Underwater running on uneven terrain

In this work a punting gait model, describing a robot running underwater, is studied with respect to unknown variations of the ground and design parameters of the robot. The model, described through a dynamical system, is actuated with an open-loop control and exhibits self-stabilizing running, represented by the limit cycle of the system, on flat terrain. By introducing a simulated uneven terrain and by keeping the same open-loop control, it appears that the self-stable gait is not affected by disturbances until a certain threshold, when the robot falls to the ground. Moreover, the stability appears to be proportional to the density of the robot and inversely proportional to the drag coefficient of the body, thus suggesting some criteria for the design of underwater running robots.