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The paper introduces the constructed prototype of the hexapod robot designed based on the biomechanics of insects for inspection and operation applications as well as for different research investigations related to the walking robots. A detailed discussion on the design and realization of mechanical construction, electronic control system and devices installed on the robot body are presented. Moreover, the control problem of the robot legs is studied in detail. In order to find the relationship between movements commonly used by insects legs and stable trajectories of mechanical systems, first we analyze different previous papers and leg movements of real insects. Next, we are focus on the control the robot leg with several oscillators working as a so-called Central Pattern Generator (CPG) and we propose other model of CPG based on the oscillator describing stick-slip induced vibrations. Some advantages of the proposed model are presented and compared with other previous applied mechanical oscillators with help of numerical simulations performed for both single robot leg and the whole robot. In order to confirm the mentioned numerical simulations, the conducted real experiments are described and some interesting results are reported. Both numerical and experimental results indicate some analogies between the characteristics of the simulated walking robot and animals met in nature as well as the benefits of the proposed stick-slip vibrations as a CPG are outlined. Our research work has been preceded by a biological inspiration, scientific literature review devoted to the six-legged insects met in nature as well as various prototypes and methods of control hexapod robots which can be found in engineering applications.