The presented article considers the formation and engagement of a mixed heterogeneous team within a robotic system designed for completing collaborative tasks. A qualitative comparative analysis of approaches, methods and algorithms related to efficient task allocation in a collaborative robotic system by reducing the time and/or costs is carried out. A method and its corresponding algorithm for task allocation in a mixed heterogeneous team of a collaborative robotic system are presented. The proposed algorithm for task allocation with cost minimization is applicable for a mixed heterogeneous team consisting of humans and collaborative robots (i.e., heterogeneous groups of participants of various types). Thus, the within the problem statement the following is considered: different cost functions for different types of team members; limited robot activity; the dependence of the cost of robots for performing a certain type of work on the number of people. The developed method and algorithm of task allocation and work distribution within a CRS with minimizing the costs is applicable to a mixed heterogeneous team consisting of humans and cobots (groups of participants of different types), taking into account the specific heterogeneity of team members, as well as the mandatory requirements for safe interaction of participants within a CRS. The simulation of five scenarios of task allocation between the participants using the proposed solution is carried out. The results of the experiment showed the increased efficiency of a mixed heterogeneous team functioning.