arXiv subjects

Andreas Mueller

Publications and source records attributed to Andreas Mueller.

At least 37 records · Page 2Linked to original sources

arXiv2025

Robot Path and Trajectory Planning Considering a Spatially Fixed TCP

This paper presents a method for planning a trajectory in workspace coordinates using a spatially fixed tool center point (TCP), while taking into account the processing path on a part. This approach is beneficial if it is easier to move the part rather than moving the tool. Whether a mathematical description that defines the shape to be processed or single points from a design program are used, the robot path is finally represented using B-splines. The use of splines enables the path to be continuous with a desired degree, which finally leads to a smooth robot trajectory. While calculating the robot trajectory through prescribed orientation, additionally a given velocity at the TCP has to be considered. The procedure was validated on a real system using an industrial robot moving an arbitrary defined part.

cs.RO↗

arXiv2025

Simultaneous Stiffness and Trajectory Optimization for Energy Minimization of Pick-and-Place Tasks of SEA-Actuated Parallel Kinematic Manipulators

A major field of industrial robot applications deals with repetitive tasks that alternate between operating points. For these so-called pick-and-place operations, parallel kinematic manipulators (PKM) are frequently employed. These tasks tend to automatically run for a long period of time and therefore minimizing energy consumption is always of interest. Recent research addresses this topic by the use of elastic elements and particularly series elastic actuators (SEA). This paper explores the possibilities of minimizing energy consumption of SEA actuated PKM performing pick-and-place tasks. The basic idea is to excite eigenmotions that result from the actuator springs and exploit their oscillating characteristics. To this end, a prescribed cyclic pick-and-place operation is analyzed and a dynamic model of SEA driven PKM is derived. Subsequently, an energy minimizing optimal control problem is formulated where operating trajectories as well as SEA stiffnesses are optimized simultaneously. Here, optimizing the actuator stiffness does not account for variable stiffness actuators. It serves as a tool for the design and dimensioning process. The hypothesis on energy reduction is tested on two (parallel) robot applications where redundant actuation is also addressed. The results confirm the validity of this approach.

cs.RO↗

arXiv2025

Geometric Interpolation of Rigid Body Motions

The problem of interpolating a rigid body motion is to find a spatial trajectory between a prescribed initial and terminal pose. Two variants of this interpolation problem are addressed. The first is to find a solution that satisfies initial conditions on the k-1 derivatives of the rigid body twist. This is called the kth-order initial value trajectory interpolation problem (k-IV-TIP). The second is to find a solution that satisfies conditions on the rigid body twist and its k-1 derivatives at the initial and terminal pose. This is called the kth-order boundary value trajectory interpolation problem (k-BV-TIP). Solutions to the k-IV-TIP for k=1,...,4, i.e. the initial twist and up to the 4th time derivative are prescribed. Further, a solution to the 1-IV-TBP is presented, i.e. the initial and terminal twist are prescribed. The latter is a novel cubic interpolation between two spatial configurations with given initial and terminal twist. This interpolation is automatically identical to the minimum acceleration curve when the twists are set to zero. The general approach to derive higher-order solutions is presented. Numerical results are shown for two examples.

cs.RO↗

arXiv2025

Wohlhart's Three-Loop Mechanism: An Overconstrained and Shaky Linkage

This paper revisits a three-loop spatial linkage that was proposed in an ARK 2004 paper by Karl Wohlhart (as extension of a two-loop linkage proposed by Eddie Baker in 1980) and later analyzed in an ARK 2006 paper by Diez-Martinez et. al. A local analysis shows that this linkage has a finite degree of freedom (DOF) 3 (and is thus overconstrained) while in its reference configuration the differential DOF is 5. It is shown that its configuration space is locally a smooth manifold so that the reference configuration is not a c-space singularity. It is shown that the differential DOF is locally constant, which makes this linkage shaky (so that the reference configuration is not a singularity). The higher-order local analysis is facilitated by the computation of the kinematic tangent cone as well as a local approximation of the c-space.

