This paper deals with the dual-space adaptive control of R4 redundantly actuated parallel manipulator for applications with very high accelerations. This controller is compared experimentally with a dual-space feedforward controller (which may have good performances for specific cases, but has crucial losses of performance when there is any operational change (such as a change of load)), for a pick-and-place task with accelerations of 30G (without payload) and 20G (with a payload of 200g). The objective of this paper is to show that the proposed dual-space adaptive controller not only keeps a very good performance independently of the operational case, but also has a better performance than the dual-space feedforward controller even when this last one is best configured to the given case.