In this master's thesis, we will explore how to control a redundant robotic mechanism. We will begin by providing some definitions to describe what a redundant robotic mechanism is. Further we will explain that there are two essential spaces for a redundant robotic mechanism, which we will also mathematically describe. The first space pertains to the joints, while the second space relates to the tasks the mechanism is intended to perform. We will introduce the fundamental equation that describes how to map from the joint space to the task space, known as the direct kinematic equation. Additionally, we will learn about rotation matrices and discuss three approaches for generating them. Furthermore, we will proceed with a section dedicated to the inverse kinematic equation, which relates to the mapping from the task space back to the joint space. Inverse kinematics enables us to control a redundant robotic mechanism. In a second part of the thesis, we will define problems that we aim to solve and illustrate with examples how to solve them. To deepen the understanding, we will initially explore examples in a two-dimensional space, and subsequently, we will investigate solutions in a three-dimensional space, which we will implement also on an actual robot for practical application.
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