The multi-contact nonlinear complementarity problem (NCP) is a naturally arising challenge in robotic simulations. Achieving high performance in terms of both accuracy and efficiency remains a significant challenge, particularly in scenarios involving intensive contacts and stiff interactions. In this article, we introduce a new class of multi-contact NCP solvers based on the theory of the Augmented Lagrangian (AL). We detail how the standard derivation of AL in convex optimization can be adapted to handle multi-contact NCP through the iteration of surrogate problem solutions and the subsequent update of primal-dual variables. Specifically, we present two tailored variations of AL for robotic simulations: the Cascaded Newton-based Augmented Lagrangian (CANAL) and the Subsystem-based Alternating Direction Method of Multipliers (SubADMM). We demonstrate how CANAL can manage multi-contact NCP in an accurate and robust manner, while SubADMM offers superior computational speed, scalability, and parallelizability for high degrees-of-freedom multibody systems with numerous contacts. Our results showcase the effectiveness of the proposed solver framework, illustrating its advantages in various robotic manipulation scenarios.

Personal use of this material is permitted. Abstract --This paper proposes an online friction coefficient identification framework for legged robots on slippery terrain. The approach formulates the optimization problem to minimize the sum of residuals between actual and predicted states pa-rameterized by the friction coefficient in rigid body contact dynamics. Notably, the proposed framework leverages the analytic smoothed gradient of contact impulses, obtained by smoothing the complementarity condition of Coulomb friction, to solve the issue of non-informative gradients induced from the nonsmooth contact dynamics. Moreover, we introduce the rejection method to filter out data with high normal contact velocity following contact initiations during friction coefficient identification for legged robots. T o validate the proposed framework, we conduct the experiments using a quadrupedal robot platform, KAIST HOUND, on slippery and nonslippery terrain. We observe that our framework achieves fast and consistent friction coefficient identification within various initial conditions. OR legged robots navigating challenging terrain, contact modeling for considering the interaction between the robot and terrain is crucial. The modeling is particularly critical on slippery terrain, where the robots encounter nonlinear and hybrid dynamics due to foot slippage. Recently, contact modelings using rigid body contact dynamics have gained attention in the field of legged robots [1]-[4].

Principal Component Analysis (PCA) is a widely used method for dimensionality reduction, but it often overlooks fairness, especially when working with data that includes demographic characteristics. This can lead to biased representations that disproportionately affect certain groups. To address this issue, our approach incorporates Joint Eigenvalue Decomposition (JEVD), a technique that enables the simultaneous diagonalization of multiple matrices, ensuring both fair and efficient representations. We formally show that the optimal solution of JEVD leads to a fair PCA solution. By integrating JEVD with PCA, we strike an optimal balance between preserving data structure and promoting fairness across diverse groups. We demonstrate that our method outperforms existing baseline approaches in fairness and representational quality on various datasets. It retains the core advantages of PCA while ensuring that sensitive demographic attributes do not create disparities in the reduced representation.

On Enhancing Structural Resilience of Multirobot Coverage Control with Bearing Rigidity Kartik A. Pant, Vishnu Vijay, Minhyun Cho, and Inseok Hwang Abstract -- The problem of multi-robot coverage control has been widely studied to efficiently coordinate a team of robots to cover a desired area of interest. However, this problem faces significant challenges when some robots are lost or deviate from their desired formation during the mission due to faults or cyberattacks. Since a majority of multi-robot systems (MRSs) rely on communication and relative sensing for their efficient operation, a failure in one robot could result in a cascade of failures in the entire system. In this work, we propose a hierarchical framework for area coverage, combining centralized coordination by leveraging Voronoi partitioning with decentralized reference tracking model predictive control (MPC) for control design. In addition to reference tracking, the decentralized MPC also performs bearing maintenance to enforce a rigid MRS network, thereby enhancing the structural resilience, i.e., the ability to detect and mitigate the effects of localization errors and robot loss during the mission. Furthermore, we show that the resulting control architecture guarantees the recovery of the MRS network in the event of robot loss while maintaining a minimally rigid structure. The effectiveness of the proposed algorithm is validated through numerical simulations. I NTRODUCTION Recent advances in multi-robot systems (MRSs), with their superior sensing, communication, and computational capabilities, allow them to perform complicated tasks otherwise impossible with only single-robot systems. MRSs have been widely adopted for numerous applications such as cooperative sensor coverage [1], search and rescue [2], and environmental monitoring [3]. In recent catastrophic wildfires in Los Angeles, drone swarms have been actively utilized for monitoring and prevention of wildfires [4]. However, as the complexity of these systems increases, the number of failure modes affecting MRS performance and safety also increases. Furthermore, the sensing [5], [6], and communication networks [7] also open up new cyberattack surfaces, network vulnerabilities, and backdoors, which adversaries can exploit to degrade and disrupt the performance of the MRS. Thus, designing control architectures ensuring the system's resiliency under these unknown failure modes becomes essential. A key application of MRSs is to cover a desired area of interest, often denoted by a density function that indicates The authors are with the School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47906.

