Convergent evolution creates one of those goose-bumps moments for biologists. I mean, how cool is it that dolphins and whales evolved from mammals to look like extinct ichthyosaurs and mosasaurs that were, in turn, independently evolved from reptiles? Not only does convergence provide great evidence for evolution by natural selection, but it also suggests that, in some kinds of situations, only a few options exist for pushing the performance envelope in the game of life.
When the game moves from land back to water, the aquatic tetrapods basically have two choices to overcome their locomotor roadblock: limbs or body axis. Frank Fish, professor of biology at West Chester University and an expert in the biomechanics of aquatic locomotion, has proposed a functional path for the evolution of aquatic tetrapods in mammals.[156] According to Fish, it’s probably the case that swimming with appendages is the way that the shift back to water starts; this seems likely because almost every terrestrial mammal we see will swim using a variant of the “dog paddle” when they hit the water. Some lineages, such as seals and sea lions, stick with appendages, expanding and oscillating their rear flippers, in the case of seals, or flapping their front flippers, in the case of sea lions. Others—whales and manatees, for example—evolve their developmental programs to stop building appendages, losing the rear limbs and using the body axis, anchored by that pesky vertebral column again, to move the evolutionarily novel flukes up and down.
Pleiosaurs evolved along roughly the same track as seals, sea lions, and sea turtles, sticking with appendages as they readapted to life in the water. Here’s a curious observation, one that makes me wonder and drives me mad with evolutionary might-have-beens: none of the living aquatic tetrapods ever use all four appendages to swim underwater—they use only two. The plesiosaurs, however, appear to have used all four limbs, which were modified into wing-shaped flippers (see again Figure 7.6). If four flippers were good enough for plesiosaurs to rule the seas as the top-level predators in the Mesozoic, why aren’t they good enough now?
Let’s ring the bell and bite the apple! We want to know: why, why, why? Why don’t mammals and sea turtles alive today use all four flippers for propulsion? From a mechanical point of view, it sure seems like using four flippers for propulsion should be better in almost any way imaginable. If you think about each flipper as a propeller, then any agent—animal or robotic—using four flippers instead of two should be able to accelerate more rapidly, reach a faster cruising speed, and brake more quickly. So why wouldn’t they? That, then, was the behavioral mystery within the context of evolutionary paths taken and not taken that we set out to solve with an Evolutionary Trekker.
Here’s where we need Robot Madeleine. We built her as a generalized aquatic tetrapod, with four identical flippers that propel her as she swims underwater. She’s 0.78 meters long stem to stern and weighs twenty kilograms dry, roughly the length and mass of an adult green sea turtle or a small species of plesiosaur, minus the long neck (see Figure 7.6). Each of her flippers, called a Nektor by engineers, has the cross-sectional shape of a wing or, to be precise, a hydrofoil.[157] Each flipper is oscillated around an axis, “in pitch” as the engineers say, by separate motors inside Madeleine’s hull. To avoid building an overly powerful super ’bot, we chose motors that would approximate the power density of vertebrate skeletal muscle, about ten watts per kilogram of body weight. And of course, Maddie has a body shaped like a petit madeleine pastry. From a biological point of view, this pastry shape would be described as bilaterally symmetrical, with a fusiform shape for streamlining.[158]
All of Maddie’s features just mentioned were chosen with mechanistic accuracy in mind. So as convergent evolution seems to do for aquatic tetrapods, we focused on her locomotor behavior and the structures related to generating propulsion. To judge whether we’d done a good job of recreating an aquatic tetrapod, we rely on five of Webb’s criteria for a model robot: biological relevance (criterion 1), behavioral match between the target and the model (criterion 2), mechanistic accuracy (criterion 3), level of structure (criterion 5), and substrate (criterion 7).
Perhaps the biggest complaint we get about Maddie is that she does not represent any species in particular, giving her low concreteness (or, conversely, high abstraction, Webb’s fourth criterion). But … precisely! That’s what we wanted, and Webb’s criteria help us recognize and explain that Robot Madeleine can’t—and shouldn’t even be able to—do it all. In fact, that’s why I named her after a French pastry. I didn’t want to pretend that she was a robotic turtle, for example, as she has come to be named in the popular press. Can I have my pastry and eat it too? If Madeleine is not a robotic turtle, then how can I claim that she is a robotic plesiosaur? I don’t. What I claim is that Maddie uses some of the same propulsive principles that we think both turtles and plesiosaurs use and used. Thus, Maddie’s mechanistic accuracy is high for any aquatic tetrapod that flaps flippers to swim. Thinking about modeling as the process of representing, Maddie’s behavior represents the behavior of turtles and plesiosaurs in the specific sense that she is about their size and swims with flippers.
