  We propose a method to generate actuation plans for a reduced order, dynamic
model of bipedal running. This method explicitly enforces robustness to ground
uncertainty. The plan generated is not a fixed body trajectory that is
aggressively stabilized: instead, the plan interacts with the passive dynamics
of the reduced order model to create emergent robustness. The goal is to create
plans for legged robots that will be robust to imperfect perception of the
environment, and to work with dynamics that are too complex to optimize in
real-time. Working within this dynamic model of legged locomotion, we optimize
a set of disturbance cases together with the nominal case, all with linked
inputs. The input linking is nontrivial due to the hybrid dynamics of the
running model but our solution is effective and has analytical gradients. The
optimization procedure proposed is significantly slower than a standard
trajectory optimization, but results in robust gaits that reject disturbances
extremely effectively without any replanning required.
