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J. Herault et al.
their slender morphology, which makes them particularly sensitive to rolling
motions (solid rotation about the longitudinal axis) due to their low axial inertia
and their generally highly located centre of mass relative to the buoyancy center
(the geometric center of the immersed surface). Rolling motion is considered to
be the most harmful degree of freedom, since it produces the highest angular
accelerations. To mitigate these effects, current robots are therefore equipped
with floats [2], thus increasing their volume and added mass. The empirical
adjustment of robot buoyancy is performed a posteriori, after the robot design,
thus demonstrating the lack of technological solutions dedicated to this problem.
Other stabilizers commonly used in marine engineering (roll dampers, fins, etc.)
would have an equally detrimental impact (or even worse) on manoeuvrability,
since they would considerably increase turbulent drag. Semi-aquatic snakes living near rivers, which can be considered to be true equilibrists “levitating” on
the surface, such as the grass snake (Natrix natrix), have developed extraordinary stabilization capacities at the surface. Indeed, the overall stability of the
snake is ensured by the cumulative effect of imbalances and balances of each
cross-section of the snake. Going into further details, a section may be locally
in a stable equilibrium configuration or be unstable due to morphological (muscular deformation of its rib cage) or kinematic (vertebral torsion and bending)
deformations or by buoyancy adjustment (lungs). By analogy, one can consider
the body of the snake as a continuous chain of torsion pendulums (some of which
can be reversed) remaining globally stable thanks to the active control of the
distribution of local inclinations. Thus, the snake can play on stabilizing or destabilizing local effects, in order to quickly readjust its position, and counterbalance
external disturbances (swell, wind, current).
The present study aims to investigate some aspects of the stability mechanisms of semi-aquatic snakes thanks to biological observations, a theoretical
approach, and numerical simulations. More precisely, we address the following
questions:
– What are the features of a (semi-)aquatic snake that could explain its stability? (Sect. 2)
– How to model the stability of a floating body undergoing large 3D deformations? (Sect. 3)
– How can the snake stabilize its head while deforming its body? (Sect. 4)
– How can these features be embodied into a bioinspired robot? (conclusion).
2 Morphology, Physiology and Ethology of Aquatic
Snakes
To structure our bio-inspired approach, we review for the first time the documented morphological features of partially or fully aquatic snakes that are
determinant for static equilibrium on water surface.
Morphology. The morphology of snakes evolving in aquatic environment is
determined by a compromise between maritime and terrestrial locomotion.
J. Herault et al.
their slender morphology, which makes them particularly sensitive to rolling
motions (solid rotation about the longitudinal axis) due to their low axial inertia
and their generally highly located centre of mass relative to the buoyancy center
(the geometric center of the immersed surface). Rolling motion is considered to
be the most harmful degree of freedom, since it produces the highest angular
accelerations. To mitigate these effects, current robots are therefore equipped
with floats [2], thus increasing their volume and added mass. The empirical
adjustment of robot buoyancy is performed a posteriori, after the robot design,
thus demonstrating the lack of technological solutions dedicated to this problem.
Other stabilizers commonly used in marine engineering (roll dampers, fins, etc.)
would have an equally detrimental impact (or even worse) on manoeuvrability,
since they would considerably increase turbulent drag. Semi-aquatic snakes living near rivers, which can be considered to be true equilibrists “levitating” on
the surface, such as the grass snake (Natrix natrix), have developed extraordinary stabilization capacities at the surface. Indeed, the overall stability of the
snake is ensured by the cumulative effect of imbalances and balances of each
cross-section of the snake. Going into further details, a section may be locally
in a stable equilibrium configuration or be unstable due to morphological (muscular deformation of its rib cage) or kinematic (vertebral torsion and bending)
deformations or by buoyancy adjustment (lungs). By analogy, one can consider
the body of the snake as a continuous chain of torsion pendulums (some of which
can be reversed) remaining globally stable thanks to the active control of the
distribution of local inclinations. Thus, the snake can play on stabilizing or destabilizing local effects, in order to quickly readjust its position, and counterbalance
external disturbances (swell, wind, current).
The present study aims to investigate some aspects of the stability mechanisms of semi-aquatic snakes thanks to biological observations, a theoretical
approach, and numerical simulations. More precisely, we address the following
questions:
– What are the features of a (semi-)aquatic snake that could explain its stability? (Sect. 2)
– How to model the stability of a floating body undergoing large 3D deformations? (Sect. 3)
– How can the snake stabilize its head while deforming its body? (Sect. 4)
– How can these features be embodied into a bioinspired robot? (conclusion).
2 Morphology, Physiology and Ethology of Aquatic
Snakes
To structure our bio-inspired approach, we review for the first time the documented morphological features of partially or fully aquatic snakes that are
determinant for static equilibrium on water surface.
Morphology. The morphology of snakes evolving in aquatic environment is
determined by a compromise between maritime and terrestrial locomotion.