The research is devoted to the solution to the development of a methodology for the synthesis of mobile robots of arbitrary orientation in the technological space with systems for holding mobile robots on the moving surface to compensate for the gravitational and technological load. Mobile robots, also known in international publications as Climber Robot, are a new modification of mobile robots. The creation of this type of robotics is dictated by the need to perform
 technological operations in such areas as monitoring industrial facilities, erection and dismantling of building structures, repair and preventive maintenance of their components, maintenance of high-rise buildings of urban utilities, forest and park woodlands, etc. The operation of mobile robots acquires particular relevance in the extreme conditions of manmade disasters, which are dangerous and even unacceptable for a person's stay. The paper proposes designs of mobile robots, which are based on new principles of their synthesis. In the performed studies, in addition to the latest patented designs of mobile robots, a strategy of active synthesis of a new class of mobile robots is proposed.