<p>This paper considers a planar legged robot that moves at high speed on low-elastic floating plates that continue to sink as soon as the robot transfers to it and discusses the motion generation and zero dynamics stabilization methods. First, we introduce a planar 6-DOF legged robot model that has an upper-body link with a reaction wheel and can apply three control torques. The reaction wheel is driven to control the upper-body posture, and its position on the upper-body link can also be controlled by a control force. We then develop the mathematical equations of motion and inelastic collision including the floating plate dynamics which is reproduced as a 1-DOF mass-spring-damper model. Second, we design an output following control system that sets the upper-body angle and the horizontal and vertical positions of the center of mass as the control outputs and numerically generate a stable limit cycle gait on a hard ground. Third, we extend the control system to water surface walking and numerically show that a stable gait can be generated by slightly modifying the target trajectories, with the most significant effect being an approximately 80% reduction in the instantaneous maximum absolute value of the horizontal ground reaction force. Furthermore, we propose two algorithms for stabilizing the zero dynamics of the reaction wheel and show that the entire walking motion including the reaction wheel can be stabilized by appropriately setting the target upper-body angle or the target step period.</p>