Biquaternion Solution of the Problem of Optimal Minimum Time Control of the Spacecraft Spatial Motion

In this report the problem of time-optimal program control of the spacecraft spatial motion in an inertial coordinate system is solved in a nonlinear formulation, using new biquaternion differential equations of spatial motion of a rigid body. The spacecraft is considered as a free rigid body of arbitrary dynamic configuration performing spatial motion equivalent to the composition of angular (rotational) and translational (orbital) motions. The boundary conditions for the angular and linear positions of the spacecraft, as well as for its angular and linear velocities are arbitrary; the dual vector control function (composition of angular and linear accelerations) is limited by the dual module. A differential boundary value problem of the twenty-eighth order was obtained within the framework of the concept of solving inverse problems of dynamics using the Pontryagin maximum principle. Examples of numerical solutions of the boundary value problem are given for the cases when spacecraft mass distribution corresponds to a spherically symmetric rigid body or to the International Space Station (ISS). At the same time, the difference between the initial and final orientations of the spacecraft is large in angular measure and small in linear displacement (the problem of spatial maneuvering of the spacecraft). The analysis of the obtained numerical solutions is given; their characteristic properties and patterns are revealed.