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

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.