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