In this paper, we introduce a hexapedal locomotion controller that simulation evidence suggests will be capable of driving our RHex robot at speeds exceeding five body lengths per second with reliable stability and rapid maneuverability. We use a low dimensional passively compliant biped as a “template” — a control target for the alternating tripod gait of the physical machine. We impose upon the physical machine an approrimate inverse dynamics within-stride controller designed to force the true high dimensional system dynamics down onto the lower dimensional subspace corresponding to the template. Numerical simulations suggest the presence of asymptotically stable mnning gaits with large basins of attraction. Moreover, this controller improves substantially the maneuverability and dynamic range of RHex’s running behaviors relative to the initial prototype open-loop algorithms.