Minimum-time sliding mode control of robot manipulators

Abstract

Robot manipulators have a complex and highly nonlinear dynamics, accompanied with a high degree of uncertainty. These properties make them difficult for time-optimal control. The theory of sliding mode control can provide methods, able to cope with the uncertainty and nonlinearity in the system. However, besides the chattering problem it does not provide time-optimal behavior. The optimal control theory provides the appropriate design methodology for minimum-time control, but the designed system lacks robustness. In this thesis we combine these two approaches to obtain new control techniques, which have the robust properties of the sliding mode control and a performance, close to the time-optimal control. Two methods for minimum-time sliding mode control based on the concept of maximum slope sliding line are developed with a theoretical proof of their properties. In the time-optimal sliding mode control we prove that the time-optimal switching line of a simple linear system (double integrator) can be used as a sliding surface for a complex second order nonlinear system (robot manipulator) if the control gain is sufficiently high. Optimal performance is achieved by scaling the surface in such way that the maximum control action is efficiently used. The fuzzy minimum-time sliding mode control is developed employing a Takagi-Sugeno fuzzy model for the sliding surface. We demonstrate that designs, based on a single sliding line tend to be conservative, due to the nonlinearities in the robot's dynamics. The Takagi-Sugeno model represents the maximum slope sliding lines for different values of the joint angles taking into account the variation in the gravity and inertia terms. This gives a convenient way to provide adaptation and incorporate additional knowledge in the controller design. Design procedures for all the methods are developed and evaluated in simulation and in experiments with real robot manipulators.