In the past three decades, various optimization based redundancy-resolution schemes have been proposed and developed for the motion planning and control of robot manipulators. However, how to achieve optimal and efficient performance for the online motion planning of redundant manipulators is still a challenging problem, in which the study on performance indices is one of the most important issues. This book focuses on the combination of different performance indices and the relationship of different-level performance indices for redundancy resolution, which includes the studies of same-level bi-criteria resolution, equivalence of different-level (velocity-level and acceleration-level) resolution and mixed-level resolution. Moreover, quadratic programming and recurrent neural network are employed to solve the redundancy-resolution problem against the weaknesses of the traditional pseudo-inverse methods (e.g., being difficult to incorporate inequality constraints and high computational complexity). The book, as a fruitful memory of the authors’ robotics research, is intended primarily for researchers, engineers and postgraduates studying in robotics, neural networks, and so on.