cs.RO↗

arXiv2025

On the Performance of Linear Adaptive Filters driven by the Ergodic Chaotic Logistic Map

Chaotic dynamical systems are increasingly considered for use in coding and transmission systems. This stems from their parameter sensitivity and spectral characteristics. The latter are relevant for channel estimation methods. In particular the logistic map $f_λ=λx\left( 1-x\right) $ has been employed in chaotic coding and spread spectrum transmission systems. For $λ=4$ the statistical properties of sequences generated by $f_4$ are considered as ideal drive signals for channel estimation schemes. This assumption is proven in the present paper. To this end the higher order statistical moments and the autocorrelation of time series generated by $f_4$ are derived. It is shown that for $λ=4$ the zero mean time series is uncorrelated. The adaptation performance of finite impulse response (FIR) digital adaptive filters (DAF) used for channel estimation is analyzed. It is shown that using zero mean sequences of $f_4$ leads to the maximal possible FIR DAF performance. An optimal value for the damping parameter in the LMS scheme is derived that leads to the maximal performance and ensures stability. The analytic considerations are confirmed by simulation results.

math.DS↗

arXiv2025

A Screw Approach to the Approximation of the Local Geometry of the Configuration Space and of the set of Configurations of Certain Rank of Lower Pair Linkages

A motion of a mechanism is a curve in its configuration space (c-space). Singularities of the c-space are kinematic singularities of the mechanism. Any mobility analysis of a particular mechanism amounts to investigating the c-space geometry at a given configuration. A higher-order analysis is necessary to determine the finite mobility. To this end, past research lead to approaches using higher-order time derivatives of loop closure constraints assuming (implicitly) that all possible motions are smooth. This continuity assumption limits the generality of these methods. In this paper an approach to the higher-order local mobility analysis of lower pair multi-loop linkages is presented. This is based on a higher-order Taylor series expansion of the geometric constraint mapping, for which a recursive algebraic expression in terms of joint screws is presented. An exhaustive local analysis includes analysis of the set of constraint singularities (configurations where the constraint Jacobian has certain corank). A local approximation of the set of configurations with certain rank is presented, along with an explicit expression for the differentials of Jacobian minors in terms of instantaneous joint screws. The c-space and the set of points of certain corank are therewith locally approximated by an algebraic variety determined algebraically from the mechanism's screw system. Results are shown for a simple planar 4-bar linkage, which exhibits a bifurcation singularity, and for a planar three-loop linkage exhibiting a cusp in c-space. The latter cannot be treated by the higher-order local analysis methods proposed in the literature.

math.DG↗

arXiv2025

A Recursive Lie-Group Formulation for the Second-Order Time Derivatives of the Inverse Dynamics of parallel Kinematic Manipulators

Series elastic actuators (SEA) were introduced for serial robotic arms. Their model-based trajectory tracking control requires the second time derivatives of the inverse dynamics solution, for which algorithms were proposed. Trajectory control of parallel kinematics manipulators (PKM) equipped with SEAs has not yet been pursued. Key element for this is the computationally efficient evaluation of the second time derivative of the inverse dynamics solution. This has not been presented in the literature, and is addressed in the present paper for the first time. The special topology of PKM is exploited reusing the recursive algorithms for evaluating the inverse dynamics of serial robots. A Lie group formulation is used and all relations are derived within this framework. Numerical results are presented for a 6-DOF Gough-Stewart platform (as part of an exoskeleton), and for a planar PKM when a flatness-based control scheme is applied.

cs.RO↗

arXiv2025

Closed Form Time Derivatives of the Equations of Motion of Rigid Body Systems

Derivatives of equations of motion(EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

cs.RO↗

arXiv2025

Cosmology and general relativity (GR) in upper secondary school through new targeted teaching materials: a study on student learning and motivation

