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Planar controlled gliding, tumbling and descent

Published online by Cambridge University Press:  05 December 2011

P. Paoletti  and
L. Mahadevan
P. Paoletti
Affiliation:
School of Engineering and Applied Sciences, Harvard University, 29 Oxford Street, Cambridge, MA 02138, USA
L. Mahadevan*
Affiliation:
School of Engineering and Applied Sciences, Harvard University, 29 Oxford Street, Cambridge, MA 02138, USA Department of Physics, Harvard University, 29 Oxford Street, Cambridge, MA 02138, USA
*
†Email address for correspondence: [email protected]
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Abstract

Controlled gliding during descent has been thought of as a crucial intermediate step toward the evolution of powered flight in a variety of animals. Here we develop and analyse a model for the controlled descent of thin bodies in quiescent fluids. Focusing on motion in two dimensions for simplicity, we formulate the question of steering an elliptical body to a desired landing location with a specific orientation using the framework of optimal control theory with a single control variable. We derive both time- and energy-optimal trajectories using a combination of numerical and analytical approximations. In particular, we find that energy-optimal strategies converge to constant control, while time-optimal strategies converge to bang–coast–bang control that leads to bounding flight, alternating between tumbling and gliding phases. Our study of these optimal strategies thus places natural limits on how they may be implemented in biological and biomimetic systems.

JFM classification

Flow Control: Control theory Biological Fluid Dynamics: Swimming/flying
Type
Papers
Information
Journal of Fluid Mechanics , Volume 689 , 25 December 2011 , pp. 489 - 516
Copyright
Copyright © Cambridge University Press 2011

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