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In this section a quantitative analysis of the disturbances in the system is attempted. In order to deal in an easier way with the assumption of monotonicity and with the coupling between the steer and the motor input, the model is linearized and the lateral and the longitudinal components are separated. The coupling effect is seen as a disturbance. In the following the coordinate system will be relative to the path as represented in Figure coord_sys.jpg. In other words, y represents the position along the path while x the lateral distance from the path.
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LONGITUDINAL MODEL
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A linear model of the car along the longitudinal component of the path is represented in figure long_block.jpg. Symbols represent
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