QUICK SEARCH:   [advanced] Author: Keyword(s):
Home     Help     Feedback     Subscriptions     Archive     Search     Table of Contents

First published online November 17, 2006
Journal of Experimental Biology 209, 4732-4746 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.02559

This Article Summary Full Text Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Related articles in JEB Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Long, J. H. Articles by Schumacher, J. Search for Related Content PubMed PubMed Citation Articles by Long, J. H., Jr Articles by Schumacher, J.

Biomimetic evolutionary analysis: testing the adaptive value of vertebrate tail stiffness in autonomous swimming robots

J. H. Long, Jr^1,*, T. J. Koob², K. Irving¹, K. Combie¹, V. Engel¹, N. Livingston³, A. Lammert⁴ and J. Schumacher⁵

¹ Department of Biology, Program in Cognitive Science, and the Interdisciplinary Robotics Research Laboratory, Vassar College, Poughkeepsie, NY 12604, USA
² Skeletal Biology, Shriners Hospital for Children, Tampa, FL 33612, USA
³ Department of Electrical Engineering and Computer Science, Case Western Reserve University, Cleveland, OH 44106, USA
⁴ Speech and Hearing Research, VA Medical Center and East Bay Institute for Research and Education, Martinez, CA 94553, USA
⁵ Department of Neurology, Columbia University, New York, NY 10032, USA

View larger version (25K): [in a new window]   Fig. 1. Methodological approach to biomimetic evolutionary analysis using evolutionary robotics. In software (red font), a genetic algorithm is used to create randomly variable genotypes. In hardware (black font), those genotypic codes are used to manufacture biomimetic tail phenotypes that, in turn, are outfitted onto autonomous robots for biomechanical testing and competition experiments. The research cycle is repeated for ten generations.

View larger version (29K): [in a new window]   Fig. 2. Biomimetic tadpole robot (`Tadro') with biomimetic tail. Modeled after the free-swimming larvae of the sea squirts (subphylum Urochordata), the robots have a single eyespot (photoresistor), a flapping tail, and a microcontroller that converts the light intensity at the eyespot into a turning angle at the tail. This sensorimotor system produces autonomous phototactic navigation (Long, Jr et al., 2004b). New to this version of the Tadro are the digital microcontroller, servo tail flapper, and the biomimetic gelatin hydrogel of the tail serving as a notochord. The notochord's spring stiffness, k, is determined by bending modulus E and length L, which are coded as quantitative trait loci. The flapping amplitude of the servo motor was constant at ±30°. The tail position had a range of 180°. See Table 1 for additional operating and morphological parameters.

View larger version (58K): [in a new window]   Fig. 3. Biomimetic Tadros compete in phototactic forage navigation. (A) Three prototype Tadros swim during the initial light-detection phase. Note that Tadros interact physically and compete within a generation; thus they are an evolving part of the otherwise stable selective environment. (B) Trajectories of three Tadros in one trial (generation 1, trial 4 of 12), showing the differences in orbital radius around the light target. Fitness rewards a small orbital radius R, short time to find the target t, fast swimming speed U and low robot wobble W. Here tail stiffness k is correlated with fitness and navigational prowess NP.

View larger version (57K): [in a new window]   Fig. 4. Light and perceptual environments for Tadros. (A) Overhead view of light environment in experimental tank, with color gradient showing position of light source. Arrow indicates radial slice shown in B. (B) Light intensity gradient along radial indicated in A. (C) Perception of light gradient by Tadros. Polar plots indicate light intensity (along radii, with origin at 0 lux) registered by Tadros at different headings every 0.1 m along radial slice shown in B. A heading of 0° means that the Tadro was facing in the direction indicated by the arrow in A. Note eyespot is located 45° to the left of the Tadro's centerline (see Fig. 2).

View larger version (29K): [in a new window]   Fig. 5. Wobble W measures unsteady turning maneuvers. Defined as the standard deviation of the angular acceleration experienced by the Tadro's hull, W includes acceleration from the yaw recoil of swimming and the turning maneuvers exercised by the Tadro as it seeks light and maintains station about the light source. (A) This hypothetical situation shows how angular velocity added to swimming yaw (dark line) yields the total angular velocity (red) line, the difference being the maneuvering velocity added to swimming. (B) Angular acceleration of the data from the hypothetical situation shows how W measures its dispersion about the mean value. Simple sinusoidal model of angular velocity with realistic values for tailbeat frequency (1.7 Hz) and W chosen as parameters (see Results). The value for unsteady turning maneuvers (0.17 Hz) was estimated from trials.

