Walking gait optimization for accommodation of unknown terrain height variations

We investigate the design of periodic gaits that will also function well in the presence of modestly uneven terrain. We use parameter optimization and, inspired by recent work of Dai and Tedrake, augment a cost function with terms that account for perturbations arising from a finite set of terrain height changes. Trajectory and control deviations are related to a nominal periodic orbit via a mechanical phase variable, which is more natural than comparing solutions on the basis of time. The mechanical phase variable is also used to penalize more heavily deviations that persist “late” into the gait. The method is illustrated both in simulation and in experiments on a planar bipedal robot.