The fascinating idea of shepherding asteroids for science and resource utilisation is being considered as a very credible concept in a not too distant future. Past studies have identified asteroids which could be injected into manifolds which wind onto periodic orbits around collinear Lagrangian points of the Sun-Earth system, by means of a low-cost manoeuvre. However, the periodic orbits as well as the manifolds are highly unstable, and small errors in the capture manoeuvre would bring to complete mission failure, with potential danger of collision with the Earth itself. The main source of injection error in position and velocity is the epistemic uncertainty of the asteroid mass, which cannot be measured directly. For this reason, asteroid orbit control will be a strict requirement for such mission. This paper investigates the controllability of some asteroids during the transfer and along the period orbits, assuming the use of a solar-electric low-thrust engine. The control scheme is based on a linear quadratic regulator. A stochastic simulation with a Monte Carlo approach is used to simulate a range of different perturbed initial conditions. Results show that only a small subset of the considered combinations of trajectories/asteroids are reliably controllable, and therefore controllability must be taken into account in the selection of potential targets.
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