In the last decade, research studies on parking planning mainly focused on path planning rather than trajectory planning. The results of trajectory planning are more instructive for a practical parking process. Therefore, this paper proposes a trajectory planning method in which the optimal autonomous valet parking (AVP) trajectory is obtained by solving an optimal control problem. Additionally, a vehicle kinematics model is established with the consideration of dynamic obstacle avoidance and terminal constraints. Then the parking trajectory planning problem is modeled as an optimal control problem, while the parking time and driving distance are set as the cost function. The homotopic method is used for the expansion of obstacle boundaries, and the Gauss pseudospectral method (GPM) is utilized to discretize this optimal control problem into a nonlinear programming (NLP) problem. In order to solve this NLP problem, sequential quadratic programming is applied. Considering that the GPM is insensitive to the initial guess, an online calculation method of vertical parking trajectory is proposed. In this approach, the offline vertical parking trajectory, which is calculated and stored in advance, is taken as the initial guess of the online calculation. The selection of an appropriate initial guess is based on the actual starting position of parking. A small parking lot is selected as the verification scenario of the AVP. In the validation of the algorithm, the parking trajectory planning is divided into two phases, which are simulated and analyzed. Simulation results show that the proposed algorithm is efficient in solving a parking trajectory planning problem. The online calculation time of the vertical parking trajectory is less than 2 s, which meets the real-time requirement.
Keywords: autonomous parking; homotopic method; optimal control; trajectory planning.