This paper addresses the problem of mapping an application, which is highly dynamic in the future, onto a heterogeneous multiprocessor platform in an energy efficient way. A two-phase scheduling method is used for that purpose. By exploring the Pareto curves and scenarios generated at design time, the run-time scheduler can easily find a good scheduling at a very low overhead, satisfying the system constraints and minimizing the energy consumption. A real-life example from a 3D quality of service kernel is used to show the effectiveness of our method. Categories and Subject Descriptors D.4.7 [Operating Systems]: Organization and Design— real-time systems and embedded systems; D.4.1 [Operating Systems]: Processing Management; I.6.4 [Simulation and Modeling]: Model Validation and Analysis General Terms Design, Algorithms, Performance Keywords multiprocessor, embedded system, low-power, scheduling