This study develops a technique for rotation control of spherical motors driven by electromagnetic forces. The technique uses the data of generated torque per unit current and cogging torque of an electromagnet that are obtained beforehand at relative positions between the electromagnet and the rotor. An electromagnet placed on the stator of a spherical motor gives two kinds of rotation torques to the rotor. One is the torque by flowing current to the electromagnet. The other is the cogging torque that a permanent magnet on the rotor attracts the iron core of the electromagnet. The torque map expresses the two kinds of rotation torques when the unit current flows to an electromagnet in its various relative position to the rotor. In order to obtain the currents of electromagnets in the case that there are more than three electromagnets on the stator, this paper proposes a technique applying the Lagrange multiplier method under a constraint condition. This paper shows an example to obtain the currents of electromagnets by the proposed technique in the case that five electromagnets are arranged at the vertices of regular pentagon.