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