An integrated methodology for trajectory planning and tracking control has been a key need in the research of mobile robots that have a wide range of applications. Problems of planning and control can be considerably simplified if the system can be shown to have the differential flatness property. This thesis discusses how differential flatness theory can be used for planning and control of various types of mobile robots as an integrated framework. Three common types of mobile robots are proven to be differentially flat, and the property is used for planning and control for their kinematic and dynamic models.;The mobile robots can have more practical applications if a manipulator arm is mounted on them. While mobile manipulators are usually designed with a fully actuated arm, under-actuation can be a viable solution to reduce the manufacturing and operating costs. Despite the under-actuation, which makes the system more difficult to plan and control, using the differential flatness theory, mobile manipulators can be designed to be capable of executing point-to-point maneuvers as a mobile manipulator with a fully actuated arm would do. The differential flatness property is achieved by inertia redistribution, with addition of torsional springs at un-actuated joints, and a wide range of designs is possible. Using this design methodology, either a two-wheeled differentially driven mobile robot or a car-like mobile robot can be used as the mobile base and the under-actuated manipulator arm can be mounted either horizontally or vertically on the mobile base.;The structure of the differential flatness framework for integrated trajectory planning and control is extended to account for slip disturbances within the model. A feasible desired trajectory and the nominal control were determined for the model with slip, then a corrective control was added based on Lyapunov theory to overcome the disturbances due to the slip. The robust trajectory-tracking controller was developed based on the system's dynamic model as well as its kinematic model in the presence of slip. The simulation and experimental results validate the effectiveness of the proposed methodology and show that differential flatness presents a valuable and effective framework for integrated planning and control of mobile robots.
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