Probabilistic Virtual Fixtures (VFs) enable the adaptive selection of the most suitable haptic feedback for each phase of a task, based on learned or perceived uncertainty. While keeping the human in the loop remains essential, for instance, to ensure high precision, partial automation of certain task phases is critical for productivity. We present a unified framework for probabilistic VFs that seamlessly switches between manual fixtures, semi-automated fixtures (with the human handling precise tasks), and full autonomy. We introduce a novel probabilistic Dynamical System-based VF for coarse guidance, enabling the robot to autonomously complete certain task phases while keeping the human operator in the loop. For tasks requiring precise guidance, we extend probabilistic position-based trajectory fixtures with automation allowing for seamless human interaction as well as geometry-awareness and optimal impedance gains. For manual tasks requiring very precise guidance, we also extend visual servoing fixtures with the same geometry-awareness and impedance behavior. We validate our approach experimentally on different robots, showcasing multiple operation modes and the ease of programming fixtures.

The paper presents a systematic approach for stiffness modeling of manipulators with complex and hybrid structures using matrix structural analysis. In contrast to previous results, it is suitable for mixed architectures containing closed-loops, flexible links, rigid connections, passive and elastic joints with external loadings and preloadings. The proposed approach produces the Cartesian stiffness matrices in a semi-analytical manner. It presents the manipulator stiffness model as a set of conventional equations describing the link elasticities that are supplemented by a set of constraints describing connections between links. Its allows user straightforward aggregation of stiffness model equations avoiding traditional column/row merging procedures in the extended stiffness matrix. Advantages of this approach are illustrated by stiffness analysis of NaVaRo manipulator.

We present an estimation of the condition numbers of the \emph{mass} and \emph{stiffness} matrices arising from shallow ReLU$^k$ neural networks defined on the unit sphere~$\mathbb{S}^d$. In particular, when $\{θ_j^*\}_{j=1}^n \subset \mathbb{S}^d$ is \emph{antipodally quasi-uniform}, the condition number is sharp. Indeed, in this case, we obtain sharp asymptotic estimates for the full spectrum of eigenvalues and characterize the structure of the corresponding eigenspaces, showing that the smallest eigenvalues are associated with an eigenbasis of low-degree polynomials while the largest eigenvalues are linked to high-degree polynomials. This spectral analysis establishes a precise correspondence between the approximation power of the network and its numerical stability.

Low-rank pseudoinverses are widely used to approximate matrix inverses in scalable machine learning, optimization, and scientific computing. However, real-world matrices are often observed with noise, arising from sampling, sketching, and quantization. The spectral-norm robustness of low-rank inverse approximations remains poorly understood. We systematically study the spectral-norm error $\| (\tilde{A}^{-1})_p - A_p^{-1} \|$ for an $n\times n$ symmetric matrix $A$, where $A_p^{-1}$ denotes the best rank-\(p\) approximation of $A^{-1}$, and $\tilde{A} = A + E$ is a noisy observation. Under mild assumptions on the noise, we derive sharp non-asymptotic perturbation bounds that reveal how the error scales with the eigengap, spectral decay, and noise alignment with low-curvature directions of $A$. Our analysis introduces a novel application of contour integral techniques to the \emph{non-entire} function $f(z) = 1/z$, yielding bounds that improve over naive adaptations of classical full-inverse bounds by up to a factor of $\sqrt{n}$. Empirically, our bounds closely track the true perturbation error across a variety of real-world and synthetic matrices, while estimates based on classical results tend to significantly overpredict. These findings offer practical, spectrum-aware guarantees for low-rank inverse approximations in noisy computational environments.

Abstract-- Humanoid whole-body locomotion control is a critical approach for humanoid robots to leverage their inherent advantages. Learning-based control methods derived from retargeted human motion data provide an effective means of addressing this issue. However, because most current human datasets lack measured force data, and learning-based robot control is largely position-based, achieving appropriate compliance during interaction with real environments remains challenging. This paper presents Compliant Task Pipeline (CoTaP): a pipeline that leverages compliance information in the learning-based structure of humanoid robots. A two-stage dual-agent reinforcement learning framework combined with model-based compliance control for humanoid robots is proposed. In the training process, first a base policy with a position-based controller is trained; then in the distillation, the upper-body policy is combined with model-based compliance control, and the lower-body agent is guided by the base policy. In the upper-body control, adjustable task-space compliance can be specified and integrated with other controllers through compliance modulation on the symmetric positive definite (SPD) manifold, ensuring system stability. We validated the feasibility of the proposed strategy in simulation, primarily comparing the responses to external disturbances under different compliance settings. For detailed experimental results, please see the attached video. I. Introduction In recent decades, humanoid robot technology has made significant advancements.