Cosmology and GR remain largely inaccessible to high-school teaching due to the advanced prerequisites to master these topics. Integrating them into upper secondary teaching is a significant challenge that remains unresolved. This contribution reports on an implementation study of a GR and cosmology course for upper secondary school students as part of an educational project launched during the centenary of GR and tested ever since for several years. The course aimed to expand students' knowledge to include current physics topics while highlighting their foundations in areas of classical physics such as Newtonian mechanics, electromagnetism, and waves. Targeted teaching and learning materials are focused on conceptual and qualitative understanding, while systematically combined with a mathematical treatment accessible at the upper secondary level, avoiding oversimplification. A key element is an active learning approach, incorporating activities and tasks such as engaging applications related to current research, reflective exercises, thought experiments, and hands-on tasks. The main research objective was to explore whether a conceptually deep and educationally effective GR and cosmology course could be successfully implemented for non-specialist upper secondary students. A pre-post study assessed both conceptual learning and affective outcomes, including interest, curiosity, self-concept, and perceived relevance of science. Results showed encouraging gains in both learning and motivation, with large to very large effect sizes for conceptual learning of core principles. Additionally, no or small effects of predictors such as gender were observed. We conclude that the integration of GR and cosmology into upper secondary physics teaching, in the form of courses and materials that are engaging, comprehensible, and impactful, is feasible.

physics.ed-ph↗

arXiv2025

An $O(n$)-Algorithm for the Higher-Order Kinematics and Inverse Dynamics of Serial Manipulators using Spatial Representation of Twists

Optimal control in general, and flatness-based control in particular, of robotic arms necessitate to compute the first and second time derivatives of the joint torques/forces required to achieve a desired motion. In view of the required computational efficiency, recursive $O(n)$-algorithms were proposed to this end. Aiming at compact yet efficient formulations, a Lie group formulation was recently proposed, making use of body-fixed and hybrid representation of twists and wrenches. In this paper a formulation is introduced using the spatial representation. The second-order inverse dynamics algorithm is accompanied by a fourth-order forward and inverse kinematics algorithm. An advantage of all Lie group formulations is that they can be parameterized in terms of vectorial quantities that are readily available. The method is demonstrated for the 7 DOF Franka Emika Panda robot.

cs.RO↗

arXiv2025

Optimizing open-domain question answering with graph-based retrieval augmented generation

In this work, we benchmark various graph-based retrieval-augmented generation (RAG) systems across a broad spectrum of query types, including OLTP-style (fact-based) and OLAP-style (thematic) queries, to address the complex demands of open-domain question answering (QA). Traditional RAG methods often fall short in handling nuanced, multi-document synthesis tasks. By structuring knowledge as graphs, we can facilitate the retrieval of context that captures greater semantic depth and enhances language model operations. We explore graph-based RAG methodologies and introduce TREX, a novel, cost-effective alternative that combines graph-based and vector-based retrieval techniques. Our benchmarking across four diverse datasets highlights the strengths of different RAG methodologies, demonstrates TREX's ability to handle multiple open-domain QA types, and reveals the limitations of current evaluation methods. In a real-world technical support case study, we demonstrate how TREX solutions can surpass conventional vector-based RAG in efficiently synthesizing data from heterogeneous sources. Our findings underscore the potential of augmenting large language models with advanced retrieval and orchestration capabilities, advancing scalable, graph-based AI solutions.

cs.IR↗

arXiv2025

Open Challenges in Time Series Anomaly Detection: An Industry Perspective

Current research in time-series anomaly detection is using definitions that miss critical aspects of how anomaly detection is commonly used in practice. We list several areas that are of practical relevance and that we believe are either under-investigated or missing entirely from the current discourse. Based on an investigation of systems deployed in a cloud environment, we motivate the areas of streaming algorithms, human-in-the-loop scenarios, point processes, conditional anomalies and populations analysis of time series. This paper serves as a motivation and call for action, including opportunities for theoretical and applied research, as well as for building new dataset and benchmarks.

