Autonomous parking: A unified motion planning framework based on simultaneous dynamic optimization

Autonomous parking refers to driving a vehicle into a parking spot without manual operation. The emerging and prevailing methods are either effective on specific scenarios only or focus on overly simplified scenarios, lacking the capability to tackle general cases. In our viewpoint, a general parking motion planning problem is a dynamic optimization problem associated with complicated constraints. This paper proposes a unified formulation that can cover various kinds of parking scenarios when time-optimal solutions are pursued. First, we use differential equations to describe the kinematics of a car, and then use algebraic equalities/inequalities to restrict the car not collide with the parking slot frontiers. Through this, we formulate a time-optimal dynamic optimization (DO) problem that is identical to the original parking motion planning mission. Thereafter, the formulated DO is solved by a simultaneous approach. Although we pursue for time-optimal motions, this approach can be extended to consider other user-specific optimization criteria (such as minimum driving length or minimal fuel usage) with almost none additional effort.