| In this dissertation, we study the control of gray-box robotic systems, about which only partial information is known. A fuzzy-logic approach is used to design the general controllers. Starting from the standard low-level fuzzy-logic controllers, which has two inputs and one output, we extend it to MIMO (Multi-input multi-output) systems by synthesizing the output of the low-level control actions. We also give the conditions under which the performance index will decrease monotontically. We propose the rule base for standard fuzzy-logic controllers, which consists of nine rules and it can be interpreted as a PD (Proportional-Derivative) controller. The characteristic of such a rule base is that it always gives the right direction of control, which will decrease the dominant errors. And by introducing two parameters (one is responsible for the direction and the other for magnitude), the fuzzy-logic controllers are made adaptive. For the first time ever, we give the closed-form expressions of the standard linguistic fuzzy-logic controllers by dividing the error inputs into 16 regions. The fuzzy-logic controllers are designed in detail to control a truck/truck-trailer system, which is nonholonomic and nonlinear and a robotic manipulator with two links and two flexible joints. For trajectory planning, parabolas passing through the initial positions and the final parking positions are used as the reference trajectories for truck/truck-trailer systems; cubic curves which pass through the initial positions and the final positions are used as the position reference trajectories. By taking the derivative of these cubic curves, we obtain a set of parabolas, which are used as the velocity reference trajectories. Complete computer simulation has been carried out and the results are satisfactory. The stability analysis has been done in detail using as many as four methods: the model-free analysis, the small gain theorem, the graphic method, and the Lyapunov function method. |
