Efficient Modeling of Morphing Wing Flight Using Neural Networks and Cubature Rules

Fluidic locomotion of flapping Micro Aerial Vehicles (MAVs) can be very complex, particularly when the rules from insect flight dynamics (fast flapping dynamics and light wings) are not applicable. In these situations, widely used averaging techniques can fail quickly. The primary motivation is to find efficient models for complex forms of aerial locomotion where wings constitute a large part of body mass (i.e., dominant inertial effects) and deform in multiple directions (i.e., morphing wing). In these systems, high degrees of freedom yields complex inertial, Coriolis, and gravity terms. We use Algorithmic Differentiation (AD) and Bayesian filters computed with cubature rules conjointly to quickly estimate complex fluid-structure interactions. In general, Bayesian filters involve finding complex numerical integration (e.g., find posterior integrals). Using cubature rules to compute Gaussian-weighted integrals and AD, we show that the complex multi-degrees-of-freedom dynamics of morphing MAVs can be computed very efficiently and accurately. Therefore, our work facilitates closed-loop feedback control of these morphing MAVs.

[1]  S. Haykin,et al.  Cubature Kalman Filters , 2009, IEEE Transactions on Automatic Control.

[2]  Christopher G. Atkeson,et al.  Bayesian Optimization Using Domain Knowledge on the ATRIAS Biped , 2017, 2018 IEEE International Conference on Robotics and Automation (ICRA).

[3]  Paris Perdikaris,et al.  Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations , 2019, J. Comput. Phys..

[4]  M. Triantafyllou,et al.  State-Space Adaptation of Unsteady Lifting Line Theory: Twisting/Flapping Wings of Finite Span , 2017 .

[5]  Alireza Ramezani,et al.  Computational Structure Design of a Bio-Inspired Armwing Mechanism , 2020, IEEE Robotics and Automation Letters.

[6]  Steve B. Jiang,et al.  Nonlinear Systems Identification Using Deep Dynamic Neural Networks , 2016, ArXiv.

[7]  Spyros Chatzivasileiadis,et al.  Physics-Informed Neural Networks for Non-linear System Identification for Power System Dynamics , 2021, 2021 IEEE Madrid PowerTech.

[8]  Behrouz Safarinejadian,et al.  Predict time series using extended, unscented, and cubature Kalman filters based on feed-forward neural network algorithm , 2013, The 3rd International Conference on Control, Instrumentation, and Automation.

[9]  Marco Hutter,et al.  Trajectory Optimization With Implicit Hard Contacts , 2018, IEEE Robotics and Automation Letters.

[10]  Kun Qian,et al.  Physics Informed Data Driven model for Flood Prediction: Application of Deep Learning in prediction of urban flood development , 2019, ArXiv.

[11]  Jan Peters,et al.  Bayesian optimization for learning gaits under uncertainty , 2015, Annals of Mathematics and Artificial Intelligence.

[12]  Songwu Lu,et al.  Robust nonlinear system identification using neural-network models , 1998, IEEE Trans. Neural Networks.

[13]  Sharad Singhal,et al.  Training Multilayer Perceptrons with the Extende Kalman Algorithm , 1988, NIPS.

[14]  T. Westerlund,et al.  Remarks on "Asymptotic behavior of the extended Kalman filter as a parameter estimator for linear systems" , 1980 .

[15]  Y. Ho,et al.  A Bayesian approach to problems in stochastic estimation and control , 1964 .

[16]  Yong Huang,et al.  Convergence Study in Extended Kalman Filter-Based Training of Recurrent Neural Networks , 2011, IEEE Transactions on Neural Networks.