View larger version (25K): [in a new window]   Fig. 6. Evolution of morphology and behavior of the robotic population. Significant changes in population means between generations are indicated with an asterisk midway between the points (=0.05; planned a priori contrasts in nested ANCOVA on data transformed to create normal distribution, with logL, k; arcsine R, U, W, NP; inverse t). Red asterisks indicate changes driven by selection and chance (drift + mutation); blue asterisks chance only. Selection occurred in generations 1, 5, 6 and 9. Values are means ± s.e.m.

View larger version (20K): [in a new window]   Fig. 7. Unidirectional evolution in response to selection. Evolutionary change measured as the difference in population means between generations, x, with changes grouped by absence (N=5) and presence (N=4) of selection. Selection occurred in generations 1, 5, 6 and 9; chance occurs throughout. Neither of the genetically based traits, E and L, evolved unidirectionally in response to selection. The four components of fitness, R, t, U and W, evolved unidirectionally in response to selection. Navigational prowess increases in response to selection, while tail stiffness k does not. Significance determined using one-way ANOVA on data transformed to create normal distributions (logL, k; arcsine R, U, W, NP; inverse t). Values are means ± s.e.m.

View larger version (14K): [in a new window]   Fig. 8. Tail stiffness k predicts the kinematic phenotypes (A) swimming speed U and (B) robot wobble W. Data for competition experiments (open circles) are means of 12 navigation trials for each of 30 tails. Data for biomechanical analysis (closed circles) are means of three straight-swimming trials for each of 30 tails. Lines indicate significant (<0.01) regressions on log-transformed data; data without a line failed the significance test at <0.05. Note that W for the competition experiments includes wobble caused by swimming and maneuvering (see Fig. 5).

View larger version (10K): [in a new window]   Fig. 9. Causal connection between tail stiffness k and swimming speed U. (A) Tail stiffness increases tailbeat amplitude a. (B) In turn, tailbeat amplitude increases swimming speed U. Data for biomechanical analysis are means of three straight-swimming trials for each of 30 tails. Lines indicate significant (<0.01) regressions on logtransformed data.

View larger version (17K): [in a new window]   Fig. 10. Evolutionary steps in [E, L] morphospace. Trajectory of the population mean from generation 1 to 10 (italic numbers). Arrowheads indicate transitions where selection was present; all transitions include change by chance (drift + mutation). The ellipses represent the population's footprint in morphospace (axes ± 1 s.e.m.). Contours represent isoclines for tail stiffness k. Note that selection operates in directions that both increase and decrease k.

View larger version (12K): [in a new window]   Fig. 11. Predicting navigational prowess, NP. (A) Tail stiffness k predicts NP. Predicted values of NP were generated from values of kinematic variables R, t, U and W predicted by k in univariate regressions (Table 4). Stiffness predicts 40% of the variance in NP. (B) Stiffness-independent correlates of NP. Residuals (observed minus predicted value) of NP, by definition independent of k, are correlated with the residuals of two of the four kinematic variables, orbital radius R (P<0.0001) and swimming speed U (P<0.001) as determined by stepwise linear regression (r2=0.81). Residuals for kinematic variables from regression onto k. All observed values are means of 12 trials for each of three tails for ten generations (N=30).

View larger version (12K): [in a new window]   Fig. 12. Navigational and mechanical behaviors decoupled. Evolutionary trajectory of the population mean in [NP, k] behavior space, from generation 1 to 10 (italic numbers). Arrowheads indicate the presence of selection. Note that while selection always acts to increase NP, two selection events increase and two decrease k. Moreover, large changes in NP, from generation 2 to 4, driven by chance, occur with little or no change in k. The points are the mean values for the population (N=3), and the ellipses represent the population's footprint in behavior space (axes ± 1 s.e.m.).

View larger version (11K): [in a new window]   Fig. 13. Summary of the evolution of Tadros' morphology, mechanics and behavior. Plus and minus signs represent a statistically significant (P<0.05) correlation or regression. Blue arrows indicate relations established in biomechanical analysis (Fig. 9). Red arrow indicates relation detected only in competition trials (Fig. 8). Green arrows indicate relations by formulaic definition (Eqn 1, Eqn 3). Broken lines with double-headed arrows indicate correlations among kinematic phenotypes during competition (Table 4). Solid black lines with single-headed arrows show conceptual path of the phenotypic system through the genotypic manipulations that produce novel offspring from the adult population.