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Spatially recursive estimation and Gaussian process dynamic models of bat flapping flight

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Abstract

Bats exhibit exceptional agility, maneuverability, and efficiency during flight due to the complex articulated multibody structure of their wings and to the nonlinear and unsteady dynamics that govern their motion. While excellent progress has been made in the study of the kinematics of bat flapping flight, there still does not exist a dynamic model which is suitable for use in state estimation. This issue is typically overcome by using a few high-frame-rate cameras to capture motion; however, such systems are expensive and prone to measurement occlusion. This paper establishes a methodology that is designed to exploit an emerging class of experimental hardware which employs low-resolution, low-cost, and highly redundant imaging networks. The redundant camera network ameliorates the issue of self-occlusion, but the large-baseline, nonlinear motion of points in image space makes tracking difficult without a suitable motion prior. To remedy this issue, this paper exploits the tree topology of the bat skeleton and introduces a conditionally independent Bayes’ filter implemented with inboard state correction. Our results show that at low frame rates, this estimator performs better than both the standard and conditionally independent without inboard correction approaches for state estimation of an open kinematic chain. In addition to the estimation strategy, we construct a Gaussian process dynamic model (GPDM) of flight dynamics which we will use in future work as a suitable motion prior for state estimation. The GPDM presented in this paper is the first nonlinear dimensionality reduction of bat flight.

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References

  1. Aldridge, H.D.: Kinematics and aerodynamics of the greater horseshoe bat, Rhinolophus ferrumequinum, in horizontal flight at various flight speeds. J. Exp. Biol. 126, 479–97 (1986)

    Google Scholar 

  2. Àlvarez, M.A., Rosasco, L., Lawrence, N.D.: Kernels for Vector-valued Functions: A Review. Now Publishers Inc., Dordrecht (2012)

    MATH  Google Scholar 

  3. Bahlman, J.W., Price-Waldman, R.M., Lippe, H.W., Breuer, K.S., Swartz, S.M.: Simplifying a wing: diversity and functional consequences of digital joint reduction in bat wings. J. Anat. 229(1), 14–27 (2016)

    Article  Google Scholar 

  4. Bender, M.J., McClelland, H.G., Bledt, G., Kurdila, A.J., Furukawa, T., Mueller, R.: Trajectory estimation of bat flight using a multi-view camera system. In: AIAA SciTech, AIAA, Kissimmee, FL, USA, pp. 1–13 (2015)

  5. Bender, M.J., McClelland, H.G., Kurdila, A.J., Müller, R.: Recursive Bayesian estimation of bat flapping flight using kinematic trees. In: AIAA SciTech, AIAA, San Diego, CA, USA, pp. 1–12 (2016)

  6. Bender, M.J., McClelland, H.M., Kurdila, A., Müller, R.: Recursive Bayesian estimation of bat flapping flight using kinematic trees. In: AIAA Modeling and Simulation Technologies Conference (January), pp. 1–12 (2016)

  7. Bergou, A.J., Swartz, S., Breuer, K., Taubin, G.: 3D reconstruction of bat flight kinematics from sparse multiple views. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 1618–1625 (2011)

  8. Bradski, G.: OpenCV Library. Dr. Dobb’s Journal of Software Tools (2000)

  9. Canton-Ferrer, C., Casas, J.R., Pardas, M.: Towards a low cost multi-camera marker based human motion capture system. In: 2009 16th IEEE International Conference on Image Processing (ICIP), pp. 2581–2584 (2009)

  10. Cheney, J.A., Ton, D., Konow, N., Riskin, D.K., Breuer, K.S., Swartz, S.M.: Hindlimb motion during steady flight of the lesser dog-faced fruit bat. Cynopterus brachyotis. PLoS ONE 9(5), 1–8 (2014)

    Article  Google Scholar 

  11. Colorado, J., Barrientos, A., Rossi, C., Breuer, K.S.: Biomechanics of smart wings in a bat robot: morphing wings using SMA actuators. Bioinspiration Biomim. 7(3), 36,006 (2012)

    Article  Google Scholar 

  12. Dellaert, F., Seitz, S., Thrun, S., Thorpe, C.: Feature correspondence : a Markov chain Monte Carlo approach. In: Advances in Neural Information Processing Systems, pp. 852–858 (2001)

  13. Erol, A., Bebis, G., Nicolescu, M., Boyle, R.D., Twombly, X.: A review on vision-based full DOF hand motion estimation. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 1, p. 75 (2005)

  14. Gopalakrishnan, P., Tafti, D.K.: Effect of wing flexibility on lift and thrust production in flapping flight. AIAA J. 48(5), 865–877 (2010)

    Article  Google Scholar 

  15. Hauberg, S., Lauze, F., Pedersen, K.S.: Unscented Kalman filtering on Riemannian manifolds. J. Math. Imaging Vis. 46(1), 103–120 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  16. Hedrick, T.L.: Software techniques for two- and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration Biomim. 3(3), 1–6 (2008)

