Tethering and depth of submergence affect the swimming performance of undulatory robots

Over the past few decades, biomimetic robotic experiments have significantly advanced our understanding of undulatory swimming. Compared to animal experiments, robotic experiments offer repeatability and controlled parameter variations, but the robots operate under constraints that differ from those experienced by their natural counterparts. Freely swimming robots often remain on the surface, whereas most undulatory fish, including eels, are typically fully submerged during locomotion. Studies focusing on submerged swimming commonly rely on tethered robots to maintain depth control. This study examines the performance implications for free versus tethered swimming at the surface, and for tethered swimming at the surface to tethered fully submerged swimming, using the robotic undulatory swimmer 1-guilla. The robot was tested in two configurations: free swimming in a pool and tethered swimming in a water channel at the surface and at varying depths down to three body heights. We varied kinematic input parameters and quantified performance in terms of swimming speed, cost of transport, and body kinematics. Our results reveal that at the surface, tethered swimming achieves speeds comparable to free swimming but at a lower energetic cost. This reduction in cost of transport is attributed to the mechanical stabilisation imposed by tethering, including the suppression of body roll and lateral head motion. Increasing submergence depth improved both the maximum speed and energy efficiency by more than 10\% relative to the surface swimming performance. As the body kinematics remained unchanged when submerged, the performance deficit near the surface is attributed to increased wave drag. Overall, our findings provide explanations and insights into discrepancies in results obtained for tethered and free-swimming robotic studies, they highlight the hydrodynamic challenges of surface locomotion, and can help explain why natural undulatory swimmers predominantly favour submerged propulsion.