A fuzzy approximation to the Jacobian condition number

This paper presents a method to approximate the Jacobian condition number based on computational intelligence methods by training a fuzzy system. To start with, a brief overview of the concept of robotic isotropy and the use of Jacobian norms to characterize the dexterity of a robot is presented. Then, the computational cost of the condition number is shown for both the l2-norm and the Frobenius norm. A fuzzy system is then trained with an input of the robot’s configuration and an output of the condition number. The calculation of the output of a fuzzy system is a simple task, with a computational cost depending to the number of rules and membership functions. The success of the method is examined and the results are presented. Lastly, topics for further research are discussed as well as examples for the use of this method.