In this paper, we present dead-beat control of a torso-actuated rimless wheel model. We compute the steady state walking gait using a Poincaré map. When disturbed, this walking gait takes a few steps to cancel the effect of the disturbance but our goal is to develop a faster response. To do this, we develop an event-based, linear, discrete controller designed to cancel the effect of the disturbance in a single step — a one-step dead-beat controller. The controller uses the measured deviation of the stance leg velocity at mid-stance to set the torso angle to get the wheel back to the limit cycle at the following step. We show that this linear controller can correct for a height disturbance up to 3% leg length. The same controller can be used to transition from one walking speed to another in a single step. We make the model-based controller insensitive to modeling errors by adding a small integral term allowing the robot to walk blindly on a 7° uphill incline and tolerate a 30% added mass. Finally, we report preliminary progress on a hardware prototype based on the model.

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