相关论文: A non-cubic space-filling modular robot

We consider the configuration space of ordered points on the two-dimensional sphere that satisfy a specific system of quadratic equations. We construct periodic orbits in this configuration space using elliptic theta functions and show that…

Traditional aerial vehicles are constrained to perform specific tasks due to their adhoc designs. Based on modularity, we propose a versatile robot, H-ModQuad, that can adapt to different tasks by increasing its load capacity and actuated…

Much of the Earth and many surfaces of extraterrestrial bodies are composed of in-cohesive particle matter. Locomoting on granular terrain is challenging for common robotic devices, either wheeled or legged. In this work, we discover a…

First, we prove a special case of Knaster's problem, implying that each symmetric convex body in R^3 admits an inscribed cube. We deduce it from a theorem in equivariant topology, which says that there is no S_4-equivariant map from SO(3)…

This article presents the development and validation of a hybrid multi-sphere discrete element framework - Rigid3D, for the simulation of granular systems with arbitrarily shaped particles in 3D space. In this DEM framework, a non-spherical…

One of the strategies to detect the pose and shape of unknown objects is their geometric modeling, consisting on fitting known geometric entities. Classical geometric modeling fits simple shapes such as spheres or cylinders, but often those…

3D-facets of the Delone cells representing the deep and shallow holes of the root lattice D6 which tile the six-dimensional Euclidean space in an alternating order are projected into three-dimensional space. They are classified into six…

A central problem of geometry is the tiling of space with simple structures. The classical solutions, such as triangles, squares, and hexagons in the plane and cubes and other polyhedra in three-dimensional space are built with sharp…

This presentation starts with the regular polygons, of course, then with the Platonic and Archimedean solids. The latter ones are whose symmetry groups are transitive on the vertices, and in addition, whose faces are regular polygons (see…

We investigate the exploration problem of a short-sighted mobile robot moving in an unknown cellular room. To explore a cell, the robot must enter it. Once inside, the robot knows which of the 4 adjacent cells exist and which are boundary…

Modular small-scale robots offer the potential for on-demand assembly and disassembly, enabling task-specific adaptation in dynamic and constrained environments. However, existing modular magnetic platforms often depend on workspace…

We consider search in a finite 3D cubic grid by a metamorphic robotic system (MRS), that consists of anonymous modules. A module can perform a sliding and rotation while the whole modules keep connectivity. As the number of modules…

A number of recent results in Euclidean Harmonic Analysis have exploited several adjacent systems of dyadic cubes, instead of just one fixed system. In this paper, we extend such constructions to general spaces of homogeneous type, making…

In this paper we present algorithms for collective construction systems in which a large number of autonomous mobile robots trans- port modular building elements to construct a desired structure. We focus on building block structures…

Imagine a swarm of terrestrial robots that can explore an environment, and, upon completion of this task, reconfigure into a spherical ball and roll out. This dimensional change alters the dynamics of locomotion and can assist them to…

Many current robot designs prioritize efficiency and one-size-fits-all solutions, oftentimes overlooking personalization, adaptability, and sustainability. To explore alternatives, we conducted two co-design workshops with 23 participants,…

Traditional aerial vehicles have limitations in their capabilities due to actuator constraints, such as motor saturation. The hardware components and their arrangement are designed to satisfy specific requirements and are difficult to…

I present a jaunty little $[[14, 3, 3]]$ non-CSS surface code that can be described using a rhombic dodecahedron. Do with it what you will.

In 3-dimensional Euclidean space there exist two exceptional polyhedra, the rhombic dodecahedron and the rhombic triacontahedron, the only known polytopes (besides polygons) that are edge-transitive without being vertex-transitive. We show…

Let M_0^R be the moduli space of smooth real cubic surfaces. We show that each of its components admits a real hyperbolic structure. More precisely, one can remove some lower-dimensional geodesic subspaces from a real hyperbolic space H^4…