Robust Control Design for Two-link Nonlinear Robotic System

Abstract

A good performance of robot control requires the consideration of efficient dynamic models and sophisticated control approaches. Traditionally, control law is designed based on a good understanding of system model and parameters. Thus, a detailed and correct model of a robot manipulator is needed for this approach [1, 2]. A two-link planar nonlinear robotic system is a well-used robotic system, e.g., for welding in manufacturing and so on. Generally, a dynamic model can be derived from the general Lagrange equation method. The modeling of a two-link planar nonlinear robotic system with assumption of only masses in the two joints can be found in the literature, e.g., [3, 4]. Here, the authors revise centrifugal and Coriolis force matrix in the literature [3, 4] as pointed out in the next section. Furthermore, in practice, the robot arms have their mass distributed along their arms, not only masses in the joints as assumed. Thus, it is desired to develop a detailed model for two-link planar robotic systems with the mass distributed along the arms. Distributed mass along robot arms was discussed by inertia in SCARA robot [5]. Here, we present a new detailed consideration of any mass distributions along robot arms in addition to the joint mass. Moreover, it is also necessary to consider numerous uncertainties in parameters and modeling. Thus, robust control, robust adaptive control and learning control become important when knowledge of the system is limited. We need robust stabilization of uncertain robotic systems and furthermore robust performance of these uncertain robotic systems. Robust stabilization problem of uncertain robotic control systems has been discussed in [1-3, 5-6] and many others. Also, adaptive control methods have been discussed in [1, 7] and many others. Because the closed-loop control system pole locations determine internal stability and dominate system performance, such as time responses for initial conditions, papers [6, 8] consider a robust pole clustering in vertical strip on the left half splane to consider robust stability degree and degree of coupling effects of a slow subsystem (dominant model) and the other fast subsystem (non-dominant model) in a two-time-scale system. A control design method to place the system poles robustly within a vertical strip has been discussed in [6, 8-10], especially [6] for robotic systems. However, as mentioned 27