Trajectory Tracking Control of an Unconstrained Object by SIRMs Dynamically Connected Fuzzy Inference Model

Abstract

Since unconstrained moving objects are sensitive to circumstance change and their moving velocity can not be handled directly, their trajectory tracking control is considered to be a difficult problem. In this paper, a trajectory tracking experiment system taking an official table-tennis ball as its control object is constructed, and a fuzzy controller based on the recently proposed SIRMs dynamically connected fuzzy inference model is presented. The estimated tracking error, velocity and acceleration of the ball are selected as the input items of the fuzzy controller. For each input item, a SIRM (Single Input Rule Module) is designed and an importance degree is assigned. Especially for the input item corresponding to the velocity, its importance degree is allowed to change with the moving situation. The summation of the products of the importance degree and the fuzzy inference result of the SIRMs is outputted to control the angle of a table with level surface, making the ball on the table move along a desired trajectory. In order for the ball in any position to smoothly approach and stably track a trajectory, asymptotic trajectory from its current position to the real trajectory is introduced. Experiments are done for desired trajectories of three kinds of circles and one kind of ellipses. In more than 80% of the experiments, the biggest tracking error is less than 0.05m despite of different sizes and different kinds of desired trajectories, and the unevenness of sampling steps necessary for one cycle of the trajectories is very small. All the results show that the unconstrained ball can stably and accurately track the desired trajectories under the proposed control scheme.