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An Automata Theory Method for the Analysis of Unicycle Pursuit Problems
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David Dovrat, Ph.D. Thesis Seminar
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Wednesday, 12.1.2022, 13:30
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Zoom Lecture: 8206122066
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Advisor:  Prof. Alfred M. Bruckstein
The Pursuit Problem depicts a scenario where a moving target is pursued by an agent, whose movement is prescribed by some defined policy. Examples of what can be regarded as solutions to the pursuit problem include the shape of the agent's trajectory, whether the agent ultimately captures the target, and the circumstances of the capture, including the time required for capture to be achieved, The Unicycle Model is a popular simplification used to describe the kinematics of complex vehicular systems. An agent modeled as a unicycle has three degrees of freedom: the location on the plane, and the orientation of the modeled agent; yet it is constrained to move only in the direction of the agent's orientation, and only two input signals are available to control the model: steering and speed. A Unicycle Pursuit Problem is a pursuit problem where the pursuing agent is modeled as a unicycle. This thesis describes a method used for solving unicycle pursuit problems by mapping the properties of the dynamical system describing the pursuit problem to a directed graph, which can then be regarded as a finite state machine that records the evolution of these properties. The thesis details the analysis of two particular unicycle pursuit problems, to demonstrate results that were achieved by studying the traits and structure of the corresponding finite state machines generated by the method described here.
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