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This paper is focused on planning fast, accurate, and optimal trajectories for autonomous parking. Nominally, this task should be described as an optimal control problem (OCP), wherein the collision-avoidance constraints guarantee travel safety and the kinematic constraints guarantee tracking accuracy. The dimension of the nominal OCP is high because it requires the vehicle to avoid collision with each obstacle at every moment throughout the entire parking process. With a coarse trajectory guiding a homotopic route, the intractably scaled collision-avoidance constraints are replaced by within-corridor constraints, whose scale is small and independent from the environment complexity. Constructing such a corridor sacrifices partial free spaces, which may cause loss of optimality or even feasibility. To address this issue, our proposed method reconstructs the corridor in an iterative framework, where a lightweight …