The relevance of human-robot interaction study is due to necessary to use of mathematical knowledge for building and programming robotic systems. The new stage of robotics - collaborative robotics. The paper presents a noticeable theoretical part that describes the advantages and differences of collaborative robotics from other robotic solutions. There is a mathematical representation of the kinematic characteristics of a collaborative robot is given in this paper. In particular considered the solutions to the direct and inverse problems of robot kinematics. The process of human-robot interaction was modeled in simulation environment where human and robot solve a single task in a shared workspace.