In modern aerospace technology, one of the perspective ways of assembly parts of thin metal plates is friction stir welding. The advantage of this method is the higher strength of the welds of aluminum alloy joints, compared with the traditional MIG welding for the assembly of rockets and space constructions. However, the lack of friction stir welding is a necessity of formation of the system “machine –tool - part” significantly more effort, which is caused by the need to stir the material in the weld zone in a plastic state. Friction stir welding is used to connect the individual elements of tanks and bodies, in particular, panels, elements of the bottoms with each other. In this paper, is consider the typical design for rocket and space technology bottoms of large tanks. For industrial robot equipped with a special head for friction welding with mixing, a mathematical model of obtaining a spherical bottom from individual segments is proposed. The paper presents a mathematical model describing the geometry of a spherical bottom with a flap articulation and a working zone of an industrial robot, which allows defining constraints on process operation continuous seam welding for standard designs of bottoms and hulls of rocket and space technology. The dependences allowing determining the initial position of the robot relative to the bottom for performing friction stir welding of the continuous seam are proposed.