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Abstract The Laser Interferometer Space Antenna, (LISA), is a joint ESA/NASA space mission intended to detect and measure gravitational waves throughout the universe such as those generated by massive black holes. The measurement bandwidth over which LISA operates will be the low frequency band that goes from 0.1 mHz to 1 Hz. This is provided by laser metrology that measures distance fluctuations between proof masses aboard three spacecraft when a gravitational wave disturbs the space-time field between them. The three spacecraft are arranged in an equilateral triangle forming the arms of a giant Michelson interferometer. Each spacecraft has two incoming and two outgoing laser beams for a total of six laser links. These links are established sequentially at the start of the mission, and the spacecraft control systems must aim their lasers at each other with very small pointing motions. A mathematical description of the controller algorithm design on LISA, during the Constellation Acquisition Phase, is developed in order to achieve the aforementioned results. This implies possible executed considerations on concepts, i.e. the Lorentz transformation, based on the two famous postulates of the Special Relativity Theory. In particular, it is demonstrated that these transformations can be neglected, considering the passage between two reference frames referred to different spacecraft, because of the velocities involved and the approximations made on the spacecraft motion described in the calculation algorithm. This work concentrates on the drawing up of the guidance algorithm in order to establish the six aforementioned links. It also focuses on the different strategies used for the attitude correction of the spacecraft. To verify the accuracy of the considered relations and approximations, the guidance algorithm is consequently implemented in a simulator. The results obtained, besides satisfying the project requirements, ensured the establishment of the links necessary to complete the Acquisition Constellation Phase.