arXiv subjects

Andreas Mueller

Publications and source records attributed to Andreas Mueller.

At least 19 recordsLinked to original sources

arXiv2026

Product Of Exponentials (POE) Splines on Lie-Groups: Limitations, Extensions, and Application to SO(3) and SE(3)

Existing methods for constructing splines and Bezier curves on a Lie group G involve repeated products of exponentials deduced from local geodesics, w.r.t. a Riemannian metric, or rely on general polynomials. Moreover, each of these local curves is supposed to start at the identity of $G$. Both assumptions may not reflect the actual curve to be interpolated. This paper pursues a different approach to construct splines on $G$. Local curves are expressed as solutions of the Poisson equation on G. Therewith, the local interpolations satisfies the boundary conditions while respecting the geometry of $G$. A $k$th-order approximation of the solutions gives rise to a $k$th-order product of exponential (POE) spline. Algorithms for constructing 3rd- and 4th-order splines are derived from closed form expressions for the approximate solutions. Additionally, spline algorithms are introduced that allow prescribing a vector field the curve must follow at the interpolation points. It is shown that the established algorithms, where $k$th-order POE-splines are constructed by concatenating local curves starting at the identity, cannot exactly reconstruct a $k$th-order motion. To tackle this issue, the formulations are extended by allowing for local curves between arbitrary points, rather than curves emanating from the identity. This gives rise to a global $k$th-order spline with arbitrary initial conditions. Several examples are presented, in particular the shape reconstruction of slender rods modeled as geometrically non-linear Cosserat rods.

math.NA↗

arXiv2026

An Overview of Formulae for the Higher-Order Kinematics of Lower-Pair Chains with Applications in Robotics and Mechanism Theory

The motions of mechanisms can be described in terms of screw coordinates by means of an exponential mapping. The product of exponentials (POE) describes the configuration of a chain of bodies connected by lower pair joints. The kinematics is thus given in terms of joint screws. The POE serves to express loop constraints for mechanisms as well as the forward kinematics of serial manipulators. Besides the compact formulations, the POE gives rise to purely algebraic relations for derivatives wrt. joint variables. It is known that the partial derivatives of the instantaneous joint screws (columns of the geometric Jacobian) are determined by Lie brackets the joint screws. Lesser-known is that derivative of arbitrary order can be compactly expressed by Lie brackets. This has significance for higher-order forward/inverse kinematics and dynamics of robots and multibody systems. Various relations were reported but are scattered in the literature and insufficiently recognized. This paper aims to provide a comprehensive overview of the relevant relations. Its original contributions are closed form and recursive relations for higher-order derivatives and Taylor expansions of various kinematic relations. Their application to kinematic control and dynamics of robotic manipulators and multibody systems is discussed.

cs.RO↗

arXiv2026

Identification of Non-Transversal Bifurcations of Linkages

The local analysis is an established approach to the study of singularities and mobility of linkages. Key result of such analyses is a local picture of the finite motion through a configuration. This reveals the finite mobility at that point and the tangents to smooth motion curves. It does, however, not immediately allow to distinguish between motion branches that do not intersect transversally (which is a rather uncommon situation that has only recently been discussed in the literature). The mathematical framework for such a local analysis is the kinematic tangent cone. It is shown in this paper that the constructive definition of the kinematic tangent cone already involves all information necessary to separate different motion branches. A computational method is derived by amending the algorithmic framework reported in previous publications.

cs.RO↗

arXiv2026

Closed Form Relations and Higher-Order Approximations of First and Second Derivatives of the Tangent Operator on SE(3)

The Lie group SE(3) of isometric orientation preserving transformation is used for modeling multibody systems, robots, and Cosserat continua. The use of these models in numerical simulation and optimization schemes necessitates the exponential map, its right-trivialized differential (often referred to as tangent operator), as well as higher derivatives in closed form. The $6\times 6$ matrix representation of the differential, $\mathbf{dexp}_{\mathbf{X}}:se\left( 3\right) \rightarrow se\left( 3\right) $ , and its first derivative were reported using a $3\times 3$ block partitioning. In this paper, the differential, its first and second derivative, as well as the Jacobian and Hessian of the evaluation maps, $\mathbf{dexp}_{\mathbf{X}}\mathbf{Z}$ and $\mathbf{dexp}_{\mathbf{X}}^{T}% \mathbf{Z}$, are reported avoiding the block partitioning. For all of them, higher-order approximations are derived. Besides the compactness, the advantage of the presented closed form relations is their numerical robustness when combined with the local approximation. The formulations are demonstrated for computation of the deformation field and the strain rates of an elastic Cosserat-Simo-Reissner rod.

