. These high performance control systems need, in general, the dynamical model of the robotic manipulator in order to generate the control input (Yurkovich, 1992).Robotic manipulator is highly nonlinear, highly time-varying, and highly coupled. Moreover, there always exists uncertainty in the system model such as external disturbances, parameter uncertainty, sensor errors and so on, which cause unstable performance in the robotic system (Sadati et al, 2005). Almost all kinds of robust control schemes, including the classical sliding mode control (SMC) (Yong, 1978), have been proposed in the field of robotic control during the past decades. SMC design provides a systematic approach to the problem of maintaining stability in the face of modeling imprecision and uncertainty. Application of traditional SMC in nonlinear system uses exact feedback linearization. The main weak point of the exact linearization is that its implementation is di...