In the context of future human spaceflight exploration missions, Rendezvous and Docking (RVD) activities are critical for the assembly and maintenance of cislunar structures. The scope of this research is to investigate the specifics of orbits of interest for RVD in the cislunar realm and to propose novel strategies to safely perform these kinds of operations. This paper focuses on far rendezvous approaches and passively safe drift trajectories in the Ephemeris model. The goal is to exhibit phasing orbit requirements to ensure a safe far approach. Ephemeris representations of Near Rectilinear Halo Orbits (NRHOs) were derived using multiple-shooting and adaptive receding-horizon targeting algorithms. Simulations showed significant drift and overlapping properties for phasing and target orbits of interest, motivating the search for safe natural drift trajectories and using impact prediction strategies.

The symmetric rendezvous problem on a network Q asks how two players, forced to use the same mixed strategy, can minimize their expected meeting time, starting from a known initial distribution on the nodes of Q. This minimum is called the (symmetric) ‘rendezvous value’ of Q. Traditionally, the players are assumed to receive no information while playing the game. We consider the effect on rendezvous times of giving the players some information about past actions and chance moves, enabling each of them to apply Bayesian updates to improve his knowledge of the other's whereabouts. This technique can be used to give lower bounds on the rendezvous times of the original game (without any revealed information). We consider the case in which they are placed a known distance apart on the line graph Q (known as ‘symmetric rendezvous on the line’). Our approach is to concentrate on a general analysis of the effect of revelations, rather than compute the best bounds possible with our technique.

We develop a family of transfer orbits suitable for the peculiarity of NEAs orbits. They involve one or more carefully planned deep-space maneuvers and one or more close encounters with the Earth. Basically, it is a gravity assist technique, but only Earth is used as the driving planet. In this manner, the orbit of the spacecraft stays near the Earth, as the orbits of NEAs. The idea is to obtain a large relative velocity in respect to the Earth, using these impulsive maneuvers. Next, successive rotations of this relative velocity vector due to resonant encounters with the Earth will, finally, shape the orbit of the spacecraft, in order to match the inclination and the orientation of apsidal line of the asteroid's orbit.

With a velocity budget less than 9 km/s most of NEAs orbits are reachable, even highly inclined ones, or orbits with relatively large nodal distances. An example is given: a rendezvous mission to asteroid (1036) Ganymed.

The spacecraft Hayabusa, which was launched in 2003, arrived at its destination, asteroid (25143) Itokawa in September 2005. The appearance of Itokawa, a small S-type near Earth asteroids, was totally unexpected. The surface is covered with a lot of boulders and there are only a few craters on it. It looks like a contact binary asteroid. The surface composition is quite similar to LL-chondrite. The estimated density is 1.9 ± 0.13 (g/cm3), so the macro-porosity is about 40%. This means that Itokawa is a rubble pile object. In Itokawa, we may see such things that are very close to building blocks of asteroids. In this paper, we review the mission and the first scientific results.

We consider a problem proposed by S. Alpern (European Journal of Operational Research (1997)) of how two players can optimally rendezvous while at the same time evading an enemy searcher. This problem can be modelled as a two-person, zero-sum game between the rendezvous team R (with agents R1, R2) and the searcher S. This paper gives the first solution to such a rendezvous-evasion game by considering a version that is discrete in time and space, as in the pure rendezvous problem of Anderson and Weber (Journal of Applied Probability28, pp. 839–851). R1,R2 and S start at different locations among the n identical locations where there is no common labelling and at each integer time they may rellocate to any one of the n locations. When some location is occupied by more than one player, the game ends. If S is at this location, S (maximizer) wins and the payoff is 1; otherwise R(minimizer) wins and the payoff is 0. The value of the game is the probability that Swins under optimal play. We assume that R1 and R2 can jointly randomize their strategies. When n equals 3, the value of the game is . We also prove that the value of the game is bounded above by asymptotically. If, in addition, the players share a common notion of a directed cycle containing all the nlocations (while still able to move between any two locations), the value of the game is ((1 – 2/n)n–1 + l)/2. Finally, we prove that with this extra information, R can secure a strictly lower value for all n.