research

 

My primary research activities — from which this website borrows its name — pertain to the modeling, analysis, and control of fluid-body interactions underpinning biomorphic locomotion in fluids. This includes both swimming and flight, but most of my current work addresses the former.

The locomotion of marine animals is as subtle as it is diverse, and illuminating its fundamentals requires one to confront a unique set of problems in theoretical mechanics and nonlinear dynamics. This topic is of patent scientific interest, but has also been the focus of increasing attention from the robotics community, eager to decrypt the means by which animals achieve superior agility, energy efficiency, and stealth underwater.

There's a lot to this topic — too much to cover in detail here — but I can provide a few points of entry...

Here's a simulation depicting a free Joukoski foil with time-varying camber shedding point vortices in accordance with a periodically-enforced Kutta condition in an otherwise ideal fluid. The model was developed by my student Hailong Xiong, who's studying the basic properties of such models in the context of geometric mechanics and using them to explore the energetics and control of fishlike locomotion in the plane. Here's part of an experimental apparatus built by my students Will Burgoyne and Yi-Fu Wu to validate some of the force and moment predictions made by Xiong's models.

Here's a photograph depicting an array of three independently actuated oscillating hydrofoils propelling themselves as a group across a swimming pool in my lab. This apparatus was built by my former students Nathan Hoople and Jon Craig. Hydrodynamic interactions among the foils have a significant influence on their collective propulsive efficiency; here are plots of position versus time corresponding to two different spacings among the foils in the array with the same control inputs sent to the foils. Whether or not fish swim in schools to improve their collective propulsive efficiency is a topic of debate, but schooling fish must contend with the effects of hydrodynamic interactions for good or bad. UCLA's Jeff Eldredege has joined me in trying to figure out what's going on; here and here are viscous vortex particle method simulations of his depicting the shedding of vorticity from foils in an array that's fixed in place. The array in the first movie generates more than thrice the thrust of a solitary foil, the array in the second movie generates less than thrice the thrust of a solitary foil.

In treating problems in biomorphic aquatic locomotion as control problems, it's not clear whether one wants to think in terms of directly controlling the forces developed on a swimming device or in terms of controlling the hydrodynamic phenomena — such as vortex shedding and the development of circulatory flows — that generate these forces. Here's a photograph of a robot simulating fishlke propulsion with a rotating cylinder in place of a caudal fin, placing the emphasis on circulation control. A family of such devices was built by my former student Ramadev Hukkeri; our models for these devices accommodate the formalism of Lagrangian mechanics in an interesting way.

Here's some video of a simple robot that propels itself like a jellyfish, built by my students Joe Tigue and Will Burgoyne. Note that the tether visible in the video is pushing down on the robot as it surfaces, not helping it to rise. My student Yi-Fu Wu photographed the robot shedding a vortex ring. I've been working with Artan Sheshmani (a student in UIUC's math department), Banavara Shashikanth (from NMSU), and Jerry Marsden (from Caltech) to develop Hamiltonian models for the interactions of free solid bodies and vortex rings.

Here's some video of cownose rays at the Shedd Aquarium in Chicago, shot by my student Aras Buntinas. Aras is working on a prototype for a robotic ray of this kind.

It's one thing to figure out how a robotic vehicle resembling a dolphin or ray should undulate to propel itself through a quiescent fluid, but it's quite another to succesfully program such a vehicle to negotiate a realistic aquatic environment. Marine animals possess sophisticated means to sense the unsteady flows around them so that they may respond accordingly; the absence of flow sensing for feedback control is a poignant limitation of the present generation of biomorphic underwater vehicles. Indeed, the energy-efficient deployment of vehicles in hydrodynamically coupled schools demands that such vehicles possess distributed flow sensing technology. I'm currently working to advance this technology, and to realize compatible motion control methods, in collaboration with UIUC's Chang Liu, who has developed millimeter-scale sensors mimicking the haircells comprising piscine lateral lines.

Good models and feedback control methods for hydrodynamic interactions are necessary but not sufficient for the coordinated maneuvering of robotic fish schools, let alone for their viability as a platform for, say, adaptive ocean sampling networks. Decentralized control strategies must be developed to orchestrate collective motions on a higher level, and such strategies must be compatible with the nonlinearities inherent to individual vehicle dynamics. Here's an animation depicting the initiation of a coordinated maneuver by four underactuated vehicles, described by simple hydrodynamic models with parametric uncertainty, subject to a model reference adaptive control law realized in terms of partial difference equations on a graph reflecting the underlying communication structure. The simulation was generated by Jun Kim, a former student of UIUC's Joesph Bentsman, with whom I'm collaborating in this area.

 

Quite apart from problems peraining to mechanical systems, I'm also interested in the dynamics and control of physiological regulatory networks like the human immune system. But that's a summary for another day.