Biquaternion Quasi-optimal Analytical Solution for the Problem of Programmed Control of Spatial Motion of a Spacecraft

This report describes the analytical solution for a problem of constructing quasi-optimal programmed control for spatial motion of a spacecraft of an arbitrary dynamic configuration in the inertial coordinate frame using dual Euler (Rodrigues–Hamilton) parameters and Clifford’s biquaternions (dual quaternions). A new model of spatial motion of a spacecraft is used to solve the problem. This new model includes differential equations for dual Euler parameters and dual velocities of a spacecraft, and dynamic algebraic relations for vectors of control force and control moment. Boundary conditions for angular and linear positions of a spacecraft in the inertial space and for its angular and linear velocities are arbitrary. Dual auxiliary controls are non-limited. Control time is fixed. Dual integral quadratic quality functional is minimized with respect to correlated control of angular (rotational) and translational (orbital) motion of a spacecraft. The solution is derived in the class of generalized dual coning motions using the method of solving inverse dynamic problems and the principle of maximum.