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.

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.

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.

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.

Generalized Additive Models (GAMs) are widely recognized for their ability to create fully interpretable machine learning models for tabular data. Traditionally, training GAMs involves iterative learning algorithms, such as splines, boosted trees, or neural networks, which refine the additive components through repeated error reduction. In this paper, we introduce GAMformer, the first method to leverage in-context learning to estimate shape functions of a GAM in a single forward pass, representing a significant departure from the conventional iterative approaches to GAM fitting. Building on previous research applying in-context learning to tabular data, we exclusively use complex, synthetic data to train GAMformer, yet find it extrapolates well to real-world data. Our experiments show that GAMformer performs on par with other leading GAMs across various classification benchmarks while generating highly interpretable shape functions. The growing importance of interpretability in machine learning is evident, especially in areas where transparency, fairness, and accountability are critical (Barocas and Selbst, 2016; Rudin et al., 2022). Interpretable models are essential for building trust between humans and AI systems by allowing users to understand the reasoning behind the model's predictions and decisions (Ribeiro et al., 2016). This is crucial in safety-critical fields like healthcare, where incorrect or biased decisions can have severe consequences (Caruana et al., 2015). Additionally, interpretability is vital for regulatory compliance in sectors like finance and hiring, where explaining and justifying model outcomes is necessary (Arun et al., 2016; Dattner et al., 2019). Interpretable models also help detect and mitigate bias by revealing the factors influencing predictions, ensuring fair and unbiased decisions across different population groups (Mehrabi et al., 2021). Generalized Additive Models (GAMs) have proven a popular choice for interpretable modeling due to their high accuracy and interpretability. In GAMs, the target variable is expressed as a sum of non-linearly transformed features.

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.

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.

Automated machine learning (AutoML) was formed around the fundamental objectives of automatically and efficiently configuring machine learning (ML) workflows, aiding the research of new ML algorithms, and contributing to the democratization of ML by making it accessible to a broader audience. Over the past decade, commendable achievements in AutoML have primarily focused on optimizing predictive performance. This focused progress, while substantial, raises questions about how well AutoML has met its broader, original goals. In this position paper, we argue that a key to unlocking AutoML's full potential lies in addressing the currently underexplored aspect of user interaction with AutoML systems, including their diverse roles, expectations, and expertise. We envision a more human-centered approach in future AutoML research, promoting the collaborative design of ML systems that tightly integrates the complementary strengths of human expertise and AutoML methodologies.

The exponential and Cayley map on SE(3) are the prevailing coordinate maps used in Lie group integration schemes for rigid body and flexible body systems. Such geometric integrators are the Munthe-Kaas and generalized-alpha schemes, which involve the differential and its directional derivative of the respective coordinate map. Relevant closed form expressions, which were reported over the last two decades, are scattered in the literature, and some are reported without proof. This paper provides a reference summarizing all relevant closed form relations along with the relevant proofs. including the right-trivialized differential of the exponential and Cayley map and their directional derivatives (resembling the Hessian). The latter gives rise to an implicit generalized-alpha scheme for rigid/flexible multibody systems in terms of the Cayley map with improved computational efficiency.

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.