Angular motion control of spacecraft by vector measurements

Problems of spacecraft (SC) reorientation are the problems of control of angular motion of the spacecraft body about its own mass center and they are urgent because of growing requirements to dynamic characteristics of SC spatial maneuvers. The success of solving the problems of SC angular motion control depends considerably on the selected model of SC angular motion. The most widespread model among diverse models of angular motion is the model, in which dynamics is described by the Euler equation, and the kinematics is described by the kinematical equation in the Rodrigo-Hamilton parameters. Advantage of this model consists in the absence of computational singularities and the minimal redundancy of the state vector, while the defect consists in model nonlinearity, which complicates the synthesis of control laws. For the construction of control besides this model, it is possible to use the model of motion in the form of a system of differential equations of the second order in the Rodrigo-Hamilton parameters. This model is based on dynamic equations of motion of a point on the sphere. Using this approach, the dynamic model of motion of the vector in the connected reference frame was obtained, and two problems of construction of the prescribed SC orientation were solved immediately by the vector measurements without determination the quaternion of orientation, namely, the problem of uniaxial orientation; the problem of triaxial orientation immediately by the vector measurements. Moreover, in contrast to the well-known publications, where for solving the problem of uniaxial orientation the direct Lyapunov method is used, we succeeded for the first time to reduce the problem of determination of the required control to a trivial problem of determination of control for a linear system with constant coefficients. Results of the adduced computer modeling confirm the efficiency of the suggested algorithms. © 2019 by Begell House Inc.