Meshing hybrid zero dynamics for rough terrain walking

For an underactuated biped on a constant-slope terrain, the hybrid zero dynamics (HZD) controller framework provides exponentially stable walking motions. In this paper, we quantify the stability of such a control system on rough terrain by estimating the expected number of steps before failure. In addition, we show how to switch between multiple HZD controllers (optionally using terrain look-ahead) to increase the stability dramatically, e.g., 10 thousand steps compared to 10. To do this robustly, we make use of the new meshing method proposed in this paper.