The design and control of uncertain manipulator arms with decoupled inertia matrix.

摘要

The complexity and nonlinearity of manipulator arm dynamics, as well as the existence of uncertainties during the manufacture and operation of the arms make their control very difficult, especially their on-line control. Thus, making every effort to ease the control burden becomes the motivation of this research work. The thesis can be divided into three parts: structural design, controller design and a design example.; Reducing the model complexity through structural design is a fundamental method. The thesis introduces the standard form of the transmission and the concept of time-invariant transmission. Then, the transmission for n-link spatial arms is designed such that the inertia matrix of their model can be decoupled. Based on this transmission, the necessary and sufficient conditions for the inertia matrix to be decoupled are given. Finally, these results are extended to cover closed-loop arms.; One promising way to handle uncertainties in plants is {dollar}Hsb{lcub}infty{rcub}{dollar} control and {dollar}mu{dollar} synthesis, but the theory is only applicable to linear, time-invariant systems. The thesis first extends feedback linearization technique to deal with uncertain nonlinear model of manipulator arms. The upper bounds for the nonlinear uncertainties are computed based on assumed command trajectories. Then, it shows the formulation of the tracking problem ready for {dollar}mu{dollar} controller design.; Since the method to design a {dollar}mu{dollar} controller for the uncertain nonlinear model of manipulator arms is a systematic one, a series of steps for such design work are given through two examples which offer {dollar}mu{dollar} controllers for an inverted pendulum with uncertain pendulum mass and a 12-link arm with the presence of mass uncertainties of both links.; The thesis is concluded by recommendations for further research work.