Some issues of time-optimal control over a spacecraft programmed turn

The problem of optimal turn of a spacecraft from an arbitrary initial position to a final specified angular position in a minimum time is considered and solved. A case is investigated, when the constraint on spacecraft’s angular momentum during the turn is essential. Based on the quaternion method a solution to the posed problem has been found, and an optimal control program is constructed taking the constraints on controlling moment into account. The optimal control is found in the class of regular motions. A condition (calculation expression) is presented for determining the moment to begin braking with the use of measurements of current motion parameters, which considerably improves the accuracy of putting the spacecraft into a preset position. For a dynamically symmetrical spacecraft the solution to the problem of optimal control by the spacecraft spatial turn is presented in analytical form (expressions in elementary functions). An example of mathematical modeling of the spacecraft motion dynamics under optimal control over reorientation is given.     

Optimization Problem in Control over a Programmed Turn of a Spacecraft

The problem of spacecraft reorientation from its initial angular position into a desired final position within a given time interval with a minimum value of the angular moment is considered and solved analytically in this work. It is shown that the control over the spacecraft reorientation, optimal in this sense, might be defined in the class of a regular precession performed by the spacecraft. The moment of the start of deceleration is determined from the principles of the terminal control by using real kinematic parameters of apparatus motion, which increases significantly the accuracy of reorientation. The results of mathematical modeling are presented, showing a high efficiency of the proposed way of reorientation.     

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.     

Optimal Control of a Programmed Turn of a Spacecraft

A problem of optimal turn of a spacecraft is considered. The time of turn is minimized, as well as the functional having a meaning of the propellant consumption. An analytical solution to the problem stated is derived. It is demonstrated that the solution optimal in this sense belongs to a class of two-impulse controls, under which a spacecraft executes the turn along the trajectory of its free motion. The solution obtained in this paper differs from earlier available solutions considerably. The estimations of the propellant consumption for a realization of the programmed turn are made.     

Control of a spacecraft’s spatial turn with minimum value of the path functional

The problem of optimal (with minimum value of the path functional) control over a spatial reorientation of a spacecraft is considered. Using the quaternion method, an analytical solution to this problem is obtained. For the symmetrical optimality index, the complete solution to the problem of spacecraft reorientation is represented in a closed form. The results of mathematical modeling of the spacecraft motion dynamics are presented, demonstrating the practical efficiency of the developed algorithm of control.     

Optimal control of reorientation of a spacecraft using free trajectory method

The problem of optimal control over spatial reorientation of a spacecraft is considered. The functional having a sense of propellant consumption is minimized. The analytical solution to the formulated problem is presented. It is shown that the optimal solution can be found in the class of two-impulse control at which the spacecraft’s turn is performed along a free motion trajectory. In order to improve the accuracy of spacecraft guidance into a specified angular position, methods of control are suggested that realize the method of free trajectories. The synthesized controls are invariant with respect to both external perturbations and parametric errors. The results of mathematical modeling are presented that demonstrate high efficiency of developed control algorithms. Propellant consumption for realizing a programmed turn is numerically estimated taking into account considerable gravitational and aerodynamic moments acting upon the spacecraft.