The combination and interconnection of the computational, cyber, and also communication devices using physical processes produced the Cyber- Physical Systems (CPSs), which turned out to be promising and extensively used in practice. These systems operating in real-world space environments have to overcome numerous challenges, chief among which are the reduction of the communication and computation burden, and the constraint upon the controller actuators. In this paper, aimed to overcome these difficulties, we have proposed the semi-global distributed parametric self-triggered constraint control protocols for the consensus task, under which the problem of achieving consensus when the agents collect information from the neighbors only at times that are designed iteratively and independently by each one of them on the basis of its current local measurements. Compared with the existing results, our approach presents several remarkable features. Both of the state feedback and output feedback policies for the constraint self-triggered frameworks are developed respectively. The consensus can be reached provided the communication graph is connected. An illustrative example is given to illustrate the effectiveness and the feasibility of the proposed control protocols.