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UBC Theses and Dissertations

Near-minimum-time control of a robot manipulator Tao, Fan


This thesis deals with the problem of minimum time control of a rigid robot manipulator with point-to-point motion subject to constraints on the control inputs. Due to the nonlinear and coupled dynamics of the robot manipulator, finding minimum time strategies is algorithmically difficult and computationally very intensive, even when the dynamic equations and parameters of the manipulator are precisely known. As a result, the practical applicability of the available methods currently is very limited. In this research, we assume the control inputs are always bang-bang and switch once. Using the Principle of Work and Energy, a simple and practical "zero-net-work" searching approach is proposed. The proposed method focuses on changes in the manipulator's kinetic energy during the time optimal motion, instead of concentrating on the system's state variables, as is usually done in conventional approaches. The "zero-net-work" method is used to develop the controllers for one-link manipulators, a 3-degree of freedom cylindrical manipulator and a two-degree of freedom revolute manipulator. The results show that if the structure of the exact minimum time control is bang-bang with a single switch, using the "zero-net-work" method we will get the exact minimum time solution. If the exact minimum time control has more than one switch, using the "zero-net-work" method we will get a near-minimum-time solution. The major advantages of the proposed method are that it does not require initial boundary value guesses and is computationally efficient.

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