Geometric analysis of the singularities of a magnetic manipulation system with several mobile coils

It has been demonstrated that magnetic fields are relevant for manipulating an untethered magnet, either using fixed coils or mobile permanent magnets. This paper shows however, that any magnetic manipulation method is prone to singular configurations and that the simple numerical analysis of the rank of the "manipulation matrix" is not enough to detect them. Alternatively, we propose a geometrical analysis to interpret and detect the singularities as well as to decide on the acceptability of a reference trajectory. Then, we present results obtained by simulating a planar manipulation system including a multiple mobile coils and a Helmholtz like set-up.