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Purpose In this study, human activity with finite and specific ranking is modeled with finite state machine, and an application for human–robot interaction was realized. A robot arm was designed that makes specific movements. The purpose of this paper is to create a language associated to a complex task, which was then used to teach individuals by the robot that knows the language. Design/methodology/approach Although the complex task is known by the robot, it is not known by the human. When the application is started, the robot continuously checks the specific task performed by the human. To carry out the control, the human hand is tracked. For this, the image processing techniques and the particle filter (PF) based on the Bayesian tracking method are used. To determine the complex task performed by the human, the task is divided into a series of sub-tasks. To identify the sequence of the sub-tasks, a push-down automata that uses a context-free grammar language structure is developed. Depending on the correctness of the sequence of the sub-tasks performed by humans, the robot produces different outputs. Findings This application was carried out for 15 individuals. In total, 11 out of the 15 individuals completed the complex task correctly by following the different outputs. Originality/value This type of study is suitable for applications to improve human intelligence and to enable people to learn quickly. Also, the risky tasks of a person working in a production or assembly line can be controlled with such applications by the robots.

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