arXiv subjects

Tom Kaufmann

Publications and source records attributed to Tom Kaufmann.

17 recordsLinked to original sources

arXiv2025

On robotic manipulators with time-dependent inertial parameters: From physical consistency to boundedness of the mass matrix

We generalize the robotics equation describing the dynamics of open kinematic chains by including the effect of time-dependent change of inertial parameters as well as the effects of causative mass-density redistribution, triggered by internal movement of mass-carrying particles relative to their body-fixed frames. Time dependency of inertial parameters that results from the sole addition of mass to the robot prominently occurs during the loading of end-effectors--a scenario covered by our model without restriction from the restraint that kinematic parameters of the robot must remain constant. Further, our model also includes internal mass-density redistributions that adhere to this kinematic restraint such as trolleys attached to the robot or the movement of passengers. To accompany the generalized robotics equation with some theoretical infrastructure, we then introduce the concepts of uniform physical consistency and upper boundedness of inertial parameters under which desirable, structural properties regarding the existence of finite, positive uniform bounds of the mass matrix can be shown to carry over to the more involved case of time-dependent inertial parameters. These findings have implications for adaptive control, as they facilitate more realistic testing for robustness against unforeseen time dependencies. Moreover, the results in this paper also provide a pathway to ensuring the desirable existence of finite, positive uniform bounds of the estimated mass matrix under upper bounded, uniformly physically consistent estimation regimes.

math.OC↗

arXiv2025

Enhancing Situational Awareness in ISAC Networks via Drone Swarms: A Real-World Channel Sounding Data Set

With the upcoming capabilities of integrated sensing and communication (ISAC) and the incorporation of user equipment (UE) like unmanned aerial vehicles (UAVs) in 6G mobile networks, there is a significant opportunity to enhance situational awareness through multi-static radar sensing in meshed ISAC networks. This paper presents a real-world channel sounding data set acquired using a testbed with synchronized, distributed ground-based sensor nodes and flying sensor nodes within a swarm of up to four drones. The conducted measurement campaign is designed to sense the bi-static reflectivity of objects such as parking cars, vertical take-off and landing (VTOL) aircraft, and small drones in multi-path environments. We detail the rationale behind the selection of the included scenarios and the configuration of the participating nodesand present exemplary results to demonstrate the potential of using collaborating drone swarms for multi-static radar tracking and localization in air-to-air (A2A) and air-to-ground (A2G) scenarios. The data sets are publicly available to support the development and validation of future ISAC algorithms in real-world environments rather than relying solely on simulation.

eess.SP↗

arXiv2025

Real-Time Sounding in ISAC networks: Design and Implementation of a Multi-Node Testbed with Synchronized Airborne and Ground-Based Sensors

As integrated sensing and communication (ISAC) capabilities become more prevalent in the mobile 6G radio landscape, there is a substantial opportunity to enhance situational awareness across diverse applications through multi-static radar sensing within meshed ISAC networks. To facilitate the development and testing of detection and localization algorithms across diverse scenarios, this paper introduces a synchronized distributed channel sounding testbed with airborne and ground-based multi-channel transceiver nodes with centimeter-level positioning accuracy enabled by real-time kinematic (RTK) and inertial navigation system (INS) data. Our modular experimental measurement system is designed to include stationary sensor nodes and light-weight to medium-weight mobile nodes deployable on unmanned aerial vehicles (UAVs), cars, pedestrians, and cyclists. Utilizing commercial off-the-shelf (COTS) hardware, specifically software defined radios (SDRs), the testbed encourages reproducibility in academic research laboratories. We detail the individual modules and integration steps required to achieve the specified performance. The testbed's capabilities are validated through a real-world measurement campaign, including stationary and flying sensor nodes, aimed at detecting radar targets such as vertical take-off and landing (VTOL) aircrafts, small hexacopters, cars and vulnerable road users (VRUs) in air-to-air (A2A) and air-to-ground (A2G) scenarios.

eess.SP↗

arXiv2024

Indirect Adaptive Control Using a Static Update Law

The update law in the indirect adaptive control scheme can be extended to include feedthrough of an error term. This reduces undesired oscillations of the calculated weights. When the ${\sigma}$-modification is used for achieving robustness against unstructured uncertainties, the gain of the feedthrough in the update law cannot be chosen arbitrarily. Compared to our previous result, we show stability of the closed loop for a larger parameter-range for the gain of the feedthrough in the update law. This parameter-range includes a configuration for which the influence of the integration in the update law diminishes over time, i.e. for which the adaptation for large times is governed solely by the feedthrough in the update law. By initializing at zero, this allows for removing the integration from the update law, resulting in a static update law. For the purely linear case, the adaptation acts like a disturbance observer. Frequency-domain analysis of the closed loop with a second order plant shows that removing the integration from the update law with ${\sigma}$-modification and feedthrough affects how precisely disturbances in the low-frequency band are observed. If the damping injected into the adaptation process by the ${\sigma}$-modification exceeds certain bounds, then the precision is increased by using the static update law.

