Modelling and control of direct drive robot manipulators

Abstract

This thesis is concerned with the problems of modeling and controlling of direct drive robot manipulators. To achieve these goals, an integrated mathematical model of direct drive robot manipulator is developed. The model considered comprises the mechanical part of the robot manipulator as well as the actuators that drive the joint of the robot. The formulation results in nonlinear time varying state equations, which represent a realistic model of the robotic system. Based on the known bounds on the system parameters, the robot dynamic is treated as an uncertain system whereby deterministic approach can be used in controlling the system. By treating the uncertain robot system as a large-scale system, the MIMO direct drive robot manipulator dynamics may be decomposed into an interconnected uncertain system whereby decentralized approach may be used in the design of the controller. In the second part of this study, two robust output tracking controllers using the concept of Sliding Mode Control (SMC) are proposed under centralized and decentralized frameworks. In the centralized approach, the controller is designed with assumption that the state information of each sub-system can be sensed and transmitted to the centralized controller. The calculation for the control signals is also centered in one location. On the other hand, the decentralized control presented in this research adopts the local approach, where the local controllers utilize only the state information of each sub-system. In each of the approach, a variant of the SMC known as the Proportional-Integral Sliding Mode (PISMC) is chosen to ensure the stability of the system dynamics during the sliding phase. The system dynamics during the sliding phase may be determined using any conventional pole placement method. Using Lyapunov's stability theory, it is shown theoretically that for system with matched uncertainties, the system's trajectories are guaranteed to be stable during the reaching phase. A tuning algorithm is also presented to assure that not only the desired tracking response is achieved, but also assure that the system control input is within the permissible range of operation. The proposed controllers are synthesized with the assumptions that the upper bounds on the non-linearities, couplings and uncertainties present in the direct drive robot system are available. The performance and robustness of each controller design is evaluated through extensive computer simulations and the results show that the proposed centralized and decentralized PISMC controllers render the nonlinear direct drive robot manipulator practically stable to track the desired reference trajectory.