Decentralized and hierarchical control of robot manipulators
arxiv: Computer Science::Robotics
This thesis deals with the decentralized and hierarchical control of a class of robot manipulators, where the robot manipulator is treated as a large scale uncertain system. The work is divided into three parts. The first part is concerned with the development of an integrated mathematical model of the robot manipulator. The model of the system considered comprises the mechanical part of the robot manipulator, the actuators, as well as the gear trains. The formulation results in nonlinear time varying state equations, which represent a more realistic model of the robotic system. A procedure to decompose and reduce the integrated model of the robot manipulator into a set of interconnected subsystems with bounded uncertainties description is then presented. In the second part of the research, two decentralized control approaches based on a deterministic approach are outlined. The first method uses only the local states as the feedback information. It is shown that the robot manipulator utilizing the proposed controller is practically stable and tracks a reference trajectory if a given sufficient condition is satisfied. In the second approach, the controller is designed based on the local states as well as the states of the neighbouring subsystems as the feedback information. It is shown that the controller will force the nonlinear uncertain robot manipulator to track a desired trajectory to within a small uniform ultimate boundedness set. In the final part of the study, two hierarchical control concepts for robot manipulator are proposed. The controllers are formulated based on a deterministic approach. It is shown that the hierarchical control strategies are capable of withstanding the expected variations and uncertainties and will render the robot manipulator to track a prescribed trajectory satisfactorily. In synthesizing the proposed controllers, it is assumed that the upper bounds on the nonlinearities, couplings and uncertainties present in the system are available. The proposed methods are simple and robust to parameter variations and uncertainties present in the system. The performance of the proposed control algorithms are evaluated by means of computer simulations. The proposed control laws are applied to a three degree of freedom revolute robot manipulator actuated by DC motors. Several case studies have been considered, and the simulation results are presented and discussed. In this thesis, the term practical stability means bounded stability in the sense of Lyapunov.