相关论文: Hexapods with a small linear span

This paper presents a derivation of the parallel transport equation expressed in the Lie algebra of a Lie group endowed with a left-invariant metric.The use of this equation is exemplified on the group of rigid body motions SE(3), using…

In this article, we investigate Hecke modifications of vector bundles on a smooth projective curve $X$ defined over an arbitrary field. We obtain structural results that allow us to reduce the classification problem of Hecke modifications…

We study the configuration space of equilateral and equiangular spatial hexagons for any bond angle by giving explicit expressions of all the possible shapes. We show that the chair configuration is isolated, whereas the boat configuration…

In cable driven parallel robots (CDPRs), the payload is suspended using a network of cables whose length can be controlled to maneuver the payload within the workspace. Compared to rigid link robots, CDPRs provide better maneuverability due…

Robots "in-the-wild" encounter and must traverse widely varying terrain, ranging from solid ground to granular materials like sand to full liquids. Numerous approaches exist, including wheeled and legged robots, each excelling in specific…

In this paper we collect the main properties of free curves in the complex projective plane and a lot of conjectures and open problems, both old and new. In the quest to understand the mystery of free curves, many tools were developed and…

We study topology of configuration spaces of planar linkages having one leg of variable length. Such telescopic legs are common in modern robotics where they are used for shock absorbtion and serve a variety of other purposes. Using a Morse…

High-dimensional multiplex graphs are characterized by their high number of complementary and divergent dimensions. The existence of multiple hierarchical latent relations between the graph dimensions poses significant challenges to…

A theory of graded manifolds can be viewed as a generalization of differential geometry of smooth manifolds. It allows one to work with functions which locally depend not only on ordinary real variables, but also on $\mathbb{Z}$-graded…

Elongate limbless robots have the potential to locomote through tightly packed spaces for applications such as search-and-rescue and industrial inspections. The capability to effectively and robustly maneuver elongate limbless robots is…

In this paper we focus on dynamical properties of (real) convex projective surfaces. Our main theorem provides an asymptotic formula for the number of free homotopy classes with roughly the same renormalized Hilbert length for two distinct…

The relationship between convex geometry and algebraic geometry has deep historical roots, tracing back to classical works in enumerative geometry. In this paper, we continue this theme by studying two interconnected problems regarding…

Salamander-like quadruped robots are designed inspired by the skeletal structure of their biological counterparts. However, existing controllers cannot fully exploit these morphological features and largely rely on predefined gait patterns…

We give both efficient algorithms and hardness results for reconfiguring between two connected configurations of modules in the hexagonal grid. The reconfiguration moves that we consider are "pivots", where a hexagonal module rotates around…

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…

Let $X$ be an integral projective variety of codimension two, degree $d$ and dimension $r$ and $Y$ be its general hyperplane section. The problem of lifting generators of minimal degree $\sigma$ from the homogeneous ideal of $Y$ to the…

We give a constructive proof for the existence of a unique rational motion of minimal degree in the dual quaternion model of Euclidean displacements with a given rational parametric curve as trajectory. The minimal motion degree equals the…

Solid-solid phase transitions are ubiquitous in nature, but the kinetic pathway of anisotropic particle systems remains elusive, where the coupling between translational and rotational motions plays a critical role in various kinetic…

Partial duality generalizes the fundamental concept of the geometric dual of an embedded graph. A partial dual is obtained by forming the geometric dual with respect to only a subset of edges. While geometric duality preserves the genus of…

Quadruped-based mobile manipulation presents significant challenges in robotics due to the diversity of required skills, the extended task horizon, and partial observability. After presenting a multi-stage pick-and-place task as a succinct…