The present invention relates to a magnetic manipulation and navigation system for moving a magnetic element through a body comprising at least six electromagnets (24) with soft-magnetic cores arranged in a predetermined position to said body. It allows for the operation of one or more of the electromagnets in the non-linear regime of the magnetization curve of the cores. The system comprises at least one magnetic field sensor (104) at one or more predetermined positions outside of the operating region. While during operation in the linear region no feedback is required to set the magnetic field strength, during operation in the non-linear region feedback from the magnetic field sensors is used for closed-loop control. The system allows for operation in two separate modes, an open-loop mode operation in the linear regime for fast control signals such as they are required for stabilization during displacement of the magnetic element and a closed-loop operation in the non-linear regime for higher field strengths such as they may be required to apply forces and moments on the magnetic element while it is in contact with a surface.
