6 Varying Joint-Velocity Limits Handled by QP Available to Purchase

Redundant manipulators can achieve subtasks readily and smartly such as generating cyclic motion, avoiding joint limits, avoiding singularities, tolerating faults, avoiding obstacles, and optimization of multiple performance criteria because they have more DOF than required to execute a desired primary task. Motion planning (or resolving the redundancy problem) of the manipulators is thus an appealing topic in the robotics area. The pseudoinverse-based approach is the conventional method for resolving the redundancy problem of the manipulators. Research in the last decade 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. Such a QP is then converted into linear variational inequality (LVI), which may be solved approximately by many methods and techniques efficiently, such as numerical methods and some types of neural networks (NNs). 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], another NN, called zeroing dynamics, is used to solve the time-varying problem. In this chapter, for implementing the scheme on the digital computer and physical hardware system more readily, a numerical algorithm formulated in a difference equation is adopted to solve the QP.