Mathematical modelling and control of a robotic manipulator : a thesis presented in partial fulfilment of the requirements of the degree of Masters of Technology at Massey University

Abstract

Control system engineering strives to alter a systems performance to suit the objectives of the user. This requires pre-requisite knowledge of the system behaviour. This is often in the form of mathematical models of the system. These models can then be used to simulate the system and obtain a sound understanding of the systems operation, these can then be used in controller design. Every real world physical system has its own unique characteristics. These must be modelled to develop a simulation of the system. The uniqueness of a real world system necessitates the use of experimental practices and procedures to obtain information about the system. This information is then used to form models representing the system. A simulation of the system can then be based on these models. In this project a robotic system comprising of a link structure, a pneumatic driving system and a valve regulating system, is investigated. Mathematical models describing each component of the robotic system are investigated. Mathematical models describing the dynamic interactions of the link structure are developed and implemented in a fashion to facilitate control of the robot mechanism. The equations are in an explicit form which do not require the use of a numerical method for development of state space equations used in controller development. The pneumatic muscle used as the desired actuator for the robot structure is analysed. Analytical models obtained from the available literature are examined and new models are developed to describe the characteristics of the pneumatic muscle. A proto-type valve specially developed for supplying air to the pneumatic muscle is investigated. Experiments are conducted on this valve to characterise the valves behaviour. A model of the valves behaviour is then developed. A selection of controllers are then applied to the valve pneumatic muscle system. The investigation of alternative actuation systems proposes a new rotary pneumatic muscle design. Analytical models for the rotary pneumatic muscle are developed, a prototype is constructed as part of a feasibility study.