Synthesis of Ballistic Capture Corridors at Mars via Polynomial Chaos Expansion

The space sector is experiencing a flourishing growth and evidence is mounting that the near future will be characterized by a large amount of deep-space missions. In the last decade, CubeSats have granted affordable access to space due to their reduced manufacturing costs compared to traditional missions. At the present-day, most miniaturized spacecraft have thus far been deployed into near-Earth orbits, but soon a multitude of interplanetary CubeSats will be employed for deep-space missions as well. Nevertheless, the current paradigm for deep-space missions strongly relies on ground-based operations. Although reliable, this approach will rapidly cause saturation of ground slots, thereby hampering the current momentum in space exploration. At the actual pace, human-in-the-loop, flight-related operations for deep-space missions will soon become unsustainable. Self-driving spacecraft are challenging the current paradigm under which spacecraft are piloted in interplanetary space. They are intended as machines capable of traveling in deep space and autonomously reaching their destination. In EXTREMA, these systems are used to engineer ballistic capture (BC), thereby proving the effectiveness of autonomy in a complex scenario. The key is to accomplish low-thrust orbits culminating in BC. For this, a bundle of BC orbits named ballistic capture corridor (BCC) can be targeted far away from a planet. To achieve BC at Mars without any a priori instruction, an inexpensive and accurate method to construct BCC directly on board is required. Therefore, granting spacecraft the capability to manipulate stable sets in order to self-compute a BCC is crucial. The goal of the paper is to numerically synthesize a corridor exploiting the polynomial chaos expansion (PCE) technique, thereby applying a suited uncertainty propagation technique to BC orbit propagation.