The cross-scale piezoelectric positioning platform, with its millimeter-scale travel range and nanometer-level positioning accuracy, is considered a core component for enabling atomic-scale manufacturing systems. However, the inherent hysteresis nonlinear characteristics of piezoelectric ceramic actuators severely restrict their trajectory tracking accuracy under micro-positioning mode, making it difficult to meet the sub-nanometer precision requirements. In this context, the precise identification of hysteresis model parameters becomes a crucial step in improving tracking accuracy. To address the issue that traditional particle swarm optimization struggles to obtain the global optimal solution for identifying multi-dimensional complex hysteresis model parameters, a multi-modal Bayesian optimization PSO parameter identification algorithm is proposed. First, a system dynamics model capable of characterizing hysteresis nonlinearity is formulated based on the asymmetric Bouc-Wen model. Then, based on the analysis of the parameter identification results of the traditional PSO algorithm, a modal division mechanism is introduced, and Bayesian optimization is integrated for local search. In this way, the MB-PSO algorithm is developed. This is intended to overcome the limitations of traditional identification algorithms, such as being easily trapped in local optima. To evaluate the effectiveness of the proposed algorithm, a comparative experiment is implemented against PSO, the genetic algorithm, and the differential evolution algorithm. The experimental results show that the parameter fluctuation under MB-PSO is suppressed to within 12.3%. Furthermore, to evaluate the efficacy of the algorithm in improving both hysteresis modeling accuracy and trajectory tracking performance of the piezoelectric positioning platform, comparative tests on hysteresis characterization and trajectory tracking accuracy are carried out. The results show that the maximum displacement error of the hysteresis model identified by MB-PSO is limited to 6.871 nm, and the trajectory tracking error, when incorporating this model into the control system, is reduced to within 0.976 nm, achieving sub-nanometer tracking accuracy. The foundation is laid by this work for atomic-level manufacturing to be achieved with piezoelectric positioning platform systems.