Roll and Pitch Motion Analysis of a Biologically Inspired Quadruped Water Runner Robot

In this paper, the roll and pitch dynamics of a biologically inspired quadruped water runner robot are analyzed, and a stable robot design is proposed and tested. The robot's foot-water interaction force is derived using drag equations. Roll direction instability is attributed to a small roll moment of inertia and large instantaneous roll moments generated by the foot-water interaction forces. Roll dynamics are modeled by approximating the water as a linear spring. Using this model, estimates on the roll moment of inertia that can endure moments generated by water interactions are derived. Instability in the pitch direction is caused by the thrust force the four feet exert on the water. To correct this, a circular tail which can negate the pitch moment around the center of mass is proposed. Both passive and active tail designs which can cope with disturbances are introduced. Based on these analyses, a stable water runner is designed, and built. Experimental high-speed video footage demonstrates the stable roll and pitch motion of the robot. Simulations are used to estimate robustness against disturbances, waves, and leg running frequency variations. It is found that roll motion is more sensitive to disturbances when compared with the pitch direction.