arXiv research

Alternative discrete Dirac mechanics using Dirac structures.

Proposes KStar Diffuser for kinematics-aware bimanual robotic manipulation.

Study explores kinematics of surfaces under metric restrictions.

Self-driving vehicles (SDVs) hold great potential for improving traffic safety and are poised to positively affect the quality of life of millions of people. To unlock this potential one of the critical aspects of the autonomous technology is understanding and predicting future movement of vehicles surrounding the SDV.…

A novel controller for wheeled robots handles joystick inputs for smooth steering.

Proves a special case of the Gaussian kinematic formula using large sphere limits.

In this research, Artificial Neural Networks (ANNs) have been used as a powerful tool to solve the inverse kinematic equations of a parallel robot. For this purpose, we have developed the kinematic equations of a Tricept parallel kinematic mechanism with two rotational and one translational degrees of freedom (DoF). Us…

New formalism solves kinematical constraints in curved backgrounds and non-trivial states.

The paper uses complex-valued functions to simplify plane differential geometry and kinematics.

New formulas for measuring geometric properties of definable sets.

Physics-informed diffusion model detects anomalous trajectories in GPS data.

Paper proposes a smart neck-band for detecting neck postures using integrated kinematic and kinetic data.

We show that there exists a natural Tulczyjew triple in the dynamics of objects for which the standard kinematic configuration space $TM$, i.e. the tangent bundle, is replaced with its $n$-th exterior power, i.e. the bundle of tangent $n$-vectors. In this framework, which is fully covariant, we geometrically derive pha…

The thesis explores kinematical symmetries beyond Lorentzian spacetime.

We use the notion of generalized connection over a bundle map in order to present an alternative approach to sub-Riemannian geometry. Known concepts, such as normal and abnormal extremals, will be studied in terms of this new formalism. In particular, some necessary and sufficient conditions for the existence of abnorm…

Explains non-lorentzian theories and their dynamics.

We introduce different bases for the vector space of $\mathrm{Sp}(2)\mathrm{Sp}(1)$-invariant, translation invariant continuous valuations on the quaternionic plane and determine a complete set of kinematic formulas.

Study the geometry and dynamics of skew evolutes and involutes, related to bicycle kinematics.

Researchers prove formulas for flag area measures, extending previous work.

The existence of kinematic formulas for area measures with respect to any connected, closed subgroup of the orthogonal group acting transitively on the unit sphere is established. In particular, the kinematic operator for area measures is shown to have the structure of a co-product. In the case of the unitary group the…

In this contribution we review results on the kinematics of a quantum system localized on a connected configuration manifold and compatible dynamics for the quantum system including external fields and leading to non-linear Schrödinger equations for pure states.

A kinematics of the motion of a car is reformulated in terms of the theory of gauge potentials (connection on principal bundle). E(2)-connection originates in the no-slipping contact of the car with a road.

New kinematic model for a spin-rolling sphere using Darboux frame.

We consider the kinematics of specific fluid spacetimes admitting timelike congruences of Ricci Solitons. These fluids includes string cloud, string fluid, perfect fluid, radially symmetric fluid, anisotropic fluid and relativistic magneto-fluid. Results are obtained and important physical aspects are discussed.

DRMMs enable flexible conditional sampling for interactive machine learning.

We prove that higher moment maps on area measures of a euclidean vector space are injective, while the kernel of the centroid map equals the image of the first variation map. Based on this, we introduce the space of smooth dual area measures on a finite-dimensional euclidean vector space and prove that it admits a natu…

In this paper, we carry a detailed study of mechanical systems with configuration space $Q\longrightarrow Q/G$ for which the base $Q/G$ variables are being controlled. The overall system's motion is considered to be induced from the base one due to the presence of general non-holonomic constraints. It is shown that the…

Generalizes kinematical Lie algebras for isotropic spacetimes.

We consider the problem of inverse kinematics (IK), where one wants to find the parameters of a given kinematic skeleton that best explain a set of observed 3D joint locations. The kinematic skeleton has a tree structure, where each node is a joint that has an associated geometric transformation that is propagated to a…

We present a unified approach to constrained implicit Lagrangian and Hamiltonian systems based on the introduced concept of Dirac algebroid. The latter is a certain almost Dirac structure associated with the Courant algebroid on the dual $E^\ast$ to a vector bundle $E$. If this almost Dirac structure is integrable (Dir…

We revisit the contact measures introduced by Firey, and further developed by Schneider and Teufel, from the perspective of the theory of valuations on manifolds. This reveals a link between the kinematic formulas for area measures studied by Wannerer and the integral geometry of curved isotropic spaces. As an applicat…

New proof confirms operations on constructible functions match theory.

A kinematic method selects the deformation Laplacian for fluid dynamics on Riemannian manifolds.

We prove new kinematic formulas for tensor valuations and simplify previously known Crofton formulas by using the recently developed algebraic theory of translation invariant valuations. The heart of the paper is the computation of the Alesker-Fourier transform on the large class of spherical valuations, which is achie…

A close relationship between the classical Hamilton-Jacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric interpretation of this relationship relies on new mathematical techniques for mechanics defined on a skew-symmetric algebroid. This geometric…

Study examines how body segments respond to random vibrations.

This paper explores non-periodic folding of Spidron units, revealing nonlinear dynamics.

Deep neural networks (DNNs) have recently received vast attention in applications requiring classification of radar returns, including radar-based human activity recognition for security, smart homes, assisted living, and biomedicine. However,acquiring a sufficiently large training dataset remains a daunting task due t…

We survey recent results in hermitian integral geometry, i.e. integral geometry on complex vector spaces and complex space forms. We study valuations and curvature measures on complex space forms and describe how the global and local kinematic formulas on such spaces were recently obtained. While the local and global k…

We give in explicit form the principal kinematic formula for the action of the affine unitary group on $\C^n$, together with a straightforward algebraic method for computing the full array of unitary kinematic formulas, expressed in terms of certain convex valuations introduced, essentially, by H. Tasaki. We introduce …

Robust visual tracking for long video sequences is a research area that has many important applications. The main challenges include how the target image can be modeled and how this model can be updated. In this paper, we model the target using a covariance descriptor, as this descriptor is robust to problems such as p…

We formulate a kinematical extension of Double Field Theory on a $2d$-dimensional para-Hermitian manifold $(\mathcal{P},η,ω)$ where the $O(d,d)$ metric $η$ is supplemented by an almost symplectic two-form $ω$. Together $η$ and $ω$ define an almost bi-Lagrangian structure $K$ which provides a splitting of the tangent bu…

Survey of global geometry for double field theory.

Study of rigid body displacements in a projective space over dual numbers with geometric interpretations.

The local kinematic formulas on complex space forms induce the structure of a commutative algebra on the space $\mathrm{Curv}^{\mathrm{U}(n)*}$ of dual unitarily invariant curvature measures. Building on the recent results from integral geometry in complex space forms, we describe this algebra structure explicitly as a…

Extends particle classification to curved space-times using groupoids.

Improved sensitivity to Higgs potential through neural simulation-based inference for di-Higgs events.

In this note we show that the configuration spaces of the kinematic system constructed in [4] and [12] gives rise to a natural tower of sphere bundles. Moreover, we prove that, each tower of projective bundles associated to special multi- flags (cf [1], [13], [2], [3]), we can associate such a tower of sphere bundles w…