We study two microswimmers consisting of a spherical rigid head and a passive elastic tail. In the first one the tail is clamped to the head, and the system oscillates under the action of an external torque. In the second one, head and tail are connected by a joint allowing the angle between them to vary periodically, as a result of an oscillating internal torque. Previous studies on these models were restricted to sinusoidal actuations, showing that the swimmers can propel while moving on average along a straight line, in the direction given by the symmetry axis around which beating takes place. We extend these results to motions produced by generic (non-sinusoidal) periodic actuations within the regime of small compliance of the tail. We find that modulation in the velocity of actuation can provide a mechanism to select different directions of motion. With velocity-modulated inputs, the externally actuated swimmer can translate laterally with respect to the symmetry axis of beating, while the internally actuated one is able to move along curved trajectories. The governing equations are analysed with an asymptotic perturbation scheme, providing explicit formulas, whose results are expressed through motility maps. Asymptotic approximations are further validated by numerical simulations.

1 aCicconofri, Giancarlo1 aDeSimone, Antonio uhttps://doi.org/10.1140/epje/i2016-16072-y00496nas a2200109 4500008004100000245010000041210006900141260001000210653001300220100002600233856012700259 2015 en d00aMathematical Models of Locomotion: Legged Crawling, Snake-like Motility, and Flagellar Swimming0 aMathematical Models of Locomotion Legged Crawling Snakelike Moti bSISSA10aMotility1 aCicconofri, Giancarlo uhttps://www.math.sissa.it/publication/mathematical-models-locomotion-legged-crawling-snake-motility-and-flagellar-swimming01569nas a2200181 4500008004100000022001400041245006000055210005800115300001400173490000700187520100500194653001901199653002201218653002801240100002601268700002201294856007101316 2015 eng d a0020-746200aMotility of a model bristle-bot: A theoretical analysis0 aMotility of a model bristlebot A theoretical analysis a233 - 2390 v763 aBristle-bots are legged robots that can be easily made out of a toothbrush head and a small vibrating engine. Despite their simple appearance, the mechanism enabling them to propel themselves by exploiting friction with the substrate is far from trivial. Numerical experiments on a model bristle-bot have been able to reproduce such a mechanism revealing, in addition, the ability to switch direction of motion by varying the vibration frequency. This paper provides a detailed account of these phenomena through a fully analytical treatment of the model. The equations of motion are solved through an expansion in terms of a properly chosen small parameter. The convergence of the expansion is rigorously proven. In addition, the analysis delivers formulas for the average velocity of the robot and for the frequency at which the direction switch takes place. A quantitative description of the mechanism for the friction modulation underlying the motility of the bristle-bot is also provided.

10aBristle-robots10aCrawling motility10aFrictional interactions1 aCicconofri, Giancarlo1 aDeSimone, Antonio uhttp://www.sciencedirect.com/science/article/pii/S002074621500002501791nas a2200133 4500008004100000245008400041210006900125300001300194490000800207520132400215100002601539700002201565856007001587 2015 eng d00aA study of snake-like locomotion through the analysis of a flexible robot model0 astudy of snakelike locomotion through the analysis of a flexible a201500540 v4713 aWe examine the problem of snake-like locomotion by studying a system consisting of a planar inextensible elastic rod with adjustable spontaneous curvature, which provides an internal actuation mechanism that mimics muscular action in a snake. Using a Cosserat model, we derive the equations of motion in two special cases: one in which the rod can only move along a prescribed curve, and one in which the rod is constrained to slide longitudinally without slipping laterally, but the path is not fixed a priori (free-path case). The second setting is inspired by undulatory locomotion of snakes on flat surfaces. The presence of constraints leads in both cases to non-standard boundary conditions that allow us to close and solve the equations of motion. The kinematics and dynamics of the system can be recovered from a one-dimensional equation, without any restrictive assumption on the followed trajectory or the actuation. We derive explicit formulae highlighting the role of spontaneous curvature in providing the driving force (and the steering, in the free-path case) needed for locomotion. We also provide analytical solutions for a special class of serpentine motions, which enable us to discuss the connection between observed trajectories, internal actuation and forces exchanged with the environment.

1 aCicconofri, Giancarlo1 aDeSimone, Antonio uhttps://royalsocietypublishing.org/doi/abs/10.1098/rspa.2015.0054