This paper is devoted to applying the method of integral manifolds to the order reduction of dynamics, control and estimation problems in the theory of gyroscopic systems and robotic devices. The main feature of the dynamics of such systems is the presence of slow motion and slowly fading high-frequency oscillations. The precessional theory equations are commonly used to reduce the dimension of the motion equations of gyroscopic systems. It is known that the presence of external disturbing factors may lead to unacceptable results. A similar situation occurs while finding a solution to problems of optimal control and estimation, when the direct use of asymptotic methods leads to unacceptably large errors. We use the method of integral manifolds to remove errors in the optimal estimation and control problems.
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