Application of the fuzzy learning algorithm to kinematic control of a redundant manipulator with subtask optimization

Abstract

The authors previously introduced the fuzzy learning control algorithm as a method of trajectory tracking control for robotic systems, based on conventional kinematic control methods but utilizing fuzzy regression to eliminate the need for modelling the kinematic equations of the manipulator. In this paper, the authors extend the algorithm to the case of redundant manipulators, i.e. manipulators which have more joints then degrees of freedom in which they can move. The redundant case presents additional challenges not found in the non-redundant case, namely, a kinematic equation which must be solved using least squares as opposed to matrix inversion, and the incorporation of subtask optimization for the utilization of the redundant degrees of freedom. The authors address these challenges by once again determining the main task, i.e. the rank solution using fuzzy regression to determine a fuzzy Jacobian matrix, and by determining a fuzzy performance index for subtask optimization using fuzzy inferencing. A simulation study is performed using a three joint planar manipulator, with singularity avoidance as the subtask. The results show that the extended fuzzy learning control algorithm causes the manipulator to satisfactorily follow the desired trajectory while keeping its configuration far from singularities. Moreover, it does so without being supplied any explicit model of the kinematics or the performance index. The former it learns through fuzzy regression, while the latter it possesses in the form of a fuzzy rule base. The disadvantages and areas of future investigation for this extension of fuzzy learning control are also discussed in this paper. >