  Controller design for bipedal walking on dynamic rigid surfaces (DRSes),
which are rigid surfaces moving in the inertial frame (e.g., ships and
airplanes), remains largely uninvestigated. This paper introduces a
hierarchical control approach that achieves stable underactuated bipedal robot
walking on a horizontally oscillating DRS. The highest layer of our approach is
a real-time motion planner that generates desired global behaviors (i.e., the
center of mass trajectories and footstep locations) by stabilizing a
reduced-order robot model. One key novelty of this layer is the derivation of
the reduced-order model by analytically extending the angular momentum based
linear inverted pendulum (ALIP) model from stationary to horizontally moving
surfaces. The other novelty is the development of a discrete-time
foot-placement controller that exponentially stabilizes the hybrid, linear,
time-varying ALIP model. The middle layer of the proposed approach is a walking
pattern generator that translates the desired global behaviors into the robot's
full-body reference trajectories for all directly actuated degrees of freedom.
The lowest layer is an input-output linearizing controller that exponentially
tracks those full-body reference trajectories based on the full-order, hybrid,
nonlinear robot dynamics. Simulations of planar underactuated bipedal walking
on a swaying DRS confirm that the proposed framework ensures the walking
stability under different DRS motions and gait types.

Robotics