Optimization of Triangular Formation Flying Configurations Under the Circular and Elliptic Three-Body Problem Dynamics Modelling

The paper studies natural triangular formations of spacecraft under the Three-Body dynamics. An equilateral triangularly-shaped formation of spacecraft is assumed as a representative geometry to be studied. Initial configurations, which provide good performance in terms of formation keeping, have been investigated and key parameters, which mainly control the formation dynamics within the three-body system, have been identified. The evolution of spacecraft formation in the proximity of point periodic orbits about collinear libration points is studied. The analysis has been performed under several degrees of freedom to define the geometry, the orientation and the location of the triangle in the synodic rotating frame. The effect of different initial conditions sets on natural formation keeping performance is studied: the aim is to find optimal solutions in terms of initial condition sets which guarantee the maximization of performance factors, which have been introduced to evaluate formation keeping. The optimization is performed using a global optimization algorithm from the domain of soft computing, to exploit its great capability of investigating a large range of potential solutions in parallel, starting from not informed initial guess to maximize performance factors, whose mathematical expression is provided analytically.