An Extension to Fuzzy Qualitative Trigonometry and Its Application to Robot Kinematics

Abstract

We propose an extension of fuzzy qualitative trigonometric derivatives to fuzzy qualitative trigonometry (FQT). First, we revisit fuzzy qualitative trigonometry, and then derive its derivative extension. Next, we replace the trigonometry role in robot kinematics using FQT and the proposed extension, which leads to a general version of robotic kinematics. Fuzzy qualitative transformation, position and velocity of a robot are derived and discussed. Finally, we highlight the impact of the proposed methods to robotics, especially the issue of closing the gap between low-level sensing & control tasks and symbolic cognitive functions, which is one of key open problems for AI robotics [1]. Simulation results are provided to support the theoretical improvement.