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Automated valet parking is a part of autonomous vehicles. Path tracking is a vital capability of autonomous vehicles. In the scenario of automatic valet parking, the existing control algorithm will produce a high tracking error and a high computational burden. This paper proposes a path-tracking algorithm based on model predictive control to adapt to low-speed driving. By using the model predictive control method and vehicle kinematics model, a path tracking controller is designed. Combining the dual algorithm to further optimize the solver, a new QPKWIK solver is proposed. The simulation results show that the solution time of the QPKWIK solver is 25% less than that of the QP solver, and the tracking error is reduced by up to 41% compared with the QP solver. In the parking lot, the tracking performance is tested under four common scenarios, and the experimental results show that this controller has better tracking performance.