Аннотация:When the robot moves off-road, various emergency situations may arise. In the absence of breakdowns, the most catastrophic case is when, due to a fall, the robot finds itself in an inverted position with its legs up, and the body lying on the reference plane. The paper investigates the optimal rotation of the robot due to the movement of the legs. This
work develops the results obtained in the preprint [1, 4] in terms of algorithms for controlling the behavior of a robot in extreme situations. In contrast to [1, 4], where the rotation of the robot is carried out using piecewise-constant
control, the function of the position of the legs of the robot in this work belongs to the class of piecewise-continuous functions.