Related papers: The CR geometry of the three-segment snake
We make a classification of codimension one degree 3 distributions on the projective three space, giving possible Chern classes of the tangent sheaf and describing de zero and one dimensional components of the singular scheme of the…
This work aims to develop a resource-efficient solution for obstacle-avoiding tracking control of a planar snake robot in a densely cluttered environment with obstacles. Particularly, Neuro-Evolution of Augmenting Topologies (NEAT) has been…
We analyze two- and three-link planar snake-like locomotion and optimize the motion for efficiency. The locomoting system consists of two or three identical inextensible links connected via hinge joints, and the angles between the links are…
Mobile ground robots operating on unstructured terrain must predict which areas of the environment they are able to pass in order to plan feasible paths. We address traversability estimation as a heightmap classification problem: we build a…
Accurate segmentation of topological tubular structures, such as blood vessels and roads, is crucial in various fields, ensuring accuracy and efficiency in downstream tasks. However, many factors complicate the task, including thin local…
We present a study of time-independent solutions of the two-dimensional discrete Allen-Cahn equation with cubic and quintic nonlinearity. Three different types of lattices are considered, i.e., square, honeycomb, and triangular lattices.…
The article presents an analysis of the trends in the development of kinematic structures of modern machine-building technological equipment. The prospects of using machines with parallel kinematics in processing, measuring and handling…
We prove that real projective space RP^{n-3} is homeomorphic to the space of all isometry classes of n-gons in the plane with one side of length n-2 and all other sides of length 1. This makes the topological complexity of real projective…
Orb-weaving spiders detect prey on a web using vibration sensors at leg joints. They often dynamically crouch their legs during prey sensing, likely an active sensing strategy. However, how leg crouching enhances sensing is poorly…
This work employs a reinforcement learning-based model identification method aimed at enhancing the accuracy of the dynamics for our snake robot, called COBRA. Leveraging gradient information and iterative optimization, the proposed…
This paper deals with the notion of quadratic differential in spherical CR geometry (or more generally on strictly pseudoconvex CR manifolds). We get to this notion by studying a splitting of Rumin complex and discuss its first features…
Concrete is the standard construction material for buildings, bridges, and roads. As safety plays a central role in the design, monitoring, and maintenance of such constructions, it is important to understand the cracking behavior of…
We introduce the notion of a manifold admitting a simple compact Cartan 3-form $\om^3$. We study algebraic types of such manifolds specializing on those having skew-symmetric torsion, or those associated with a closed or coclosed 3-form…
We construct a 3-dimensional cell complex that is the 3-skeleton for an Eilenberg--MacLane classifying space for the symmetric group $\mathfrak{S}_n$. Our complex starts with the presentation for $\mathfrak{S}_n$ with $n-1$ adjacent…
The aim of this paper is to describe the geometry of conformal structures in Lorentzian signature, which admit a lightlike conformal Killing vector field whose corresponding adjoint tractor acts as complex structure on the standard tractor…
We study the path planning problem for continuum-arm robots, in which we are given a starting and an end point, and we need to compute a path for the tip of the continuum arm between the two points. We consider both cases where obstacles…
Two isomorphic graphs can have inequivalent spatial embeddings in 3-space. In this way, an isomorphism class of graphs contains many spatial graph types. A common way to measure the complexity of a spatial graph type is to count the minimum…
This paper focuses on studying the configuration spaces of graphs realised in $\mathbb C^2$, such that the configuration space is, after normalisation, one dimensional. If this is the case, then the configuration space is, generically, a…
Quadruped mammals coordinate spinal bending and axial compression to enhance locomotion agility and efficiency. However, existing robotic spines typically lack the active compliance required to support such dynamic behaviours. We present…
We define a CR structure on a distinguished hyperplane in $\mathbb{C}^{n+1}$ and the CR sub-Laplacian on this CR manifold. We also define symmetries of the CR sub-Laplacian in general and for this special case construct all of them using…