Reachability of a state in an embedded system, and steering the system into that state, are a frequent requirement. The technique we propose ensures reachability by construction. It pre-computes a set of local schedulers which are chosen at run-time depending on the current system state and on a predicate characterizing the set of states to be reached. This quasi-static scheduling approach combines the efficiency of pre-computed schedulers with flexibility during execution, making it possible to change at run-time the predicate to be reached. Our method uses both local controller synthesis and sufficient conditions to compositionally ensure reachability properties, in order to ensure a small memory footprint and efficient execution. The constructed schedulers are composable with further constraints and scheduling policies, which enables an incremental construction. The underlying component model uses transition systems to express the component behaviors, and composition and restriction to express coordination and constraints between components, and allow for heterogeneous models. The results have been implemented and validated in several case studies.