Final Angular Position Research Articles

The problem of the time-optimal control of spacecraft reorientation

The use of Pontryagin's maximum principle to solve spacecraft motion control problems is demonstrated. The problem of the optimal control of the spatial reorientation of a spacecraft (as a rigid body) from an arbitrary initial angular position to an assigned final angular position in the minimum rotation time is investigated in detail. The case in which velocity parameters of the motion are constrained is considered. An analytical solution of the problem is obtained in closed form using the method of quaternions, and mathematical expressions for synthesizing the optimal control programme are given. The kinematic problem of spacecraft reorientation is solved completely. A design scheme for solving the maximum principle boundary-value problem for arbitrary turning conditions and inertial characteristics of the spacecraft is given. A solution of the problem of the optimal control of spatial reorientation for a dynamically symmetrical spacecraft is presented in analytical form (to expressions in elementary functions). The results of mathematical modelling of the motion of a spacecraft under optimal control, which confirm the practical feasibility of the control algorithm developed, are given. Estimates have shown that the turn time of modern spacecraft with a constrained magnitude of the angular momentum can be reduced by 15–25% compared with conventional reorientation methods. The greatest effect is achieved for turns through large angles (90° or more) when the final rotation vector is equidistant from the longitudinal axis and the transverse plane of the spacecraft.

Pontryagin’s maximum principle in optimal control problems of orientation of a spacecraft

Pontryagin’s maximum principle is used for solution of topical problems of spacecraft motion control. The dynamic optimal control problem of space orientation of a spacecraft from an arbitrary initial to a given final angular position with minimization of the turning time is studied in detail. The solution to the formulated problem is obtained and numerical expressions for synthesis of optimal control program are given. Results of mathematical simulation of the dynamics of motion of a spacecraft at optimal control are presented; these results demonstrate practical feasibility of the developed control algorithm.

Optimal Control of a Spatial Turn of a Spacecraft with Minimal Loading of Construction

The problem of optimal control of a three-dimensional turn of a spacecraft is considered and solved. The turn is performed from an initial angular position into the required final angular position in a specified time and with a minimum value of the functional that represents the degree of loading of the construction. An analytical solution to the formulated problem is presented. It is demonstrated that the optimal (in this sense) control of the spacecraft reorientation can be determined in the class of a regular precession executed by the spacecraft. The instant when braking begins is determined based on the principles of terminal control using the actual kinematical parameters of the spacecraft motion, which substantially increases the accuracy of transferring the spacecraft to a specified position. Data of mathematical modeling are also presented that confirm the efficiency of the described method of controlling the spacecraft's three-dimensional turn.