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On the Trajectory Generation of the Hydrodynamic Chaplygin Sleigh
Full text linkIn this letter we consider the asymptotic behaviour and the trajectory generation problem for the Chaplygin sleigh interacting with a potential fluid. We investigate which trajectories can be obtained, at least asymptotically as t tents to infinity, by controlling some of the coordinates (shape-control variables) and using the theory of reconstruction. Moreover we support our conclusions via numerical simulations
Optimal Motion of a Scallop: Some Case Studies
No full textIn this letter, we analyze two optimal control problems for the scallop: a two-link swimmer that is able to self-propel changing dynamics between two fluids regimes. We address and solve explicitly the minimum time problem and the minimum quadratic one, computing the cost needed to move the swimmer between two fixed positions using a periodic control. We focus on the case of only one switching in the dynamics and exploiting the structure of the equation of motion we are able to split the problem into simpler ones. We solve explicitly each sub-problem obtaining a discontinuous global solution. Then we approximate it through a suitable sequence of continuous functions
On the Trajectory Generation of the Hydrodynamic Chaplygin Sleigh
Full text linkIn this letter we consider the asymptotic behaviour and the trajectory generation problem for the Chaplygin sleigh interacting with a potential fluid. We investigate which trajectories can be obtained, at least asymptotically as t tents to infinity, by controlling some of the coordinates (shape-control variables) and using the theory of reconstruction. Moreover we support our conclusions via numerical simulations
Purcell’s swimmers in pairs
Full text linkWe investigate the effects of hydrodynamic interactions between microorganisms swimming at low Reynolds numbers, treating them as a control system. We employ Lie brackets analysis to examine the motion of two neighboring three-link swimmers interacting through the ambient fluid in which they propel themselves. Our analysis reveals that the hydrodynamic interaction has a dual consequence: on one hand, it diminishes the system's efficiency; on the other hand, it dictates that the two microswimmers must synchronize their motions to attain peak performance. Our findings are further corroborated by numerical simulations of the governing equations of motion
Hysteresis and controllability of affine driftless systems: some case studies
Full text linkWe investigate the controllability of some kinds of driftless affine systems where hysteresis effects are taken into account, both in the realization of the control and in the state evolution. In particular we consider two cases: the one when hysteresis is represented by the so-called play operator, and the one when it is represented by a so-called delayed relay. In the first case we prove that, under some hypotheses, whenever the corresponding non-hysteretic system is controllable, then we can also, at least approximately, control the hysteretic one. This is obtained by some suitably constructed approximations for the inputs in the hysteresis operator. In the second case we prove controllability for a generic hysteretic delayed switching system. Finally, we investigate some possible connections between the two cases
Bifurcation analysis of pressure-induced detachment of a rod adhered to a plate
No full textWe study the lift of an elastica adhering to a flat rigid surface induced by a pressure difference. Adhesion is modelled by a cohesive force that decreases linearly with separation. Using a nonlinear local analysis, we determine the bifurcation diagram that governs the peeling process under quasi-static conditions. We show that the delamination emerges through a discontinuous transition: a normal form of the bifurcation diagram allows us to draw in a simple way the main physical mechanism, elucidating the local validity of the theory at the transition. We predict that the pressure, as a function of the detachment length, undergoes an initial drop followed by an approximately constant behaviour, while the detachment length at the transition is always finite and is roughly proportional to the elasto-adhesion length. This analysis can be the starting point to understand more complex-related problems that arise in fracture mechanics or in biology, such as testing of adhesives in a flowfield and the arterial dissection
Controllability of dynamical systems with Play-type hysteresis via approximation by delayed relays
Full text linkIn this paper we study the controllability problem for systems exhibiting hysteresis represented by play-type operators. To this end we first formalize and study in a functional setting the approximation of the Play operators by a finite weighted sum of delayed relay. Then we prove the controllability for the case with the Play operator, by the controllability result for the case with the weighted sum of delayed relay. Finally, we discuss potential applications of our approach to the sweeping process
GAIT CONTROLLABILITY OF LENGTH-CHANGING SLENDER MICROSWIMMERS
No full textControllability results of four models of two-link microscale swimmers that are able to change the length of their links are obtained. The problems are formulated in the framework of geometric control theory, within which the notions of fiber, total, and gait controllability are presented, together with sufficient conditions for the latter two. The dynamics of a general two-link swimmer is described by resorting to resistive force theory and different mechanisms to produce a length-change in the links, namely, active deformation, a sliding hinge, growth at the tip, and telescopic links. Total controllability is proved via gait controllability in all four cases, and illustrated with the aid of numerical simulations
Control of locomotion systems and dynamics in relative periodic orbits
Full text linkThe connection between the dynamics in relative periodic orbits of vector fields with noncompact symmetry groups and periodic control for the class of control systems on Lie groups known as `(robotic) locomotion systems' is well known, and has led to the identification of (geometric) phases. We take an approach which is complementary to the existing ones, advocating the relevance|for trajectory generation in these control systems|of the quali-tative properties of the dynamics in relative periodic orbits. There are two particularly important features. One is that motions in relative periodic orbits of noncompact groups can only be of two types: Either they are quasi-periodic, or they leave any compact set as t →±∞ (`drifting motions'). Moreover, in a given group, one of the two behaviours may be predominant. The second is that motions in a relative periodic orbit exhibit `spiralling', `meandering' behaviours, which are routinely detected in numerical integrations. Since a quantitative description of meandering behaviours for drifting motions appears to be missing, we provide it here for a class of Lie groups that includes those of interest in locomotion (semidirect products of a compact group and a normal vector space). We illustrate these ideas on some examples (a kinematic car robot, a planar swimmer)
Working memory updating nella dislessia evolutiva: C’è differenza tra lettere e numeri?
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