In this paper we focus on the target capturing problem for a swarm of agents modelled as double integrators in any finite space dimension. Each agent knows the relative position of the target and has only an estimation of its velocity and acceleration. Given that the estimation errors are bounded by some known values, it is possible to design a control law that ensures that agents enter a user-defined ellipsoidal ring around the moving target. Agents know the relative position of the other members whose distance is smaller than a common detection radius. Finally, in the case of no uncertainty about target data and homogeneous agents, we show how the swarm can reach a static configuration around the moving target. Some simulations are reported to show the effectiveness of the proposed strategy.