Redundancy in robots is very much an open research area in the field of robotics. As the tasks required of robots become more and more complex, the ability of robots to perform satisfactorily in these applications must increase accordingly. Redundant manipulators have a greater ability to perform difficult tasks, such as obstacle avoidance, than non-redundant ones. In order to make use of this extra ability of redundant robots, more effective control schemes must continue to be developed and to this end, more and more researchers are looking to expand the body of knowledge in this area. This thesis addresses the problem of moving a redundant robot within a defined workspace in the presence of obstacles. Additionally, criteria are developed that may be applied to the robot to constrain the redundant equations. Finally, a neural network solution to the redundant inverse kinematic problem is presented. It will be shown that the inverse kinematics can be developed through a network architecture which provides accurate and fast solutions to a problem that is computationally and structurally complex. This effort will be kept within the context of already accepted methods currently in use for redundant robots, the overall goal of this research being to firmly establish the usefulness and applicability of neural network architectures to difficult robotic problems.