cs.LG↗

arXiv2024

Analytically Informed Inverse Kinematics Solution at Singularities

Near kinematic singularities of a serial manipulator, the inverse kinematics (IK) problem becomes ill-conditioned, which poses computational problems for the numerical solution. Computational methods to tackle this issue are based on various forms of a pseudoinverse (PI) solution to the velocity IK problem. The damped least squares (DLS) method provides a robust solution with controllable convergence rate. However, at singularities, it may not even be possible to solve the IK problem using any PI solution when certain end-effector motions are prescribed. To overcome this problem, an analytically informed inverse kinematics (AI-IK) method is proposed. The key step of the method is an explicit description of the tangent aspect of singular motions (the analytic part) to deduce a perturbation that yields a regular configuration. The latter serves as start configuration for the iterative solution (the numeric part). Numerical results are reported for a 7-DOF Kuka iiwa.

cs.RO↗

arXiv2024

Dynamics of Parallel Manipulators with Hybrid Complex Limbs -- Modular Modeling and Parallel Computing

Parallel manipulators, also called parallel kinematics machines (PKM), enable robotic solutions for highly dynamic handling and machining applications. The safe and accurate design and control necessitates high-fidelity dynamics models. Such modeling approaches have already been presented for PKM with simple limbs (i.e. each limb is a serial kinematic chain). A systematic modeling approach for PKM with complex limbs (i.e. limbs that possess kinematic loops) was not yet proposed despite the fact that many successful PKM comprise complex limbs. This paper presents a systematic modular approach to the kinematics and dynamics modeling of PKM with complex limbs that are built as serial arrangement of closed loops. The latter are referred to as hybrid limbs, and can be found in almost all PKM with complex limbs, such as the Delta robot. The proposed method generalizes the formulation for PKM with simple limbs by means of local resolution of loop constraints, which is known as constraint embedding in multibody dynamics. The constituent elements of the method are the kinematic and dynamic equations of motions (EOM), and the inverse kinematics solution of the limbs, i.e. the relation of platform motion and the motion of the limbs. While the approach is conceptually independent of the used kinematics and dynamics formulation, a Lie group formulation is employed for deriving the EOM. The frame invariance of the Lie group formulation is used for devising a modular modeling method where the EOM of a representative limb are used to derived the EOM of the limbs of a particular PKM. The PKM topology is exploited in a parallel computation scheme that shall allow for computationally efficient distributed evaluation of the overall EOM of the PKM. Finally, the method is applied to the IRSBot-2 and a 3\underline{R}R[2RR]R Delta robot, which is presented in detail.

cs.RO↗

arXiv2024

A Constraint Embedding Approach for Dynamics Modeling of Parallel Kinematic Manipulators with Hybrid Limbs

Parallel kinematic manipulators (PKM) are characterized by closed kinematic loops, due to the parallel arrangement of limbs but also due to the existence of kinematic loops within the limbs. Moreover, many PKM are built with limbs constructed by serially combining kinematic loops. Such limbs are called hybrid, which form a particular class of complex limbs. Design and model-based control requires accurate dynamic PKM models desirably without model simplifications. Dynamics modeling then necessitates kinematic relations of all members of the PKM, in contrast to the standard kinematics modeling of PKM, where only the forward and inverse kinematics solution for the manipulator (relating input and output motions) are computed. This becomes more involved for PKM with hybrid limbs. In this paper a modular modeling approach is employed, where limbs are treated separately, and the individual dynamic equations of motions (EOM) are subsequently assembled to the overall model. Key to the kinematic modeling is the constraint resolution for the individual loops within the limbs. This local constraint resolution is a special case of the general \emph{constraint embedding} technique. The proposed method finally allows for a systematic modeling of general PKM. The method is demonstrated for the IRSBot-2, where each limb comprises two independent loops.

