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.
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