  Real-world applications of bipedal robot walking require accurate, real-time
state estimation. State estimation for locomotion over dynamic rigid surfaces
(DRS), such as elevators, ships, public transport vehicles, and aircraft,
remains under-explored, although state estimator designs for stationary rigid
surfaces have been extensively studied. Addressing DRS locomotion in state
estimation is a challenging problem mainly due to the nonlinear, hybrid nature
of walking dynamics, the nonstationary surface-foot contact points, and
hardware imperfections (e.g., limited availability, noise, and drift of onboard
sensors). Towards solving this problem, we introduce an Invariant Extended
Kalman Filter (InEKF) whose process and measurement models explicitly consider
the DRS movement and hybrid walking behaviors while respectively satisfying the
group-affine condition and invariant form. Due to these attractive properties,
the estimation error convergence of the filter is provably guaranteed for
hybrid DRS locomotion. The measurement model of the filter also exploits the
holonomic constraint associated with the support-foot and surface orientations,
under which the robot's yaw angle in the world becomes observable in the
presence of general DRS movement. Experimental results of bipedal walking on a
rocking treadmill demonstrate the proposed filter ensures the rapid error
convergence and observable base yaw angle.