cs.RO↗

arXiv2024

Wireless 6G Connectivity for Massive Number of Devices and Critical Services

Compared to the generations up to 4G, whose main focus was on broadband and coverage aspects, 5G has expanded the scope of wireless cellular systems towards embracing two new types of connectivity: massive machine-type communication (mMTC) and ultra-reliable low-latency communications (URLLC). This paper discusses the possible evolution of these two types of connectivity within the umbrella of 6G wireless systems. The paper consists of three parts. The first part deals with the connectivity for a massive number of devices. While mMTC research in 5G predominantly focuses on the problem of uncoordinated access in the uplink for a large number of devices, the traffic patterns in 6G may become more symmetric, leading to closed-loop massive connectivity. One of the drivers for this is distributed learning/inference. The second part of the paper discusses the evolution of wireless connectivity for critical services. While latency and reliability are tightly coupled in 5G, 6G will support a variety of safety critical control applications with different types of timing requirements, as evidenced by the emergence of metrics related to information freshness and information value. Additionally, ensuring ultra-high reliability for safety critical control applications requires modeling and estimation of the tail statistics of the wireless channel, queue length, and delay. The fulfillment of these stringent requirements calls for the development of novel AI-based techniques, incorporating optimization theory, explainable AI, generative AI and digital twins. The third part analyzes the coexistence of massive connectivity and critical services. We will consider scenarios in which a massive number of devices need to support traffic patterns of mixed criticality. This is followed by a discussion about the management of wireless resources shared by services with different criticality.

cs.IT↗

arXiv2024

The significance of the configuration space Lie group for the constraint satisfaction in numerical time integration of multibody systems

The dynamics simulation of multibody systems (MBS) using spatial velocities (non-holonomic velocities) requires time integration of the dynamics equations together with the kinematic reconstruction equations (relating time derivatives of configuration variables to rigid body velocities). The latter are specific to the geometry of the rigid body motion underlying a particular formulation, and thus to the used configuration space (c-space). The proper c-space of a rigid body is the Lie group SE(3), and the geometry is that of the screw motions. The rigid bodies within a MBS are further subjected to geometric constraints, often due to lower kinematic pairs that define SE(3) subgroups. Traditionally, however, in MBS dynamics the translations and rotations are parameterized independently, which implies the use of the direct product group $SO\left( 3\right) \times {\Bbb R}^{3}$ as rigid body c-space, although this does not account for rigid body motions. Hence, its appropriateness was recently put into perspective. In this paper the significance of the c-space for the constraint satisfaction in numerical time stepping schemes is analyzed for holonomicaly constrained MBS modeled with the 'absolute coordinate' approach, i.e. using the Newton-Euler equations for the individual bodies subjected to geometric constraints. It is shown that the geometric constraints a body is subjected to are exactly satisfied if they constrain the motion to a subgroup of its c-space. Since only the $SE\left( 3\right) $ subgroups have a practical significance it is regarded as the appropriate c-space for the constrained rigid body. Consequently the constraints imposed by lower pair joints are exactly satisfied if the joint connects a body to the ground. For a general MBS, where the motions are not constrained to a subgroup, the SE(3) and $SO\left( 3\right) \times {\Bbb R}^{3}$ yield the same order of accuracy.

math.NA↗

arXiv2024

Is there an optimal choice of configuration space for Lie group integration schemes applied to constrained MBS?

Recently various numerical integration schemes have been proposed for numerically simulating the dynamics of constrained multibody systems (MBS) operating. These integration schemes operate directly on the MBS configuration space considered as a Lie group. For discrete spatial mechanical systems there are two Lie group that can be used as configuration space: $SE\left( 3\right) $ and $SO\left( 3\right) \times \mathbb{R}^{3}$. Since the performance of the numerical integration scheme clearly depends on the underlying configuration space it is important to analyze the effect of using either variant. For constrained MBS a crucial aspect is the constraint satisfaction. In this paper the constraint violation observed for the two variants are investigated. It is concluded that the $SE\left( 3\right) $ formulation outperforms the $SO\left( 3\right) \times \mathbb{R}^{3}$ formulation if the absolute motions of the rigid bodies, as part of a constrained MBS, belong to a motion subgroup. In all other cases both formulations are equivalent. In the latter cases the $SO\left( 3\right) \times \mathbb{R}^{3}$ formulation should be used since the $SE\left( 3\right) $ formulation is numerically more complex, however.

math.NA↗