  In this paper, a sampling-based Stochastic Model Predictive Control algorithm
is proposed for discrete-time linear systems subject to both parametric
uncertainties and additive disturbances. One of the main drivers for the
development of the proposed control strategy is the need of real-time
implementability of guidance and control strategies for automated rendezvous
and proximity operations between spacecraft. The paper presents considers the
validation of the proposed control algorithm on an experimental testbed,
showing how it may indeed be implemented in a realistic framework. Parametric
uncertainties due to the mass variations during operations, linearization
errors, and disturbances due to external space environment are simultaneously
considered.
  The approach enables to suitably tighten the constraints to guarantee robust
recursive feasibility when bounds on the uncertain variables are provided, and
under mild assumptions, asymptotic stability in probability of the origin can
be established. The offline sampling approach in the control design phase is
shown to reduce the computational cost, which usually constitutes the main
limit for the adoption of Stochastic Model Predictive Control schemes,
especially for low-cost on-board hardware. These characteristics are
demonstrated both through simulations and by means of experimental results.
