A fuzzy learning algorithm for redundant manipulators using nonlinear programming

The fuzzy learning algorithm is a control algorithm which has been developed for the kinematic control of redundant robotic manipulators without any modelling of the manipulator itself. It is based on conventional kinematic control methods for manipulators combined with the techniques of fuzzy regression and fuzzy inferencing to learn the appropriate kinematic models based on actual trajectory data. In this paper, we modify the fuzzy regression formulation itself, which is a linear programming problem, to learn a fuzzy generalized inverse of the manipulator Jacobian, which is normally a non-unique matrix. However, we impose additional constraints in the fuzzy regression formulation, and modify the cost function to maximize the effect of the additional constraints, such that the matrix that is learned is one which optimizes the subtask as well as executing the main task of trajectory tracking. The modification of the cost function results in the fuzzy regression formulation being transformed into a nonlinear programming problem