Robot Manipulator Redundancy Resolution

Chapter 6Varying Joint-Velocity Limits Handled by QP

6.1 Introduction

Redundant manipulators can achieve subtasks readily and smartly such as generating cyclic motion [102–106], avoiding joint limits [36, 107], avoiding singularities [108–112], tolerating faults [113], avoiding obstacles [114–116], and optimization of multiple performance criteria [61, 92, 117–129] because they have more DOF than required to execute a desired primary task [61, 92]. Motion planning (or resolving the redundancy problem) of the manipulators is thus an appealing topic in the robotics area [36, 61, 92, 104]. The pseudoinverse-based approach is the conventional method for resolving the redundancy problem of the manipulators [130–133]. Research in the last decade [36, 61, 92, 104, 134, 135] shows that various online optimization strategies/techniques are preferred methods, and some of these optimization strategies are usually expressed as a quadratic program (QP), which is subject to equality and inequality constraints [61, 90]. Such a QP is then converted into linear variational inequality (LVI) [61, 128, 136], which may be solved approximately by many methods and techniques efficiently, such as numerical methods [136] and some types of neural networks (NNs) [36, 61, 92, 104, 137–139]. In [104], three recurrent NNs are applied to cyclic motion generation. In [61, 105, 106, 137–139], primal-dual NNs formulated in differential equations are used to solve various redundancy resolution problems. In [23], ...