math.OC↗

arXiv2022

Second-order properties for planar Mondrian tessellations

In this paper planar STIT tesselations with weighted axis-parallel cutting directions are considered. They are known also as weighted planar Mondrian tesselations in the machine learning literature, where they are used in random forest learning and kernel methods. Various second-order properties of such random tessellations are derived, in particular, explicit formulas are obtained for suitably adapted versions of the pair- and cross-correlation functions of the length measure on the edge skeleton and the vertex point process. Also, explicit formulas and the asymptotic behaviour of variances are discussed in detail.

math.PR↗

arXiv2022

Large deviations for uniform projections of $p$-radial distributions on $\ell_p^n$-balls

We consider products of uniform random variables from the Stiefel manifold of orthonormal $k$-frames in $\mathbb{R}^n$, $k \le n$, and random vectors from the $n$-dimensional $\ell_p^n$-ball $\mathbb{B}_p^n$ with certain $p$-radial distributions, $p\in[1,\infty)$. The distribution of this product geometrically corresponds to the projection of the $p$-radial distribution on $\mathbb{B}^n_p$ onto a random $k$-dimensional subspace. We derive large deviation principles (LDPs) on the space of probability measures on $\mathbb{R}^k$ for sequences of such projections.

math.PR↗

arXiv2021

Sharpening the probabilistic Arithmetic-Geometric Mean Inequality

We consider the $p$-generalized arithmetic-geometric mean inequality for vectors chosen randomly from the $\ell_p^n$-ball in $\mathbb{R}^n$. In this setting the inequality can be improved or reversed up to a respective scalar constant with high probability, and central limit theorems and large deviation results with respect to this constant have been shown. We sharpen these large deviation results in the spirit of Bahadur and Ranga Rao, thereby providing concrete and asymptotically exact estimates on a non-logarithmic scale for the probability of the inequality being improvable or reversible up to a constant, respectively.

math.PR↗

arXiv2021

Weighted $p$-radial Distributions on Euclidean and Matrix $p$-balls with Applications to Large Deviations

A probabilistic representation for a class of weighted $p$-radial distributions, based on mixtures of a weighted cone probability measure and a weighted uniform distribution on the Euclidean $\ell_p^n$-ball, is derived. Large deviation principles for the empirical measure of the coordinates of random vectors on the $\ell_p^n$-ball with distribution from this weighted measure class are discussed. The class of $p$-radial distributions is extended to $p$-balls in classical matrix spaces, both for self-adjoint and non-self-adjoint matrices. The eigenvalue distribution of a self-adjoint random matrix, chosen in the matrix $p$-ball according to such a distribution, is determined. Similarly, the singular value distribution is identified in the non-self-adjoint case. Again, large deviation principles for the empirical spectral measures for the eigenvalues and the singular values are presented as an application.

math.PR↗

arXiv2021

Sharp Asymptotics for $q$-Norms of Random Vectors in High-Dimensional $\ell_p^n$-Balls

Sharp large deviation results of Bahadur-Ranga Rao type are provided for the $q$-norm of random vectors distributed on the $\ell _{p}^{n}$-ball ${\mathbb{B}}^{n}_{p}$ according to the cone probability measure or the uniform distribution for $1 \le q<p < \infty $, thereby furthering previous large deviation results by Kabluchko, Prochno and Th\"{a}le in the same setting. These results are then applied to deduce sharp asymptotics for intersection volumes of different $\ell _{p}^{n}$-balls in the spirit of Schechtman and Schmuckenschl\"{a}ger, and for the length of the projection of an $\ell _{p}^{n}$-ball onto a line with uniform random direction. The sharp large deviation results are proven by providing convenient probabilistic representations of the $q$-norms, employing local limit theorems to approximate their densities, and then using geometric results for asymptotic expansions of Laplace integrals to integrate these densities and derive concrete probability estimates.

math.PR↗

arXiv2019

Hadron-in-jet production at partonic threshold

We consider the longitudinal momentum distribution of hadrons inside jets in proton-proton collisions. At partonic threshold large double logarithmic corrections arise which need to be resummed to all orders. We develop a factorization formalism within SCET that allows for the joint resummation of threshold and jet radius logarithms. We achieve next-to-leading logarithmic NLL$'$ accuracy by including non-global logarithms in the leading-color approximation. Overall, we find that the threshold resummation leads to a sizable enhancement of the cross section and a reduced QCD scale dependence, suggesting that the all-order resummation can be important for the reliable extraction of fragmentation functions in global analyses when jet substructure data is included.

hep-ph↗

arXiv2018

PHOTON-2017 conference proceedings

This document collects the proceedings of the PHOTON 2017 conference ("International Conference on the Structure and the Interactions of the Photon", including the 22th "International Workshop on Photon-Photon Collisions", and the "International Workshop on High Energy Photon Colliders") held at CERN (Geneva) in May 2017. The latest experimental and theoretical developments on the topics of the PHOTON conference series are covered: (i) $\gamma\,\gamma$ processes in e$^+$e$^-$, proton-proton (pp) and nucleus-nucleus (AA) collisions at current and future colliders, (ii) $\gamma$-hadron interactions in e$^\pm$p, pp, and AA collisions, (iii) final-state photon production (including Standard Model studies and searches beyond it) in pp and AA collisions, and (iv) high-energy $\gamma$-ray astrophysics. These proceedings are dedicated to the memory of Maria Krawczyk.

