A new requirements-based programming approach to the engineering of computer-based systems offers not only an underlying formalism, but also full formal development from requirements capture through to the automatic generation of provably-correct code. The method, Requirements-to-Design-to-Code (R2D2C), is directly applicable to the development of autonomous systems and systems having autonomic properties. We describe both the R2D2C method and a prototype tool that embodies the method, and illustrate the applicability of the method by describing how the prototype tool could be used in the development of LOGOS, a NASA autonomous ground control system that exhibits autonomic behavior. Finally, we briefly discuss other possible areas of application of the approach.