The optimization problem for robot engineering systems according to the criterion of minimum consumed work is one of the important and complicated problems in robotics. Difficul-ties of this problem are caused by multi-parametrization, large number of degrees of freedom of the system, high order and bulkiness of differential equations systems, non-smoothness functional of energy consumption, etc. In spite of a large number of works, which deal with this problem, there still arise many important questions in design of systems with practically important types of drives. These demands stimulate new approaches and solutions. From the point of view of consumed energy, walking robots need more energy than wheeled platforms. Consequently, walking robots require larger electric motors and larger sources of energy. Most of walking robots are autonomous devices, in which duration of functioning is determined both by the capacity of the onboard power supply and the speed of consumption of energy. Therefore, search of theoretically achievable estimations of energy consumption from the point of view of choice of optimum laws of control and development of appropriate mathematical models and software are very urgent.

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