Kinematic Control of Redundant Robot Arms Using Neural Networks

2Adaptive Dynamic Programming Neural Networks for Control

2.1 Introduction

With the development of mechatronics, automatic systems consisting of sensors for perception and actuators for action are being more and more widely used [17]. Besides the proper choices of sensors and actuators and an elaborate fabrication of mechanical structures, the control law design also plays a crucial role in the implementation of automatic systems especially for those with complicated dynamics. For most mechanical sensor–actuator systems, it is possible to model them in Euler–Lagrange equations [17]]. In this chapter, we are concerned with the sensor–actuator systems modeled by Euler–Lagrange equations.

Due to the importance of Euler–Lagrange equations in modeling many real sensor–actuator systems, much attention has been paid to the control of such systems. According to the type of constraints, the Euler–Lagrange system can be categorized as a Euler–Lagrange system without nonholonomic constraints (e.g. fully actuated manipulator [18], omni‐directional mobile robot [19]), the under‐actuated multiple body system. For a Euler–Lagrange system without nonholonomic constraints, the input dimension are often equal to the output dimensions and the system is often able to be transformed into a double integrator system by employing feedback linearization [20]. Other methods, such as the control Lyapunov function method, passivity‐based method, and optimal control method are also successfully applied ...