I would like to share a piece of work that I think is awesome on so many levels. First, it involves the weakly electric knifefish: a curious creature that maneuvers via ribbon-finned propulsion (a marvel of fluid dynamics) and possesses an uncommon sensing modality in the form of electric field sensing (essentially electrostatic / capacitive sensing). Second, the work models the fish as a dynamic system through its measured frequency response expressed in Bode plots, a process familiar to pretty much any type of engineer. You read that right, they made Bode plots of a fish -- how cool is that!? Be sure to check out the videos and photos below.
A quick introduction to our subject:
Weakly electric fish of the order Gymnotiform (commonly called knifefish) possess a unique sensing modality, electroreception. An electric organ (EO) located in the tail generates a weak electric field. Thousands of voltage sensitive pores detect small changes in transdermal voltages; these voltage measurements collectively form an image of the proximal electric field. Fluctuations in this “electric image” correspond to objects in the fish's environment.
In essence, the electric field sensing allows the fish to "see" in murky water to locate prey and avoid predators. Curiously, scientists claim that these fish have the natural ability to solve a very difficult problem called electrical impedance tomography (EIT), also sometimes called the inverse conductivity problem. Unfortunately, humans have no such ability, though we have co-opted electric field sensing (also called electrostatic / capacitive sensing) to build some pretty amazing devices, even without closed-form EIT. My favorite examples are from Josh Smith of Intel Labs, who uses electric field sensing on robots to provide "Pretouch" sensing and to sense electrical outlets. Josh's earlier thesis work, called the School of Fish project, suggests how the knifefish might use its unique sensing modality to perceive its surroundings.
Like many small fish, the knifefish will go to great lengths to remain hidden inside crannies and crevices, as shown in the videos below, where the knifefish tries to stay hidden inside a moving PVC pipe.
Well, Dr. Noah Cowan and Dr. Eric Fortune from Johns Hopkins' LIMBS Lab and Fortune Lab (respectively) investigated sensorimotor integration in weakly electric knifefish and published their findings in the Journal of Neuroscience in a paper entitled, "The Critical Role of Locomotion in Decoding Sensory Systems." To quote from the work:
The fish (brown) maintains its position within a rectangular tube. This refuge has a clear polycarbonate top and white plastic sides with ceramic filled windows (gray). Schematic view of the video data captured using a camera positioned above the fish is shown. Three values are the position of the fish [x(t), purple lines] ,the position of the refuge [r(t), green lines], and the relative difference between the fish and the refuge [e(t), dashed blue line].
Tracking data from a fish (stimulus amplitude, 0.5 cm). The height of each trace is scaled identically; the width of each trace is scaled to show two stimulus cycles (green) at three rates of motion (labeled). The amplitude of fish movements, x(t), decreased with increasing stimulus frequency with increasing phase lag.
Bode amplitude and phase plots for stimulus rates from 0.1–1.3 Hz. Error bars indicate the standard deviation (N = 4 fish). The dashed curve indicates the first-order model (rejected), and the gold region indicates 95% confidence intervals for this model. The solid curve indicates the second-order model, and the blue region indicates 95% confidence intervals for this model.
So, apparently knifefish can be modeled (with pretty high confidence) as a 2nd order system with cutoff frequency of around 1Hz with decent phase margin -- cool. Here's the fish being a good little 2nd order system.
Many thanks to the Georgia Tech Robotics and Intelligent Machines (RIM@GT) seminar series for having Dr. Cowan come present his work last year, exposing me to this cool piece of work.