The main driving force behind research on legged robots has always been their potential for high performance locomotion on rough terrain and the outdoors. Nevertheless, most existing control algorithms for such robots either make rigid assumptions about their environments (e.g flat ground), 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 against model uncertainty and environment noise. In this paper, we introduce a new method for dynamic, fully reactive footstep planning for a simplified planar spring-mass hopper, a frequently used model for running behaviors. Our approach is based on a careful characterization of the model dynamics and an associated deadbeat controller, used within a sequential composition framework. This yields a purely reactive controller with a very large, nearly global domain of attraction that requires no explicit replanning during execution. Finally, we use a simplified hopper in simulation to illustrate the performance of the planner under different rough terrain scenarios and show that it is extremely robust to both model uncertainty and measurement noise. © 2009 IEEE.