Nonlinear Dynamics

, Volume 95, Issue 1, pp 217–237 | Cite as

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

  • Matt BenderEmail author
  • Li Tian
  • Xiaozhou Fan
  • Andrew Kurdila
  • Rolf Müller
Original Paper


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.


Motion capture Bioinspired design Gaussian process dynamic models Model learning State estimation 



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 ( 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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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Mechanical EngineeringVirginia TechBlacksburgUSA
  2. 2.Electrical and Computer EngineeringVirginia TechBlacksburgUSA
  3. 3.VT-SDU International LabJinanChina

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