Browsing by Author "Mellodge, Patricia"

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    Feedback Control for a Path Following Robotic Car
    Mellodge, Patricia (Virginia Tech, 2002-04-25)
    This thesis describes the current state of development of the Flexible Low-cost Automated Scaled Highway (FLASH) laboratory at the Virginia Tech Transportation Institute (VTTI). The FLASH lab and the scale model cars contained therein provide a testbed for the small scale development stage of intelligent transportation systems (ITS). In addition, the FLASH lab serves as a home to the prototype display being developed for an educational museum exhibit. This thesis also gives details of the path following lateral controller implemented on the FLASH car. The controller was developed using the kinematic model for a wheeled robot. The global model is converted into the path coordinate model so that only local variables are needed. then the path coordinate model is converted into chained form and a controller is given to perform path following. The path coordinate model introduces a new parameter to the system: the curvature of the path. Thus, it is necessary to provide the path's curvature value to the controller. Because of the environment in which the car is operating, the curvature values are known a priori. Several online methods for determining the curvature are developed. A MATLAB simulation environment was created with which to test the above algorithms. The simulation uses the kinematic model to show the car's behavior and implements the sensors and controller as closely as possible to the actual system. The implementation of the lateral controller in hardware is discussed. The vehicle platform is described and the harware and software architecture detailed. The car described is capable of operating manually and autonomously. In autonomous mode, several sensors are utilized including: infrared, magnetic, ultrasound, and image based technology. The operation of each sensor type is described and the information received by the processor from each is discussed.
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    Model Abstraction in Dynamical Systems: Application to Mobile Robot Control
    Mellodge, Patricia (Virginia Tech, 2007-05-10)
    To reduce complexity of system analysis and control design, simplified models that capture the behavior of interest in the original system can be obtained. These simplified models, called abstractions, can be analyzed more easily than the original complex model. Hierarchies of consistent abstractions can significantly reduce the complexity in determining the reachability properties of nonlinear systems. Such consistent hierarchies of reachability-preserving nonlinear abstractions are considered for the robotic car. Not only can these abstractions be analyzed with respect to some behavior of interest, they can also be used to transfer control design for the complex model to the simplified model. In this work, the abstraction is applied to the car/unicycle system. Working towards control design, it is seen that there are certain classes of trajectories that exist in the rolling disk system that cannot be achieved by the robotic car. In order to account for these cases, the new concepts of traceability and ε-traceability are introduced. This work also studies the relationship between the evolution of uncertain initial conditions in abstracted control systems. It is shown that a control system abstraction can capture the time evolution of the uncertainty in the original system by an appropriate choice of control input. Abstracted control systems with stochastic initial conditions show the same behavior as systems with deterministic initial conditions. A conservation law is applied to the probability density function (pdf) requiring that the area under it be unity. Application of the conservation law results in a partial differential equation known as the Liouville equation, for which a closed form solution is known. The solution provides the time evolution of the initial pdf which can be followed by the abstracted system.