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Approximate optimal control of the compass gait on rough terrain

In this paper, we explore the capabilities of actuated models of the compass gait walker on rough terrain. We solve for the optimal high-level feedback policy to negotiate a perfectly known but qualitatively complex terrain, using a fixed low-level controller which selects a high-level action once- per-step. We also demonstrate that a one-step time horizon control strategy using the same low-level controller can provide performance which is surprisingly comparable to that of the infinite time horizon optimal policy. The model presented here uses a torque at the hip and an axially-directed impulsive toe-off applied just before each ground collision. Our results provide compelling evidence that actuated robots based on passive dynamic principles (e.g. no ankle torque) should inherently be capable of walking on significantly rough terrain.