Solution of Approximate Equation for Modified Rodrigues Vector and Attitude Algorithm Design

Статья подготовлена сотрудниками: д.т.н. Молоденков А.В..
на базе: Лаборатория механики, навигации и управления движением.


Анотация

The truncated Darboux problem is analytically solved. The proposed quaternion algorithm to find the orientation of a rigid body (object using SINS), based on the analytic solution of the approximate kinematic equation for the modified Rodrigues vector, is regular for any angular motion of the rigid body because this solution is exact. In contrast to the known algorithms for determining the orientation of an object, which use the approximate numerical solutions of the truncated Bortz equation for the vector of orientation of a rigid body and read information about the angular velocity of an object directly from sensors of SINS, the essence of the approach proposed in this paper is that by transforming mentioned information, the truncated kinematic equation for the modified Rodrigues vector becomes clearly solvable. The quaternion, on which the solution of the problem is based, is written in elementary functions and quadratures.

Ключевые слова: modified Rodrigues parameters (MRPs), quaternion, analytical solution, orientation, arbitrary angular velocity, rigid body, strapdown INS, algorithm

DOI 10.2514/1.G006008

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Цитировать эту статью:

A.V. Molodenkov, S.E. Perelyaev. Solution of Approximate Equation for Modified Rodrigues Vector and Attitude Algorithm Design, Journal of Guidance, Control, and Dynamics, Vol. 44, No. 6, June 2021, pp. 1224-1227. https://doi.org/10.2514/1.G006008

О журнале AIAA Journal of Guidance, Control, and Dynamics