Variable structure control of robot manipulators (the example of the SPRINTA)
The subject of this thesis is the design and practical application of a model-based controller with variable structure control (VSC). Robot manipulators are highly non-linear systems, however they form a specific class in the non-linear group. Exact mathematical descriptions of the robot dynamics can be achieved and further, robot manipulators have specific useful properties that can be used for the design of advanced controllers. The inclusion of the inverse dynamic description of the robot manipulator as a feedforward term of the controller (model-based controller) is used to transform two non-linear systems i.e. the controller and the robot, into one linear system. The limitation of this technique arises from the accuracy of the inverse dynamic model. The linearisation only takes place if the model is known exactly. To deal with the uncertainties that arise in the model, a control methodology based on variable structure control is proposed. The design of the controller is based on a Lyapunov approach and engineering considerations of the robot. A candidate Lyapunov function of a pseudo-energy form is selected to start the controller design. The general form of the controller is selected to satisfy the negative definiteness of the Lyapunov function. The initial uncertainties between the actual robot dynamics and the model used in the controller are dealt with using a classical VSC regulator. The deficiencies of this approach are evident however because of the chattering phenomenum. The model uncertainties are examined from an engineering point of view and adjustable bounds are then devised for the VSC regulator, and simulations confirm a reduction in the chattering. Implementation on the SPRINTA robot reveals further limitations in the proposed methodology and the bound adjustment is enhanced to take into account the position of the robot and the tracking errors. Two controllers based on the same principle are then obtained and their performances are compared to a PID controller, for three types of trajectory. Tests reveal the superiority of the devised control methodology over the classic PID controller. The devised controller demonstrates that the inclusion of the robot dynamics and properties in the controller design with adequate engineering considerations lead to improved robot responses.