    Google Scholar 

  17. Hofmann, M., Gavrila, D.M.: Multi-view 3D human pose estimation in complex environment. Int. J. Comput. Vis. 96(1), 103–124 (2012)

    Article  MathSciNet  Google Scholar 

  18. Hubel, T.Y., Hristov, N.I., Swartz, S.M., Breuer, K.S.: Time-resolved wake structure and kinematics of bat flight. Exp. Fluids 46(5), 933–943 (2010)

    Article  Google Scholar 

  19. Isard, M.; Blake, A.: ICondensation: unifying low-level and high-level tracking in a stochastic framework. In: 5th European Conference on Computer Vision (1998)

  20. Lawrence, N.: Gaussian process latent variable models for visualisation of high dimensional data. Computer 16(5), 329–336 (2004)

    Google Scholar 

  21. Liu, Z., Zhu, J., Bu, J., Chen, C.: A survey of human pose estimation: the body parts parsing based methods. J. Vis. Commun. Image Represent. 32, 10–19 (2015)

    Article  Google Scholar 

  22. Ma, Y., Soatto, S., Kosecká, J., Sastry, S.S.: An Invitation to 3-D Vision: From Images to Geometric Models, 1st edn. Springer, Berlin (2004)

    Book  MATH  Google Scholar 

  23. MacCormick, J., Isard, M.: Partitioned sampling, articulated objects, and interface-quality hand tracking. Comput. Vis. ECCV 2000, 3–19 (2000)

    Google Scholar 

  24. Mackay, D.J.C.: Information Theory, Inference, and Learning Algorithms, 7.2nd edn. Cambridge University Press, Cambridge (2003)

    MATH  Google Scholar 

  25. Modeslund, T., Hilton, A., Kruger, V.: A survey of advances in vision-based human motion capture and analysis. Comput. Vis. Image Underst. 104, 90–126 (2006)

    Article  Google Scholar 

  26. Ramezani, A., Chung, S.J., Hutchinson, S.: A biomimetic robotic platform to study flight specializations of bats. Sci. Robot. 2(3), 1–12 (2017)

    Article  Google Scholar 

  27. Ramezani, A., Shi, X., Chung, S.J., Hutchinson, S.: Bat bot (b2), a biologically inspired flying machine. In: 2016 IEEE International Conference on Robotics and Automation (ICRA), pp. 3219–3226 (2016)

  28. Riskin, D.K., Bergou, B., Breuer, K.S., Swartz, S.M.: Upstroke wing flexion and the inertial cost of bat flight. Proc. R. Soc. B Biol. Sci. 279(1740), 2945–2950 (2012)

    Article  Google Scholar 

  29. Riskin, D.K., Iriarte-Díaz, J., Middleton, K.M., Breuer, K.S., Swartz, S.M.: The effect of body size on the wing movements of pteropodid bats, with insights into thrust and lift production. J. Exp. Biol. 213, 4110–4122 (2010)

    Article  Google Scholar 

  30. Riskin, D.K., Willis, D.J., Iriarte-Díaz, J., Hedrick, T.L., Kostandov, M., Chen, J., Laidlaw, D.H., Breuer, K.S., Swartz, S.M.: Quantifying the complexity of bat wing kinematics. J. Theor. Biol. 254(3), 604–615 (2008)

    Article  Google Scholar 

  31. Send, W., Fischer, M., Jebens, K., Mugrauer, R., Nagarathinam, A., Scharstein, F.: Artificial hinged-wing bird with active torsion and partially linear kinematics. In: 28th Congress of the International Council of the Aeronautical Sciences, pp. 23–28 (2012)

  32. Shyy, W., Aono, H., Chimakurthi, S., Trizila, P., Kang, C.K., Cesnik, C., Liu, H.: Recent progress in flapping wing aerodynamics and aeroelasticity. Prog. Aerosp. Sci. 46(7), 284–327 (2010)

    Article  Google Scholar 

  33. Sigal, L., Isard, M., Haussecker, H., Black, M.J.: Loose-limbed people: estimating 3D human pose and motion using non-parametric belief propagation. Int. J. Comput. Vis. 98(1), 15–48 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  34. Spong, M.W., Hutchinson, S., Vidyasagar, M.: Robot Modeling and Control, 1st edn. Wiley, Hoboken (2006)

    Google Scholar 

  35. Stenger, B., Thayananthan, A., Torr, P.H.S., Cipolla, R.: Filtering using a tree-based estimator. In: ICCV ’03 Proceedings of the Ninth IEEE International Conference on Computer Vision, vol. 2, pp. 1063–1071 (2003)

  36. Stenger, B., Thayananthan, A., Torr, P.H.S., Cipolla, R.: Model-based hand tracking using a hierarchical bayesian filter. IEEE Trans. Pattern Anal. Mach. Intell. 28(9), 1372–1384 (2006)

    Article  MATH  Google Scholar 

  37. Svoboda, T., Martinec, D., Pajdla, T.: A convenient multicamera self-calibration for virtual environments. Presence 14(4), 407–422 (2005)

