Optimization of Angular Momentum for Increase of Maneuverability of a Spacecraft with Inertial Actuators

Abstract

The problem of improvement of maneuverability of a spacecraft which is controlled by inertial actuators (system of powered gyroscopes, by gyrodynes) is considered. We suggest to increase speed of implementation of rotary maneuvers by optimization of control algorithms of spacecraft motion. The task of construction of optimal laws of variation in the angular momentum vector of a spacecraft as control function so as to ensure the transition of the spacecraft from an arbitrary initial attitude to the required final angular position at minimal time has been solved completely. Main difference is the necessity of determining during optimization the maximum admissible magnitude of the angular momentum since it is unknown a priori. The problem is solved by using Pontryagin’s maximum principle, and solution is based on the quaternion differential equation relating the vector of spacecraft angular momentum to the quaternion of orientation of the body-fixed coordinate system. The optimality conditions of reorientation regime without "unloading" of the gyro-system are written in analytical form, and the properties of optimal motion are studied. Key relations and the equations for construction of the optimal control program are given. The condition for determination of the moment of the beginning of the braking which uses current parameters of motion (information on angular position of a spacecraft and measurements of angular velocity) was given, it considerably improves accuracy of spacecraft transfer into a required position. The aspects of determination of optimal modulus of angular momentum between acceleration and braking if spacecraft rotates under disturbances are discussed in detail. The formalized equations are derived, and computational expressions for calculating the optimal value of the key parameter of control law are obtained. Results of the mathematical simulation of the spacecraft motion under the designed control method are presented.