We consider the problem of a 2D point mass model navigating a complex terrain comprising of stepping stones and stairs while optimizing an energy metric. We solve the problem using receding horizon control as follows. We preview a fixed distance ahead at mid-flight. Then we optimize the number of steps, the controls, and foot placement location, choosing the solution with least energy cost. However, we implement only the solution for the first step which takes the model to the next mid-flight. This process continues until the model reaches the end of the terrain. We improve on past approaches by (1) considering a fixed distance preview as done by humans instead of fixed time or fixed steps, and (2) adding obstacles as a cost and elevation change as a condition within the model dynamics, thus avoiding mixed-integer formulations which are computationally expensive. The resulting problem is solved using constrained nonlinear programming. We demonstrate that the approach works for randomly chosen terrain consisting of stepping stones and stairs.

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