An important motivation for work on legged robots has always been their potential for high-performance locomotion on rough terrain. Nevertheless, most existing control algorithms for such robots either make rigid assumptions about their environments or rely on kinematic planning at low speeds. Moreover, the traditional separation of planning from control often has negative impact on the robustness of the system. In this paper, we introduce a new method for dynamic, fully reactive footstep planning for a planar spring-mass hopper, based on a careful characterization of the model dynamics and the design of an associated deadbeat controller, used within a sequential composition framework. This yields a purely reactive controller with a large domain of attraction that requires no explicit replanning during execution. We show in simulation that plans constructed for a simplified dynamic model can successfully control locomotion of a more complete model across rough terrain. We also characterize the performance of the planner over rough terrain and show that it is robust against both model uncertainty and measurement noise without replanning. © 2012 IEEE.