hep-ph↗

arXiv2017

Recent developments on parton-to-photon fragmentation functions

We report on some recent developments concerning parton-to-photon fragmentation functions. We briefly summarize the main theoretical concepts on which the currently available extractions of these fragmentation functions rely: evolution and the vector meson dominance model. We present comparisons of the available sets. We argue that the single-inclusive photon production process $pp\toγX$ possesses only little sensitivity to the fragmentation contribution. Instead, the semi-inclusive process $pp\to(\text{jet}\,γ)X$, for which the photon is observed inside a fully reconstructed jet and is part of the jet, is shown to offer much potential for providing valuable new information.

hep-ph↗

arXiv2017

Using hadron-in-jet data in a global analysis of $D^{*}$ fragmentation functions

We present a novel global QCD analysis of charged $D^{*}$-meson fragmentation functions at next-to-leading order accuracy. This is achieved by making use of the available data for single-inclusive $D^{*}$-meson production in electron-positron annihilation, hadron-hadron collisions, and, for the first time, in-jet fragmentation in proton-proton scattering. It is shown how to include all relevant processes efficiently and without approximations within the Mellin moment technique, specifically for the in-jet fragmentation cross section. The presented technical framework is generic and can be straightforwardly applied to future analyses of fragmentation functions for other hadron species, as soon as more in-jet fragmentation data become available. We choose to work within the Zero Mass Variable Flavor Number Scheme which is applicable for sufficiently high energies and transverse momenta. The obtained optimum set of parton-to-$D^{*}$ fragmentation functions is accompanied by Hessian uncertainty sets which allow one to propagate hadronization uncertainties to other processes of interest.

hep-ph↗

arXiv2016

Fragmentation Functions Beyond Fixed Order Accuracy

We give a detailed account of the phenomenology of all-order resummations of logarithmically enhanced contributions at small momentum fraction of the observed hadron in semi-inclusive electron-positron annihilation and the time-like scale evolution of parton-to-hadron fragmentation functions. The formalism to perform resummations in Mellin moment space is briefly reviewed, and all relevant expressions up to next-to-next-to-leading logarithmic order are derived, including their explicit dependence on the factorization and renormalization scales. We discuss the details pertinent to a proper numerical implementation of the resummed results comprising an iterative solution to the time-like evolution equations, the matching to known fixed-order expressions, and the choice of the contour in the Mellin inverse transformation. First extractions of parton-to-pion fragmentation functions from semi-inclusive annihilation data are performed at different logarithmic orders of the resummations in order to estimate their phenomenological relevance. To this end, we compare our results to corresponding fits up to fixed, next-to-next-to-leading order accuracy and study the residual dependence on the factorization scale in each case.

hep-ph↗

arXiv2016

Access to Photon Fragmentation Functions in Hadronic Jet Production

We argue that the process $pp \to (\text{jet} γ)X$, for which a photon is observed inside a fully reconstructed jet and is treated as part of the jet, offers new probes of the so far little known fragmentation functions for photons. We present a next-to-leading-order QCD calculation of the cross section for this process in the limit that the jet is relatively narrow. We also investigate the background resulting from the two-photon decay of neutral pions. We present numerical results relevant for possible measurements at the LHC and at RHIC. These suggest that $pp \to (\text{jet} γ)X$ should provide clean access to the photon fragmentation functions, provided an efficient suppression of the background is available in experiment.

hep-ph↗

arXiv2015

Hadron Fragmentation Inside Jets in Hadronic Collisions

We present an analytical next-to-leading order QCD calculation of the partonic cross sections for the process $pp\rightarrow ({\text{jet}} \,h)X$, for which a specific hadron is observed inside a fully reconstructed jet. In order to obtain the analytical results, we assume the jet to be relatively narrow. We show that the results can be cast into a simple and systematic form based on suitable universal jet functions for the process. We confirm the validity of our calculation by comparing to previous results in the literature for which the next-to-leading order cross section was treated entirely numerically by Monte-Carlo integration techniques. We present phenomenological results for experiments at the LHC and at RHIC. These suggest that $pp\rightarrow ({\text{jet}} \,h)X$ should enable very sensitive probes of fragmentation functions, especially of the one for gluons.

hep-ph↗

arXiv2015

Next-to-leading Order Calculation for Jets Defined by a Maximized Jet Function

We present a next-to-leading order QCD calculation for the single-inclusive production of collimated jets at hadron colliders, when the jet is defined by maximizing a suitable jet function that depends on the momenta of final-state particles in the event. A jet algorithm of this type was initially proposed by Georgi and subsequently further developed into the class of "$J_{E_T}$ algorithms". Our calculation establishes the infrared safety of the algorithms at this perturbative order. We derive analytical results for the relevant partonic cross sections. We discuss similarities and differences with respect to jets defined by cone or (anti-)$k_t$ algorithms and present numerical results for the Tevatron and the LHC.

hep-ph↗