math.GR↗

arXiv2026

Forward Dynamics of Variable Topology Mechanisms - The Case of Constraint Activation

Many mechanical systems exhibit changes in their kinematic topology altering the mobility. Ideal contact is the best known cause, but also stiction and controlled locking of parts of a mechanism lead to topology changes. The latter is becoming an important issue in human-machine interaction. Anticipating the dynamic behavior of variable topology mechanisms requires solving a non-smooth dynamic problem. The core challenge is a physically meaningful transition condition at the topology switching events. Such a condition is presented in this paper. Two versions are reported, one using projected motion equations in terms of redundant coordinates, and another one using the Voronets equations in terms of minimal coordinates. Their computational properties are discussed. Results are shown for joint locking of a planar 3R mechanisms and a 6DOF industrial manipulator.

cs.RO↗

arXiv2026

On the Terminology and Geometric Aspects of Redundant Parallel Manipulators

Parallel kinematics machines (PKM) can exhibit kinematic as well as actuation redundancy. While the meaning of kinematic redundancy has been clarified already for serial manipulators, actuation redundancy, that is only possible in PKM, is differently classified in the literature. In this paper a consistent terminology for general redundant PKM is proposed. A kinematic model is introduced with the configuration space (c-space) as central part. The notion of kinematic redundancy is recalled for PKM. C-space, output, and input singularities are distinguished. The significance of the c-space geometry is emphasized, and it is pointed out geometrically that input singularities can be avoided by redundant actuation schemes. In order to distinguish different actuation schemes of PKM a non-linear control system is introduced whose dynamics evolves on the c-space. The degree of actuation (DOA) is introduced as the number of independent control vector fields, and PKM are classified as full-actuated and underactuated. Relating this DOA to the degree of freedom (DOF) allows to classify the actuation redundancy.

cs.RO↗

arXiv2026

Nexus: Inferring Join Graphs from Metadata Alone via Iterative Low-Rank Matrix Completion

Automatically inferring join relationships is a critical task for effective data discovery, integration, querying and reuse. However, accurately and efficiently identifying these relationships in large and complex schemas can be challenging, especially in enterprise settings where access to data values is constrained. In this paper, we introduce the problem of join graph inference when only metadata is available. We conduct an empirical study on a large number of real-world schemas and observe that join graphs when represented as adjacency matrices exhibit two key properties: high sparsity and low-rank structure. Based on these novel observations, we formulate join graph inference as a low-rank matrix completion problem and propose Nexus, an end-to-end solution using only metadata. To further enhance accuracy, we propose a novel Expectation-Maximization algorithm that alternates between low-rank matrix completion and refining join candidate probabilities by leveraging Large Language Models. Our extensive experiments demonstrate that Nexus outperforms existing methods by a significant margin on four datasets including a real-world production dataset. Additionally, Nexus can operate in a fast mode, providing comparable results with up to 6x speedup, offering a practical and efficient solution for real-world deployments.

cs.DB↗

arXiv2026

GAMformer: Bridging Tabular Foundation Models and Interpretable Machine Learning

While interpretability is crucial for machine learning applications in safety-critical domains and for regulatory compliance, existing tabular foundation models like TabPFN lack transparency. Generalized Additive Models (GAMs) provide the needed interpretability through their additive structure, but traditional GAM methods rely on iterative learning algorithms (such as splines, boosted trees, or neural networks) that are fundamentally incompatible with the in-context learning paradigm of foundation models. In this paper, we introduce GAMformer, the first tabular foundation model for GAMs that bridges the gap between the power of foundation models and the interpretability requirements of critical real-world applications. GAMformer estimates GAM shape functions in a single forward pass using in-context learning, representing a significant departure from conventional iterative approaches. Building on previous research on tabular foundation models, we train GAMformer exclusively on synthetically generated tables to prevent data leakage. Our experiments demonstrate that GAMformer performs comparably to other leading GAMs across various classification benchmarks.

cs.LG↗

arXiv2026

Singularity-Free Lie Group Integration and Geometrically Consistent Evaluation of Multibody System Models Described in Terms of Standard Absolute Coordinates

