Randy A. Graca

A fuzzy learning algorithm for kinematic control of a robotic system

In this paper, a new control algorithm called fuzzy learning control is proposed as a method of trajectory tracking control for a robotic system. Fuzzy learning control is an extension of differential motion control which utilizes the robotic Jacobian equations. The principles of fuzzy set theory and fuzzy regression analysis are applied to these kinematic equations. This is accomplished by treating the inverse of the Jacobian matrix as a matrix of fuzzy numbers, subsequently transforming the kinematic equations of the manipulator into a linear possibility system with fuzzy coefficients, which is solved for the fuzzy coefficients using fuzzy regression. In this way, the fuzzy Jacobian inverse is found and used to update the desired joint positions on each sampling interval. The algorithm is augmented with a PD type control law to guarantee convergence to the desired trajectory. A simulation study is performed using the 6-joint Stanford Arm. The results show that the fuzzy learning control augmented with a PD control law can converge to the desired trajectory. More significantly, it does so without the need for modeling the robotic kinematics, as would normally be required for differential motion control. Some disadvantage of the fuzzy learning control algorithm and the future work for improvement are also addressed in the paper.<<ETX>>

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.<<ETX>>