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On the dynamic Markov-Dubins problem: from path planning in robotics and biolocomotion to computational anatomy
(Maik Nauka/Interperiodica/Springer, 2013-01)
Andrei Andreyevich Markov proposed in 1889 the problem (solved by Dubins in 1957) of finding the twice continuously differentiable (arc length parameterized) curve with bounded curvature, of minimum length, connecting two ...
Micro-swimming without flagella: propulsion by internal structures
(Maik Nauka/Interperiodica/Springer, 2011-12)
Since a first proof-of-concept for an autonomous micro-swimming device appeared in 2005 a strong interest on the subject ensued. The most common configuration consists of a cell driven by an external propeller, bio-inspired ...
Vortex pairs on surfaces
(Amer Inst Physics, 2009)
A pair of infinitesimally close opposite vortices moving on a curved surface moves along a geodesic, according to a conjecture by Kimura. We outline a proof. Numerical simulations are presented for a pair of opposite ...
Rubber rolling over a sphere
(Maik Nauka/Interperiodica/Springer, 2007-04)
Rubber coated bodies rolling over a surface satisfy a no-twist condition in addition to the no slip condition satisfied by 'marble' coated bodies [1]. Rubber rolling has an interesting differential geometric appeal because ...
Self-propulsion of N-hinged 'Animats' at low Reynolds number
(2003)
Optimal locomotion of micro-organisms (on a small Reynolds number flow) can be regarded as a sub-riemannian geometry on a principal bundle with a mechanical connection. Aiming at robotic applications, flagella are modeled ...
