Underwater maneuvering of robotic sheets through buoyancy-mediated active flutter

Falling leaves flutter from side to side due to passive and intrinsic fluid-body coupling. Exploiting the dynamics of passive fluttering could lead to fresh perspectives for the locomotion and manipulation of thin, planar objects in fluid environments. Here, we show that the time-varying density distribution within a thin, planar body effectively elicits minimal momentum control to reorient the principal flutter axis and propel itself via directional fluttery motions. We validated the principle by developing a swimming leaf with a soft skin that can modulate local buoyancy distributions for active flutter dynamics. To show generality and field applicability, we demonstrated underwater maneuvering and manipulation of adhesive and oil-skimming sheets for environmental remediation. These findings could inspire future intelligent underwater robots and manipulation schemes.

Planar Body-Mounted Sensors for Electromagnetic Tracking

Electromagnetic tracking is a safe, reliable, and cost-effective method to track medical instruments in image-guided surgical navigation. However, patient motion and magnetic field distortions heavily impact the accuracy of tracked position and orientation. The use of redundant magnetic sensors can help to map and mitigate for patient movements and magnetic field distortions within the tracking region. We propose a planar inductive sensor design, printed on PCB and embedded into medical patches. The main advantage is the high repeatability and the cost benefit of using mass PCB manufacturing processes. The article presents new operative formulas for electromagnetic tracking of planar coils on the centimetre scale. The full magnetic analytical model is based on the mutual inductance between coils which can be approximated as being composed by straight conductive filaments. The full model is used to perform accurate system simulations and to assess the accuracy of faster simplified magnetic models, which are necessary to achieve real-time tracking in medical applications.

Swim-like motion of bodies immersed in an ideal fluid

The connection between swimming and control theory is attracting increasing attention in the recent literature. Starting from an idea of Alberto Bressan [A. Bressan, Discrete Contin. Dyn. Syst. 20 (2008) 1–35]. we study the system of a planar body whose position and shape are described by a finite number of parameters, and is immersed in a 2-dimensional ideal and incompressible fluid in terms of gauge field on the space of shapes. We focus on a class of deformations measure preserving which are diffeomeorphisms whose existence is ensured by the Riemann Mapping Theorem. After making the first order expansion for small deformations, we face a crucial problem: the presence of possible non vanishing initial impulse. If the body starts with zero initial impulse we recover the results present in literature (Marsden, Munnier and oths). If instead the body starts with an initial impulse different from zero, the swimmer can self-propel in almost any direction if it can undergo shape changes without any bound on their velocity. This interesting observation, together with the analysis of the controllability of this system, seems innovative.

On the Direct Static Problem of a Planar Rigid Body Suspended From Two Cables

This paper presents a general solution to the direct static problem of a planar body suspended from two cables. First, the conditions for static equilibrium are stated and a mathematical formulation of the problem is derived. A twelfth degree univariate polynomial is then obtained using the resultant of two intermediate polynomials. It is shown that up to twelve real solutions can be obtained, thereby confirming that the polynomial is of minimal degree. Since the condition used in the derivation is necessary but not sufficient, the roots must be tested a posteriori for validity. Simple mathematical conditions are provided that allow such a verification. Finally, two examples are provided to illustrate the results and highlight the importance of the proposed root validation procedure.

CLASSIFICATION OF SYMMETRY GROUPS FOR PLANAR -BODY CHOREOGRAPHIES

Since the foundational work of Chenciner and Montgomery in 2000 there has been a great deal of interest in choreographic solutions of the $n$-body problem: periodic motions where the $n$ bodies all follow one another at regular intervals along a closed path. The principal approach combines variational methods with symmetry properties. In this paper, we give a systematic treatment of the symmetry aspect. In the first part, we classify all possible symmetry groups of planar $n$-body collision-free choreographies. These symmetry groups fall into two infinite families and, if $n$ is odd, three exceptional groups. In the second part, we develop the equivariant fundamental group and use it to determine the topology of the space of loops with a given symmetry, which we show is related to certain cosets of the pure braid group in the full braid group, and to centralizers of elements of the corresponding coset. In particular, we refine the symmetry classification by classifying the connected components of the set of loops with any given symmetry. This leads to the existence of many new choreographies in $n$-body systems governed by a strong force potential.

The Periodic Solutions for Planar -Body Problems

Based on the works of Perko and Walter, Moeckel and Simo, and Zhang and Zhou, we study the necessary conditions and suffcient conditions for the uniformly rotating planar nested regular polygonal periodic solutions for the -body problems.