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Wheeled Mobile Robotics by Igor Skrjanc, Saso Blazic, Andrej Zdesar, Gregor Klancar

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3.3.4 Development of the Kinematic Trajectory-Tracking Error Model

In order to solve the control problem the transformation of robot coordinates is often performed on the form that is better suited for control purposes. The posture of the error is not given in the global coordinate system, but rather as an error in the local coordinate system of the robot that is aligned with the driving mechanism. This error is expressed as the deviation between a virtual reference robot and the actual robot as depicted in Fig. 3.21. The obtained errors are as follows: ex that gives the error in the direction of driving, ey that gives the error in the perpendicular direction, and eφ that gives the error in the orientation. These errors are illustrated in

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