Comparison of robot trajectory tracking efficiency using various nonlinear control methods

Abstract

The Denavit-Hartenberg algorithm and the Lagrange-Euler method are used to derive realistic kinematics and dynamic models of a three-axis electric driven articulated planar robot with viscous, dynamic and static frictions. These robot models are further used for testing the following presented nonlinear robot control methods: fuzzy control, variable-structure control and model-reference variable-structure control. In the fuzzy-logic control method seven fuzzy sets are defined for two input variables. Triangular input membership functions and the 7x7 fuzzy rule table are chosen. The fuzzy controller output value is calculated according to the centre of gravity principle. The same fuzzy control algorithm is used in all robot servo control loops with a proper scaling of the linguistic variables. To eliminate the chattering of the variable-structure control signal and to reduce energy consumption, sign function in the original variable-structure control law is replaced with the following functions: a continuous, saturation and exponential function, all of them with a very thin boundary layer. The same modifications are also made in the original model-reference variable-structure control method. In all presented control methods controller parameters are chosen according to the principle of maximal allowed tracking error and a minimum of energy consumption. These control methods are tested by computer simulations in C programming language in the case of moving the tool of the chosen robot arm. The simulation results proved similar efficiencies of all mentioned modified nonlinear robot control methods, although modified variable structure control algorithms are the most suitable because of their simplicity and lower number of controller parameters.