  Stabilizing legged robot locomotion on a dynamic rigid surface (DRS) (i.e.,
rigid surface that moves in the inertial frame) is a complex planning and
control problem. The complexity arises due to the hybrid nonlinear walking
dynamics subject to explicitly time-varying holonomic constraints caused by the
surface movement. The first main contribution of this study is the extension of
the capture point from walking on a static surface to locomotion on a DRS as
well as the use of the resulting capture point for online motion planning. The
second main contribution is a quadratic-programming (QP) based feedback
controller design that explicitly considers the DRS movement. The stability and
robustness of the proposed control approach are validated through simulations
of a quadrupedal robot walking on a DRS with a rocking motion. The simulation
results also demonstrate the improved walking performance compared with our
previous approach based on offline planning and input-output linearizing
control that does not explicitly guarantee the feasibility of ground contact
constraints.
