Fish-like swimmers are capable of highly efficient and agile locomotion in water. Engineers have long sought to design swimming robots that emulate the mechanics that lead to such desirable locomotion characteristics. For this purpose appropriately modeling the mechanics of fish-like swimming is essential. Such models determine how engineers design robots and the accompanying control algorithms. On the one hand complex fluid mechanics models exist to characterize the fluid-swimmer interaction that are however difficult to use from the perspective of robotics and control algorithms. On the other hand roboticists use highly simplified models that usually do not sufficiently account for the rich fluid-robot interactions. A key aim of this project is to establish a modeling framework that is simple to use but sufficiently rich enough with regards to fluid-robot interaction. The project accomplished this goal by showing the close similarity of swimming with terrestrial motion.

 The motion of a body on the ground is often subject to constraints on its velocity. In particularly friction ensures that at the points of contact with the ground some components of the velocity of a body are zero. Such constraints are called nonholonomic constraints. A major result of this project has been to show that the motion of fish-like swimmer in water is governed by similar nonholonomic constraints. At the sharp edges of a swimmer such as its tail, the rolling up of water into vortices produces an effect similar to that of the nonholonomic constraints in terrestrial motion. In particular the motion of a fish-like swimmer is similar to that of a classical terrestrial system known as the Chaplygin sleigh. The project first demonstrated this surprising result through idealized flow models, called potential flow models of the water around a swimmer. In the next step incorporating drag like forces into the model showed that due to periodic actuation the velocity of a fish-like swimmer exhibits periodic variations called limit cycles. The project verified this modeling result through experiments.  The project also demonstrated another surprising result both through models and experiments, namely that a neutrally buoyant robot without any propellers, fins or tails can swim purely through the motion of an internal oscillating rotor that is not in contact with the water. Such internal actuation can have significant applications for the design of agile and stealthy robots. Collectively the theoretical modeling and experimental results show that nonholonomic constraints play a key role in fish-like swimming. The utility of using Chaplygin systems to develop simplified models of fish-like swimming was demonstrated in the project by the control of the motion of a swimming robot while better accounting for the coupled fluid-robot interaction.

More broadly the project outcomes showed a surprising connection between terrestrial locomotion and swimming offering the promise of a simplified modeling and control framework for a variety of swimming robots. The research from this project trained two PhD students in interdisciplinary research in dynamical systems, fluid dynamics and robotics with the project grant funding the two students. Several other Masters and under graduate students were trained in research, computational methods, designing and performing experiments.

Last Modified: 11/05/2020
Modified by: Phanindra Tallapragada