The relevance of choosing the subject of research as the principles of the use of robotic systems for various purposes, including in a group, and the object of study, which are algorithmic problems that arise in the implementation of algorithms for group actions, is determined by the existing contradiction between the need for the joint use of robotic systems, most particularly autonomous, and the complexity of the software implementation of this requirement. The manifestation of such problems can be application errors that reduce the effectiveness of joint actions. The paper formulates a list of typical situations that determine the use of autonomous and controlled robots in a group with a leader. On the basis of the proposed classification, possible algorithms that provide movement control in a group are analyzed: both calculations for targeted maneuvering and for ensuring mutual safety. Based on a review analysis of typical algorithms for controlling movement in space, the formulation of the scientific problem of solving the problem of developing group algorithms and mathematical methods that determine their optimal application in the system, as an analogue of the “new morality” for robotic systems, is synthesized.