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The aim of this paper is to describe a model of the cognitive control system which allows the hexapod to static stable walk on terrain with obstacles. Therefore, the main aim is to model the decision making process of the insect. Hexapods are six-legged arthropods of the class Insecta. The nervous system of six-legged insect controls six legs. Model of the control system of the static stability of hexapods could help in the design of six-legged robots. Our control system assumes and ensures the static stable walking because the concept of static stability of walking is the most used in six-legged arthropod locomotion. The control system is based on the reinforcement learning principle because it is assumed in the real organism. The model of control system enables to walk on flat surface with small obstacles. We also describe the verification of algorithms and application of learning methods for cyclic and acyclic gait.