The research is devoted to the actual problem of upgrading the existing model of robotics training in connection with the urgent need for implementing a strategy for training highly qualified specialists in the most demanded and promising sectors of the future, taking into account the requirements of business, society, and the State. The aim of the study is to theoretically justify and experimentally test the effectiveness of the task approach in teaching robotics to form the required cross-professional competencies of the future. The methodology of the study is based on the analysis of psychological, pedagogical, methodological scientific literature, Rapid Foresight methodology, system analysis, generalization of teaching experience, pedagogical experiment. Results: First, the didactic and interdisciplinary potential of the robotics course is studied. Secondly, specific content for key cross-professional competences in the field of robotics and engineering is proposed. Thirdly, the basic ideas of the methodology for improving the existing system with a focus on the formation of key cross-professional competencies, the core of which is the system of tasks, are formulated. Fourthly, the effectiveness of the changed methodology of the training course to improve the quality of the educational process is confirmed. In conclusion, findings that confirm that the improvement of the course of robotics will provide to obtain a useful skill -- to be able to learn, to be prepared for the professions of the future are drawn.