Admissible Region ZMP Trajectory Generation for Bipedal Robots Walking Over Uneven Terrain

In this paper, the trajectory generation problem for a bipedal walking robot traversing uneven terrain is considered. Most of the well-tested approaches to walking over flat terrain are based on zero-moment point (ZMP) principle, often in combination with linear inverted pendulum model. These approaches cannot be directly transferred to uneven terrain because ZMP conditions require the supporting surface to be flat and horizontal and with sufficient friction to prevent feet slipping. In this paper, a way to generalize these approaches to uneven terrain with unknown tribological properties is given. The approach is based on numerically checking which starting points for the ZMP, and the center of mass trajectories are admissible for the given terrain. These points form convex regions, which can be explicitly included in real-time trajectory planning procedures. In order to take into account the fact that the exact properties of the supporting surface are unknown, the parameters of the surface can be varied to find robust admissible ZMP regions, as discussed in the paper. Examples of the use of admissible ZMP regions are given.