A classical approach to the multibody systems (MBS) modeling is to use absolute coordinates, i.e., a set of (possibly redundant) coordinates that describe the absolute position and orientation of the individual bodies with respect to an inertial frame (IFR). A well-known problem for the time integration of the equations of motion (EOM) is the lack of a singularity-free parameterization of spatial motions, which is usually tackled by using unit quaternions. Lie group integration methods were proposed as an alternative approach to the singularity-free time integration. At the same time, Lie group formulations of EOM naturally respect the geometry of spatial motions during integration. Lie group integration methods, operating directly on the configuration space Lie group, are incompatible with standard formulations of the EOM, and cannot be implemented in existing MBS simulation codes without a major restructuring. The contribution of this paper is twofold: (1) A framework for interfacing Lie group integrators to standard EOM formulations is presented. It allows describing MBS in terms of various absolute coordinates and at the same using Lie group integration schemes. (2) A method for consistently incorporating the geometry of rigid body motions into the evaluation of EOM in absolute coordinates integrated with standard vector space integration schemes. The direct product group and the semidirect product group SO(3)xR3 and the semidirect product group SE(3) are used for representing rigid body motions. The key element is the local-global transitions (LGT) transition map, which facilitates the update of (global) absolute coordinates in terms of the (local) coordinates on the Lie group. This LGT map is specific to the absolute coordinates, the local coordinates on the Lie group, and the Lie group used to represent rigid body configurations.

cs.RO↗

arXiv2025

Altered oscillatory brain networks during emotional face processing in ADHD: an eLORETA and functional ICA study

Attention-deficit/hyperactivity disorder (ADHD) is characterized by executive dysfunction and difficulties in processing emotional facial expressions, yet the large-scale neural dynamics underlying these impairments remain insufficiently understood. This study applied network-based EEG source analysis to examine oscillatory cortical activity during cognitive and emotional Go/NoGo tasks in individuals with ADHD. EEG data from 272 participants (ADHD n equals 102, controls n equals 170, age range 6 to 60 years) were analyzed using exact low-resolution brain electromagnetic tomography combined with functional independent component analysis, yielding ten frequency-resolved cortical networks. Mixed-effects ANCOVAs were conducted on independent component loadings with Group, Task, and Condition as factors and age and sex as covariates. ADHD participants showed statistically significant but small increases in activation across several networks, including a gamma-dominant inferior temporal component showing a Group effect and a Group by Condition interaction with stronger NoGo-related activation in ADHD. Two additional components showed similar but weaker NoGo-selective patterns. A main effect of Task emerged only for one temporal delta component, with higher activation during the VCPT than the ECPT. No Group by Task interactions were observed. Behavioral results replicated the established ADHD performance profile, with slower responses, greater variability, and higher error rates, particularly during the emotional ECPT. Overall, the findings reveal subtle alterations in oscillatory brain networks during inhibitory processing in ADHD, with modest effect sizes embedded within substantial within-group variability. These results support a dimensional view of ADHD neurobiology and highlight the limited discriminative power of network-level EEG markers.

q-bio.NC↗

arXiv2025

Analysis of Deep-Learning Methods in an ISO/TS 15066-Compliant Human-Robot Safety Framework

Over the last years collaborative robots have gained great success in manufacturing applications where human and robot work together in close proximity. However, current ISO/TS-15066-compliant implementations often limit the efficiency of collaborative tasks due to conservative speed restrictions. For this reason, this paper introduces a deep-learning-based human-robot-safety framework (HRSF) that aims at a dynamical adaptation of robot velocities depending on the separation distance between human and robot while respecting maximum biomechanical force and pressure limits. The applicability of the framework was investigated for four different deep learning approaches that can be used for human body extraction: human body recognition, human body segmentation, human pose estimation, and human body part segmentation. Unlike conventional industrial safety systems, the proposed HRSF differentiates individual human body parts from other objects, enabling optimized robot process execution. Experiments demonstrated a quantitative reduction in cycle time of up to 15% compared to conventional safety technology.

cs.RO↗

arXiv2025

An approach for combining transparency and motion assistance of a lower body exoskeleton

In this paper, an approach for gait assistance with a lower body exoskeleton is described. Two concepts, transparency and motion assistance, are combined. The transparent mode, where the system is following the user's free motion with a minimum of perceived interaction forces, is realized by exploiting the gear backlash of the actuation units. During walking a superimposed assistance mode applies an additional torque guiding the legs to their estimated future position. The concept of adaptive oscillators is utilized to learn the quasi-periodic signals typical for locomotion. First experiments showed promising results.

