I. Introduction
Optimal control for robot manipulators plays a very important role in the research of robotics. It can be divided into two subproblems: the optimal trajectory planning (OTP); and the trajectory tracking and control (TTC). The latter leads robots to follow the control commands that are deduced by the former as closely as possible [1]. The trajectory tracking and control is relatively simple and can be achieved by adopting some existing approaches, such as sliding mode controller (SMC) [2], etc. However, since there are many complex constraint conditions concerning robot kinematics and dynamics, the corresponding algorithms for solving OTP problem have been improved in recent years. Therefore, we will focus our discussion on how to solve the OTP problem effectively in this paper.