The aim of this thesis is to present various methods used for solving the differential inverse kinematics problem in the case if the manipulator is a serial redundant robotic arm and study the properties of these methods. For a redundant manipulator the inverse kinematics has infinite solutions, thus solving this problem is a complex task with a lot of challenges.
Methods for constructing the kinematic model of a serial robotic arm are presented. The thesis uses the product of exponentials formula in further discussion. Mostly the explicit Euler method is used for numerical integration.
There are three main problems discussed: when a control strategy is repeatable and how to make a repeatable control strategy, what the conditions for an algorithm to be stable are and how to improve the convergence of an algorithm.
First, the Lie-bracket condition and its usability in the repeatability analysis is discussed, then a method for making a control strategy to be repeatable is presented. After that a convergence analysis method is detailed, the conditions for an algorithm to be stable are discussed and a simulation presents what happens when these conditions are not fulfilled. At last, the implicit Euler method is presented along with the usability of the implicit methods in robotics and the Crank-Nicolson method. The convergence of the various algorithms is compared in various situations by simulations.
Robot models and algorithms used for the simulations are implemented in MATLAB environment.