相关论文: Efficient construction of contact coordinates for …

Vehicle trajectory optimization is essential to ensure vehicles travel efficiently and safely. This paper presents an infrastructure assisted constrained connected automated vehicles (CAVs) trajectory optimization method on curved roads.…

The purpose of this work is to construct a model for the functional architecture of the primary visual cortex (V1), based on a structure of metric measure space induced by the underlying organization of receptive profiles (RPs) of visual…

Contact geometry allows to describe some thermodynamic and dissipative systems. In this paper we introduce a new geometric structure in order to describe time-dependent contact systems: cocontact manifolds. Within this setting we develop…

This paper presents a framework designed to tackle a range of planning problems arise in manipulation, which typically involve complex geometric-physical reasoning related to contact and dynamic constraints. We introduce the Contact Factor…

Discrete forms of the mean and directed curvature are constructed on piecewise flat manifolds, providing local curvature approximations for smooth manifolds embedded in both Euclidean and non-Euclidean spaces. The resulting expressions take…

Planning of any motion starts by planning the trajectory of the CoM. It is of the highest importance to ensure that the robot will be able to perform planned trajectory. With increasing capabilities of the humanoid robots, the case when…

We develop a combinatorial theory of vector bundles with connection on locally ordered simplicial complexes. This is a first step towards a discrete exterior calculus for bundle-valued forms. The basic building block is the discrete…

We propose a method for efficiently computing orientation-preserving and approximately continuous correspondences between non-rigid shapes, using the functional maps framework. We first show how orientation preservation can be formulated…

A code $C$ in a generalised quadrangle ${\mathcal Q}$ is defined to be a subset of the vertex set of the point-line incidence graph $\varGamma$ of ${\mathcal Q}$. The minimum distance $\delta$ of $C$ is the smallest distance between a pair…

Let $\varphi:\mathbb{R}\rightarrow \mathbb{R}$ be a continuously differentiable function on an interval $J\subset\mathbb{R}$ and let $\boldsymbol{\alpha}=(\alpha_1,\alpha_2)$ be a point with algebraically conjugate coordinates such that the…

This paper addresses the problem of multi-robot navigation where robots maneuver on a desired \(m\)-dimensional (i.e., \(m\)-D) manifold in the $n$-dimensional Euclidean space, and maintain a {\it flexible spatial ordering}. We consider $…

We give curvature-dependant convergence rates for the optimization of weakly convex functions defined on a manifold of 1-bounded geometry via Riemannian gradient descent and via the dynamic trivialization algorithm. In order to do this, we…

We describe a novel constructive technique for devising efficient first-order methods for a wide range of large-scale convex minimization settings, including smooth, non-smooth, and strongly convex minimization. The technique builds upon a…

We study the sub-Riemannian exponential for contact distributions on manifolds of dimension greater or equal to 5. We compute an approximation of the sub-Riemannian Hamiltonian flow and show that the conjugate time can have multiplicity 2…

A globally-adaptive curvilinear coordinate formalism is shown to be easily convertible to a class of curvilinear transformations locally optimized around atom sites by a few parameters. Parameter transferability is established for a…

After reviewing manifold optimization techniques in applications like MIMO communication systems, phased array beamforming, radar, and control theory, we observed that the Complex Circle Manifold (CCM) is widely employed, yet its…

Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We…

We introduce Probabilistic Coordinate Fields (PCFs), a novel geometric-invariant coordinate representation for image correspondence problems. In contrast to standard Cartesian coordinates, PCFs encode coordinates in correspondence-specific…

In this paper, we consider the partial quantum consensus problem of a qubit network in a distributed view. The local quantum operation is designed based on the Hamiltonian by using the local information of each quantum system in a network…

On a real analytic 5-dimensional CR-generic submanifold M^5 in C^4 of codimension 3, hence of CR dimension 1, which enjoys the generically satisfied nondegeneracy condition that Lie brackets up to length 3 of T^{1,0}M generate CTM, a…