Rigorous system design requires the use of a single powerful component framework allowing the representation of the designed system at different levels of detail, from application software to its implementation. The use of a single framework allows to maintain the overall coherency and correctness by comparing different architectural solutions and their properties. In this paper, we present the BIP (Behavior, Interaction, Priority) component framework which encompasses an expressive notion of composition for heterogeneous components by combining interactions and priorities. This allows description at different levels of abstraction from application software to mixed hardware/software systems. Then, we introduce a rigorous design flow that uses BIP as a unifying semantic model to derive from an application software, a model of the target architecture and a mapping, a correct implementation. Correctness of implementation is ensured by application of source-to-source transformations in BIP which preserve correctness of essential design properties. The design is fully automated and supported by a toolset including a compiler, the D-Finder verification tool and model transformers. We illustrate the use of BIP as a modeling formalism as well as crucial aspects of the design flow for ensuring correctness, through an autonomous robot case study.