The paper presents a visio-verbal teleimpedance interface for commanding 3D stiffness ellipsoids to the remote robot with a combination of the operator's gaze and verbal interaction. The gaze is detected by an eye-tracker, allowing the system to understand the context in terms of what the operator is currently looking at in the scene. Along with verbal interaction, a Visual Language Model (VLM) processes this information, enabling the operator to communicate their intended action or provide corrections. Based on these inputs, the interface can then generate appropriate stiffness matrices for different physical interaction actions. To validate the proposed visio-verbal teleimpedance interface, we conducted a series of experiments on a setup including a Force Dimension Sigma.7 haptic device to control the motion of the remote Kuka LBR iiwa robotic arm. The human operator's gaze is tracked by Tobii Pro Glasses 2, while human verbal commands are processed by a VLM using GPT-4o. The first experiment explored the optimal prompt configuration for the interface. The second and third experiments demonstrated different functionalities of the interface on a slide-in-the-groove task.

We introduce AI University (AI-U), a flexible framework for AI-driven course content delivery that adapts to instructors' teaching styles. At its core, AI-U fine-tunes a large language model (LLM) with retrieval-augmented generation (RAG) to generate instructor-aligned responses from lecture videos, notes, and textbooks. Using a graduate-level finite-element-method (FEM) course as a case study, we present a scalable pipeline to systematically construct training data, fine-tune an open-source LLM with Low-Rank Adaptation (LoRA), and optimize its responses through RAG-based synthesis. Our evaluation - combining cosine similarity, LLM-based assessment, and expert review - demonstrates strong alignment with course materials. We also have developed a prototype web application, available at https://my-ai-university.com, that enhances traceability by linking AI-generated responses to specific sections of the relevant course material and time-stamped instances of the open-access video lectures. Our expert model is found to have greater cosine similarity with a reference on 86% of test cases. An LLM judge also found our expert model to outperform the base Llama 3.2 model approximately four times out of five. AI-U offers a scalable approach to AI-assisted education, paving the way for broader adoption in higher education. Here, our framework has been presented in the setting of a class on FEM - a subject that is central to training PhD and Master students in engineering science. However, this setting is a particular instance of a broader context: fine-tuning LLMs to research content in science.

Continuum robots offer high flexibility and multiple degrees of freedom, making them ideal for navigating narrow lumens. However, accurately modeling their behavior under large deformations and frequent environmental contacts remains challenging. Current methods for solving the deformation of these robots, such as the Model Order Reduction and Gauss-Seidel (GS) methods, suffer from significant drawbacks. They experience reduced computational speed as the number of contact points increases and struggle to balance speed with model accuracy. To overcome these limitations, we introduce a novel finite element method (FEM) named Acc-FEM. Acc-FEM employs a large deformation quasi-static finite element model and integrates an accelerated solver scheme to handle multi-contact simulations efficiently. Additionally, it utilizes parallel computing with Graphics Processing Units (GPU) for real-time updates of the finite element models and collision detection. Extensive numerical experiments demonstrate that Acc-FEM significantly improves computational efficiency in modeling continuum robots with multiple contacts while achieving satisfactory accuracy, addressing the deficiencies of existing methods.

In the realm of robotics, the concept of "controller design in the physical domain" (Sharon et al., 1989, 1991) and the associated methodology of "control by interconnection" (Stramigioli, 2001; van der Schaft, 2016) emphasize that robot controllers should be more than mere signal processors. Instead, they should have a physical interpretation (Lachner, 2022), which is especially important for robots that physically interact with the environment (Hogan, 1988; Dietrich and Hogan, 2022; Hogan, 2022). This paper delves into impedance control (Hogan, 1984) during physical interaction, specifically focusing on the symmetry of the stiffness matrix and its role in ensuring passive physical equivalent robot controllers. Passivity is a fundamental property for ensuring coupled stability when interacting with arbitrary passive objects (Colgate and Hogan, 1988a). Stability in robotics can be achieved by monitoring and controlling the energy supplied by the controller (Colgate and Hogan, 1987, 1988b,a; Stramigioli, 2015). In impedance-controlled robots, this monitoring is particularly straightforward, as energy is stored in virtual springs (potential energy) and transferred into kinetic energy during movement (Lachner et al., 2021). During physical interaction, stiffness plays a crucial role, as it defines how energy is stored and exchanged between the robot and its environment. Task-space stiffness determines interaction forces due to contact, which is especially important at low frequencies (e.g., steady-state). 1

Multiscale simulations are indispensable for connecting microstructural features to the macroscopic behavior of polycrystalline materials, but their high computational demands limit their practicality. Deep material networks (DMNs) have been proposed as efficient surrogate models, yet they fall short of capturing texture evolution. To address this limitation, we propose the orientation-aware interaction-based deep material network (ODMN), which incorporates an orientation-aware mechanism and an interaction mechanism grounded in the Hill-Mandel principle. The orientation-aware mechanism learns the crystallographic textures, while the interaction mechanism captures stress-equilibrium directions among representative volume element (RVE) subregions, offering insight into internal microstructural mechanics. Notably, ODMN requires only linear elastic data for training yet generalizes effectively to complex nonlinear and anisotropic responses. Our results show that ODMN accurately predicts both mechanical responses and texture evolution under complex plastic deformation, thus expanding the applicability of DMNs to polycrystalline materials. By balancing computational efficiency with predictive fidelity, ODMN provides a robust framework for multiscale simulations of polycrystalline materials.