Ricerc@Sapienza

An important research topic in aerospace engineering is spacecraft attitude motion planning. The objective is determining time behaviors for the control torque so that the attitude of a spacecraft is transferred from a given initial one to a desired final one. Moreover, the transfer must be achieved while fulfilling some additional constraints. Typically, it is required that some exclusion cones are avoided. Those cones arise when the spacecraft has a sensitive sensor that may become damaged if pointed within a certain angle of a bright source such as Sun, Earth, and Moon. Additional pointing constraints may be a consequence of requiring that a communication antenna of the spacecraft is kept within a maximum acceptable angle from the ground station direction. The pointing constraints described above must be checked pointwise in time. In some applications, it might be required to impose also integral constraints: this is the case, for example, when the heat input to radiators, or other spacecraft surfaces, must be limited to maintain thermal control.
This project will develop methods for solving numerically problems of spacecraft attitude motion planning using the Lie group of three dimensional rotations SO(3) to represent attitude.
It will exploit a recently derived method for optimal control on Lie groups for the control of quantum mechanical systems. This method, known as ¿Gradient Ascent in Function Space¿, (GRAFS), constructs a numerical solution to the optimal control problem by first expressing the controls as weighted sums of basis functions and minimizing an error function defining the desired final configuration of the system. The objective function can be optimized by gradient ascent algorithms simplifying the numerics.The key insight of the algorithm rests on a novel expression for the gradient of the final configuration of the system as defined by a simple product of exponentials approximate solution of the Lie group dynamics.