Parallel parking with curvature and nonholonomic constraints

This paper addresses the problem of static curvilinear path generation for parallel parking a car. The car is an autonomous robotic vehicle subject to nonholonomic constraints. A curve for parking a car is derived and examples are shown. Constraints on the curve include initial and final position, orientation and curvature. There is also a constraint on the global curvature extrema; a fifth-order polynomial results. To track the fifth-order polynomial's curvature, the relationship between the curvature of the back and the front of the car is developed. This leads to the introduction of the nonholonomic constraints on the car.<
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