High precision manipulation and optimization of actuation current are major concerns in the design of magnetic manipulation systems. In this paper, a flexible magnetic field mapping model has been employed to determine the field distribution of a compact electromagnetic manipulation system in 3D space, and validated by a high-resolution magnetic calibration system and Finite Element Analysis, which enables an improved accuracy and performance of magnetic manipulation. In addition, an iterative current optimization scheme is used to optimize the actuation current through Iterated Tikhonov Regularization. Finally, a feedback control algorithm including a Proportional-Integral-Derivative controller and Extended State Observer is conducted to solve general external disturbance during the autonomous manipulation of magnetic objects. By incorporating magnetic field mapping, feedback control, and current optimization model, the accuracy of the system has been demonstrated by navigating a small-size permanent magnet through predefined trajectories (Z-shaped, spiral curve) with the average position error of 0.27 mm (body length of 1 mm) and maximum average velocity of 3.59 mm/s. Meanwhile, the results showed that the required maximum actuation current was reduced from 4.00 A to 1.81 A. Our work provides a reliable and systematic approach for high-precision magnetic manipulation and optimization of actuation currents.