cs.RO↗

arXiv2025

Geometric Robot Calibration Using a Calibration Plate

In this paper a new method for geometric robot calibration is introduced, which uses a calibration plate with precisely known distances between its measuring points. The relative measurement between two points on the calibration plate is used to determine predefined error parameters of the system. In comparison to conventional measurement methods, like laser tracker or motion capture systems, the calibration plate provides a more mechanically robust and cheaper alternative, which is furthermore easier to transport due to its small size. The calibration method, the plate design, the mathematical description of the error system as well as the identification of the parameters are described in detail. For identifying the error parameters, the least squares method and a constrained optimization problem are used. The functionality of this method was demonstrated in experiments that led to promising results, correlated with one of a laser tracker calibration. The modeling and identification of the error parameters is done for a gantry machine, but is not restricted to that type of robot.

cs.RO↗

arXiv2025

Time-Optimal Transport of Loosely Placed Liquid Filled Cups along Prescribed Paths

Handling loosely placed objects with robotic manipulators is a difficult task from the point of view of trajectory planning and control. This becomes even more challenging when the object to be handled is a container filled with liquid. This paper addresses the task of transporting a liquid-filled cup placed on a tray along a prescribed path in shortest time. The objective is to minimize swapping, thus avoiding spillage of the fluid. To this end, the sloshing dynamics is incorporated into the dynamic model used within the optimal control problem formulation. The optimization problem is solved using a direct multiple shooting approach.

cs.RO↗

arXiv2025

An Automated Tape Laying System Employing a Uniaxial Force Control Device

This paper deals with the design of a cost effective automated tape laying system (ATL system) with integrated uniaxial force control to ensure the necessary compaction forces as well as with an accurate temperature control to guarantee the used tape being melted appropriate. It is crucial to control the substrate and the oncoming tape onto a specific temperature level to ensure an optimal consolidation between the different layers of the product. Therefore, it takes several process steps from the spooled tape on the coil until it is finally tacked onto the desired mold. The different modules are divided into the tape storage spool, a tape-guiding roller, a tape processing unit, a heating zone and the consolidation unit. Moreover, a special robot control concept for testing the ATL system is presented. In contrast to many other systems, with this approach, the tape laying device is spatially fixed and the shape is moved accordingly by the robot, which allows for handling of rather compact and complex shapes. The functionality of the subsystems and the taping process itself was finally approved in experimental results using a carbon fiber reinforced HDPE tape.

cs.RO↗

arXiv2025

Workspace Registration and Collision Detection for Industrial Robotics Applications

Motion planning for robotic manipulators relies on precise knowledge of the environment in order to be able to define restricted areas and to take collision objects into account. To capture the workspace, point clouds of the environment are acquired using various sensors. The collision objects are identified by region growing segmentation and VCCS algorithm. Subsequently the point clusters are approximated. The aim of the present paper is to compare different sensors, to illustrate the process from detection to the finished collision environment and to detect collisions between the robot and this environment.

cs.RO↗

arXiv2025

Optimal Dimensioning of Elastic-Link Manipulators regarding Lifetime Estimation

Resourceful operation and design of robots is key for sustainable industrial automation. This will be enabled by lightweight design along with time and energy optimal control of robotic manipulators. Design and control of such systems is intertwined as the control must take into account inherent mechanical compliance while the design must accommodate the dynamic requirements demanded by the control. As basis for such design optimization, a method for estimating the lifetime of elastic link robotic manipulators is presented. This is applied to the geometry optimization of flexible serial manipulators performing pick-and-place operations, where the optimization objective is a combination of overall weight and vibration amplitudes. The lifetime estimation draws from a fatigue analysis combining the rainflow counting algorithm and the method of critical cutting plane. Tresca hypothesis is used to formulate an equivalent stress, and linear damage accumulation is assumed. The final robot geometry is selected from a Pareto front as a tradeoff of lifetime and vibration characteristic. The method is illustrated for a three degrees of freedom articulated robotic manipulator.

cs.RO↗

arXiv2025

A Parameter-Linear Formulation of the Optimal Path Following Problem for Robotic Manipulator

In this paper the computational challenges of time-optimal path following are addressed. The standard approach is to minimize the travel time, which inevitably leads to singularities at zero path speed, when reformulating the optimization problem in terms of a path parameter. Thus, smooth trajectory generation while maintaining a low computational effort is quite challenging, since the singularities have to be taken into account. To this end, a different approach is presented in this paper. This approach is based on maximizing the path speed along a prescribed path. Furthermore, the approach is capable of planning smooth trajectories numerically efficient. Moreover, the discrete reformulation of the underlying problem is linear in optimization variables.

cs.RO↗