In this paper we address the problem of global real-time periodic scheduling on heterogeneous multiprocessor platforms. We give a solution based on a {\em constraint satisfaction problem} that we prove equivalent to the multiprocessor problem. A solution has to satisfy a set of constraints and there is no performance criterion to optimize. We propose two different CSP formulations. The first one is a basic encoding allowing to use state of the art CSP solvers. The second one is a more complex encoding designed to obtain solutions faster. With these encodings, we then study the resolution of the scheduling problem using systematic search algorithms based on backtracking.