Robust Control of Robotic Arms: Analysis and Design

Abstract

In this thesis we are concerned with the study of different tracking controllers of a two link robot manipulator. The control techniques used in this thesis are general for nonlinear multi­ input multi-output (MIMO) system. However, we are mainly concerned with the two link robot manipulator. First, we start with the r- a tracking controller which was developed by Corless. In r -a tracking controllers, given a prespecified rate of convergence a > 0 and a prespecified tolerance r > 0, the controller guarantees that the system's trajectory exponentially converges to any desired trajectory with rate a and to within the tolerance r. Usually the velocity states of the two link robot manipulator are unmeasurable so it is missing in practical case. Therefore, an observer is added to the r- a tracking controller for estimating the velocity states which is called High Gain Observer which has been introduced by Zenieh and Elshafei. Second, we use the Inverse Dynamics controller which has been developed by Leitrnann. This controller uses the forward dynamics of the system in order to design the controller based on the inverse of dynamics equation enhanced with robustness consideration in the design. Third, the Sliding Mode controller introduced by Slotine for robotic arm is applied to our two link robot manipulator. In this control scheme, a simplification is introduced which in effect allows n'h­ order problems to be replaced by equivalent I 51-order problems. This scheme proves to be very efficient in compensating the uncertainty in the parameters. Fourth, the Fuzzy Disturbance Observer (FDO) which was introduced by Kim for single-input single-output (SISO) system is considered. We have modified it for general MIMO system. This modification leads to the rule explosion phenomenon which means the exponential increase in the number of fuzzy rules with increase in inputs. It represents a big problem in the system implementation. To avoid this problem, we use Hierarchical Fuzzy System to decrease the number of rules and improve the performance of MIMO system. Later, an observer is added to the system to estimate the velocity states of the two link robot manipulator know as Pseudo-Velocity Filter. For better performance Genetic Algorithm is used to tune the Hierarchical Fuzzy Disturbance Observer (HFDO) parameters. Finally, a comparison of the previous controllers is made based on the simulation performance.