Another important critique of Madeleine is that her flippers don’t work in exactly the same way as the flippers of a turtle or a plesiosaur. This gets to the issue of accuracy of the model at the level of the propulsive elements. The motion of Maddie’s flippers, or Nektors, as they are known, is unbiological, in no small part because their movements are much simpler than, say, the movements of the front flippers of sea lions.[159] Both Maddie’s flippers and a sea lion’s rotate in pitch during each stroke—but that’s all Maddie’s do. A sea lion’s also roll as the front limb pivots about the joint of the shoulder. While the sea lion is rolling its flipper down and pitching it about its long axis, it is also yawing the flipper about the shoulder joint, moving the flipper’s tip rearward toward its hip. To jump into the lingo of engineering, then, the flipper of a sea lion has three degrees of freedom, whereas Maddie’s has only one. And even three degrees is still too simple! I’ve conveniently neglected to mention that the flippers change shape as they rotate, with joints at the elbow, wrist, and five fingers flexing and extending. Let’s see, if we assume that elbow, wrist, and five finger joints are all simple planar joints, that adds seven degrees of freedom. In sum, each flipper has ten degrees of freedom from ten joints, and each joint has be actuated, controlled, and, as a group, coordinated.
Are you ready to give it a try? You can do it! But before you run off and build a better flipper, keep in mind that by jumping from one to ten degrees of freedom you’d be violating the KISS principle, at your own peril. You’d be doing the opposite of making the simplest device possible. Let’s give that anti-KISS principle a name: Make It Complicated, Einstein, or MICE. With MICE, you’d need to create an internal skeleton with joints strong enough to withstand all of the hydrodynamic loads yet supple enough to bend without requiring too much force. You’d need to figure out how to move all ten of the joints that you’ve created: do you put motors out in the fingers and add bulk and weight, or do you run wires or hydraulic tubes from the inside of Maddie? Then you’d have to cover and embed the skeleton with a flexible, body-like material that maintains shape yet reconfigures as the flipper moves. And, once covered, that limb would need to allow you to get back inside for repair and maintenance.
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Start here with two of Frank’s papers: “Transitions from Drag-Based to Lift-Based Propulsion in Mammalian Aquatic Swimming,”
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These flippers, or Nektors, are themselves biologically inspired. Charles Pell, working with a graduate student at Duke University in the BioDesign Studio that he and Professor Steve Wainwright created, noticed that a fish-like piece of rubber, mounted on a stick, would generate thrust if you wiggled the stick between your fingers, rolling the stick between thumb and forefinger, with the fish in the water. Pell, then-student-of-mine Matt McHenry, and I used Nektors as model representations of blue-gill sunfish to analyze swimming propulsion: M. J. McHenry, C. A. Pell, and J. H. Long Jr., “Mechanical Control of Swimming Speed: Stiffness and Axial Wave Form in an Undulatory Fish Model,”
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Tellingly, petit madeleines are modeled after scallops! If you buy madeleine pans, you’ll notice right away the fluted and streamlined depressions into which you pour the batter. What’s cool about scallops is that they are bivalves, mollusks with two shells, that actually swim. So here we have a swimming scallop that is the model for a streamlined pastry that is the inspiration of the name of a swimming and streamlined biorobot. Does it get any more fun?
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Forgive the engineer-speak about to issue forth. Maddie’s flippers, or Nektors, are single-degree-of-freedom actuators. A shaft colinear with a rotary motor moves the flipper, the compliant material forming the shape and bulk of the appendage, which is molded around the shaft at a specified angular velocity. The flipper is oriented so that its leading edge rotates in pitch. That pitch rotation flaps the flipper and transfers angular momentum to the surrounding water. When the pitch rotation is reciprocated such that the direction of the angular velocity alters regularly, as with a sine function, then the momentum transferred from the flipper to the water can be focused as a jet. This jet, in turn, produces a net thrust, via Newton’s third law, on the oscillating flipper.