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Sensing and Control for Robotic Fish Locomotion
Richard Mason, Kristi Morgansen, Joel Burdick

Abstract. We are studying issues in fluid mechanics, nonlinear control, and sensing that are necessary for the development of self-propelled robot fish.

Motivation and Aims. Fish are very impressive swimmers in many ways, and it is possible that submersible robots would be more effective if they swam like fish than if they used propellers. For example, fish-like robots could be quieter, more maneuverable, and possibly more energy efficient. At the moment we are focusing on carangiform fish: fish with large, high-aspect-ratio tails that swim mostly by moving their tails and keep the rest of their body fairly rigid. Many large, fast fish (e.g. swordfish) fall into this category and they are arguably the easiest to replicate mechanically.

We would like to know how to control a robot "fish" so that it swims stably and efficiently. Furthermore, we would like to understand the types of sensing that are required to enable robust and efficient carangiform propulsion.

Research. We are investigating two issues. First, we are trying to understand the mechanics of fish locomotion. We hope to use this understanding to implement control of robotic fish locomotion. Second, we are using the insights gained from mechanical analysis to understand the influence of mechanics on the evolution of sensing modalities in biological fish. We ultimately hope to implement engineering versions of the interesting sensors that fish employ. Our group's particular approach to fish locomotion mechanics is to employ the tools of geometric mechanics. These have been useful in simplifying the control of other kinds of locomotion systems and we hope that they can also be applied to fluid mechanical systems.

In our theoretical analysis and in computer simulations, we are treating the water around the fish as an ideal fluid, i.e. neglecting most of the effects of viscosity. We treat the whole problem as essentially planar and consider the wake of the fish as a sequence of point vortices in an otherwise irrotational fluid. The validity of this approximation is largely supported by our experimental results.

In order to test our ideas experimentally, we have built a robot "fish" with two actuators and three links, suspended in a water tank from a gantry-like carriage. (See below for a schematic diagram.) The gantry suspends the fish so that buoyancy effects can be ignored. The carriage also simplifies the experiment by keeping the motors, electronics, etc. out of the water.

The passive gantry-like carriage is supported by low friction bearings, and allows the fish to move with three degrees of freedom in the plane: forward, sideways, and rotationally. By flapping its tail, the fish can propel itself and its supporting carriage around the tank. The drag due to the carriage is essentially negligible compared to the water's drag, and hence this apparatus is a reasonable approximation of self-propelled fish.

Robot Fish Movies

Most of the potential advantages of fish-like swimming will come from a more sophisticated exploitation of the fluid flow around the fish than would be possible with simple propellers. In particular, both the thrusting action of the tailfin and the drag forces acting on the body of the fish will cause energetic vortices to be shed in the wake of the fish. With the right tail movements, the fish might be able to recover some of the shed energy of these vortices. Biological studies support such a hypothesis.

Possibly this can be done "open-loop" without any direct sensing of the location of the vortices of of the local fluid flow filed. However, it seems more likely that sensors to measure the state of the fluid flow around the fish and provide feedback would greatly improve performance. In biological fish, Nature seems to have solved this problem by evolving a complex sensing system known as the lateral line organ. In the long term we plan to explore the use of advanced pressure sensors that could imitate the lateral line sensory organs of fish and provide the same data about the local water flow that fish use to regulate their swimming.

Schematic diagram of the fish lateral line sensor, consisting of "neuromasts" (hair cell sensors) and a associated neural processing network

Achievements. To date, we have developed models for how thrust is generated by the flapping tail movements. Our experimental data agree quite well with computer simulations of the theoretical models, as in the figure below which shows the fish displacement versus time as the robot starts from rests and propels itself forward using a repetitive flapping motion. We have found non-obvious gaits for turning and for effective forward swimming. We are continuing research into trajectory planning and swimming with sensory feedback.

Publications/References

Trajectory Stabilization for a Planar Carangiform Robot Fish. K. A. Morgansen, P. A. Vela, and J. W. Burdick. Submitted to 2002 IEEE International Conference on Robotics and Automation.

Trajectory Planning Using Reachable-State Density Functions. Richard Mason and Joel W. Burdick. Submitted to 2002 IEEE International Conference on Robotics and Automation.

Second Order Averaging Methods for Oscillatory Control of Underactuated Mechanical Systems. P. A. Vela, K. A. Morgansen, and J. W. Burdick. Submitted to 2002 American Control Conference.

Nonlinear Control Methods for Planar Carangiform Robot Locomotion Fish. K. A. Morgansen, V. Duindam, R. J. Mason, J. W. Burdick and R. M. Murray. IEEE International Conference on Robotics and Automation, 2001.

Experiments in Carangiform Robotic Fish Locomotion. Richard Mason and Joel Burdick. IEEE International Conference on Robotics and Automation, 2000.

Construction and Modelling of a Carangiform Robotic Fish. Richard Mason and Joel Burdick. International Symposium on Experimental Robotics, 1999.

Propulsion and Control of Deformable Bodies in an Ideal Fluid. Richard Mason and Joel W. Burdick. IEEE International Conference on Robotics and Automation, 1999.

Modelling and Experimental Investigation of Carangiform Locomotion for Control. Scott D. Kelly, Richard J. Mason, Carl T. Anhalt, Richard M. Murray, and Joel W. Burdick. American Control Conference, 1998.