  Legged robot locomotion on a dynamic rigid surface (i.e., a rigid surface
moving in the inertial frame) involves complex full-order dynamics that is
high-dimensional, nonlinear, and time-varying. Towards deriving an analytically
tractable dynamic model, this study theoretically extends the reduced-order
linear inverted pendulum (LIP) model from legged locomotion on a stationary
surface to locomotion on a dynamic rigid surface (DRS). The resulting model is
herein termed as DRS-LIP. Furthermore, this study introduces an approximate
analytical solution of the proposed DRS-LIP that is computationally efficient
with high accuracy. To illustrate the practical uses of the analytical results,
they are used to develop a hierarchical planning framework that efficiently
generates physically feasible trajectories for DRS locomotion. The
effectiveness of the proposed theoretical results and motion planner is
demonstrated both through simulations and experimentally on a Laikago
quadrupedal robot that walks on a rocking treadmill.