    Article  Google Scholar 

  38. Szeliski, R.: Computer Vision: Algorithms and Applications. Springer, Berlin (2004)

    MATH  Google Scholar 

  39. Thayananthan, A., Stenger, B., Torr, P., Cipolla, R.: Learning a kinematic prior for tree-based filtering. In: Proceedings of the British Machine Vision Conference, pp. 60.1–60.10 (2003)

  40. The Mathworks Inc.: Computer Vision System Toolbox (2014)

  41. Thrun, S., Burgard, W., Fox, D.: Probabilistic Robotics. MIT Press, Cambridge (2005)

    MATH  Google Scholar 

  42. Tian, X., Iriarte-Diaz, J., Middleton, K., Galvao, R., Israeli, E., Roemer, A., Sullivan, A., Song, A., Swartz, S., Breuer, K.: Direct measurements of the kinematics and dynamics of bat flight. Bioinspiration Biomim. 1(4), S10–S18 (2006)

    Article  Google Scholar 

  43. Urtasun, R., Fleet, J.D., Fua, P.: Gaussian Process Dynamical Models for 3D people tracking. In: 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (June), vol. 1 (2006)

  44. Viswanath, K., Nagendra, K.: Climbing flight of a fruit bat deconstructed. In: 52nd Aerospace Sciences Meeting (January), pp. 1–24 (2014)

  45. Viswanath, K., Nagendra, K., Cotter, J., Frauenthal, M., Tafti, D.K.: Straight-line climbing flight aerodynamics of a fruit bat. Phys. Fluids 26(2), 604 (2014)

    Article  Google Scholar 

  46. Viswanath, K., Tafti, D.K.: Effect of frontal gusts on forward flapping flight. AIAA J. 48(9), 2049–2062 (2010)

    Article  Google Scholar 

  47. Wang, J., Fleet, D., Hertzmann, A.: Gaussian process dynamical models. In: Advances in Neural Information Processing Systems, pp. 1441–1448 (2006)

  48. Wang, J.M., Fleet, D.J., Hertzmann, A.: Gaussian Process Dynamic Models MatLab Code (2008). www.dgp.toronto.edu/~jmwang/gpdm/

  49. Wang, J.M., Fleet, D.J., Member, S., Hertzmann, A.: Gaussian process dynamic models for human motion. IEEE Trans. Pattern Anal. Mach. Intell. 30(2), 283–298 (2008)

    Article  Google Scholar 

  50. Wolf, M., Johansson, L.C., von Busse, R., Winter, Y., Hedenström, A.: Kinematics of flight and the relationship to the vortex wake of a Pallas’ long tongued bat (Glossophaga soricina). J. Exp. Biol. 213(12), 2142–2153 (2010)

    Article  Google Scholar 

  51. Wood, R.J.: The first takeoff of a biologically inspired at-scale robotic insect. IEEE Trans. Robot. 24(2), 341–347 (2008)

    Article  Google Scholar 

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Acknowledgements

The authors would like to thank the following project teams from the Shandong University Virginia Tech (SDU-VT) International Laboratory’s summer 2015 and summer 2016 research collaboration: Bat Flight Motion Capture Senior Design Project, SDU-VT Flight Team, and the SDU-VT Bat Husbandry Team. The authors would like to give a special thanks to the following individuals for their extra diligence in completing this project: Yang Xu, Zhao Yanan, Wang Chenhao, Sha Qiyuan, Wang Bingcheng, Lin Yousi, Ma Zhiqiang, Zhang Liujun, Cao Ze, Wang Jinzhen, Laura Bunn, Eric Anderson, Kenton Anderson, and Hunter McClelland. Additionally we would like to thank Sharon Swartz, Andrea Rummel, and Lawrence Wang from Brown University for supporting experiments and loan of critical equipment. We would also like to thank Orangkucing Labs for developing the MewPro open-source GoPro camera control system (http://mewpro.cc/). Finally, we would like to thank the National Natural Science Foundation of China (Grant Nos. 11374192 and 11574183); Fundamental Research Fund of Shandong University (Grant No. 2014QY008); Minister of Education of China Tese grant for faculty exchange; US National Science Foundation (Grant No. 1510797); and Virginia Tech Institute for Critical Technology and Applied Science (ICTAS, through support for the BIST Center).

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Authors and Affiliations

  1. Mechanical Engineering, Virginia Tech, Blacksburg, VA, 24060, USA

    Matt Bender, Xiaozhou Fan, Andrew Kurdila & Rolf Müller

  2. Electrical and Computer Engineering, Virginia Tech, Blacksburg, VA, USA

    Li Tian

  3. VT-SDU International Lab, 27 Shanda South Road, Jinan, 250100, China

    Rolf Müller

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  1. Matt Bender
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Correspondence to Matt Bender.

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Bender, M., Tian, L., Fan, X. et al. Spatially recursive estimation and Gaussian process dynamic models of bat flapping flight. Nonlinear Dyn 95, 217–237 (2019). https://doi.org/10.1007/s11071-018-4560-z

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