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Planar controlled gliding, tumbling and descent

  • P. Paoletti (a1) and L. Mahadevan (a1) (a2)

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.

Copyright

Corresponding author

Email address for correspondence: lm@seas.harvard.edu

References

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