The Synthesis of Kinematic Structure of Robotic Manipulators

Abstract

This dissertation thesis deals with the topic of synthesis of kinematic structures of serial robotic manipulators. Beside a solution to this problem, it provides a state-of-the-art and a brief theoretical background on the topic, and an analysis of robotics and optimization toolboxes in MATLAB software, which is later used for implementation. Two preliminary tasks were solved prior to the description of the synthesis algorithm itself. First, an analytical method is presented that determines the kinematic structure of a robot for a single pose. It serves as an initial estimation of the kinematic structure and avoids randomness in the optimization process. Due to that, comparison of the performance of various robot kinematic representations and optimization constraint design methods is possible. The second preliminary task deals with automatic conversion between three selected kinematic representations: Denavit--Hartenberg convention, Tait--Bryan (roll-pitch-yaw) angles parameters with translational displacement of XYZ axes, and Product of Exponentials representation. The synthesis algorithm itself applies numerical optimization techniques to search for the local minimum of a function. It brings innovation such as the implementation of multiple representations, multiple constraint design methods, and most importantly, the possibility of combining results with each other, which was shown to significantly increase the quality of the results. In addition, a performance comparison of representations and constraint design methods is provided and discussed. In summary, the choice of representation and constraint design method has a strong impact on the output. The last part of the thesis presents a method for placing physical joints of a synthesized manipulator in positions where no collisions within a given environment appear. An experimental manipulator is designed, assembled, and proven to perform a given task.