Optimizing high-dimensional and complex black-box functions is crucial in numerous scientific applications. While Bayesian optimization (BO) is a powerful method for sample-efficient optimization, it struggles with the curse of dimensionality and scaling to thousands of evaluations. Recently, leveraging generative models to solve black-box optimization problems has emerged as a promising framework. However, those methods often underperform compared to BO methods due to limited expressivity and difficulty of uncertainty estimation in high-dimensional spaces. To overcome these issues, we introduce \textbf{DiBO}, a novel framework for solving high-dimensional black-box optimization problems. Our method iterates two stages. First, we train a diffusion model to capture the data distribution and an ensemble of proxies to predict function values with uncertainty quantification. Second, we cast the candidate selection as a posterior inference problem to balance exploration and exploitation in high-dimensional spaces. Concretely, we fine-tune diffusion models to amortize posterior inference. Extensive experiments demonstrate that our method outperforms state-of-the-art baselines across various synthetic and real-world black-box optimization tasks. Our code is publicly available \href{https://github.com/umkiyoung/DiBO}{here}

We study a ranking and selection (R&S) problem when all solutions share common parametric Bayesian input models updated with the data collected from multiple independent data-generating sources. Our objective is to identify the best system by designing a sequential sampling algorithm that collects input and simulation data given a budget. We adopt the most probable best (MPB) as the estimator of the optimum and show that its posterior probability of optimality converges to one at an exponential rate as the sampling budget increases. Assuming that the input parameters belong to a finite set, we characterize the $\epsilon$-optimal static sampling ratios for input and simulation data that maximize the convergence rate. Using these ratios as guidance, we propose the optimal sampling algorithm for R&S (OSAR) that achieves the $\epsilon$-optimal ratios almost surely in the limit. We further extend OSAR by adopting the kernel ridge regression to improve the simulation output mean prediction. This not only improves OSAR's finite-sample performance, but also lets us tackle the case where the input parameters lie in a continuous space with a strong consistency guarantee for finding the optimum. We numerically demonstrate that OSAR outperforms a state-of-the-art competitor.

Conformal Prediction is a widely studied technique to construct prediction sets of future observations. Most conformal prediction methods focus on achieving the necessary coverage guarantees, but do not provide formal guarantees on the size (volume) of the prediction sets. We first prove an impossibility of volume optimality where any distribution-free method can only find a trivial solution. We then introduce a new notion of volume optimality by restricting the prediction sets to belong to a set family (of finite VC-dimension), specifically a union of $k$-intervals. Our main contribution is an efficient distribution-free algorithm based on dynamic programming (DP) to find a union of $k$-intervals that is guaranteed for any distribution to have near-optimal volume among all unions of $k$-intervals satisfying the desired coverage property. By adopting the framework of distributional conformal prediction (Chernozhukov et al., 2021), the new DP based conformity score can also be applied to achieve approximate conditional coverage and conditional restricted volume optimality, as long as a reasonable estimator of the conditional CDF is available. While the theoretical results already establish volume-optimality guarantees, they are complemented by experiments that demonstrate that our method can significantly outperform existing methods in many settings.

Analyzing imaging and hyperspectral data is crucial across scientific fields, including biology, medicine, chemistry, and physics. The primary goal is to transform high-resolution or high-dimensional data into an interpretable format to generate actionable insights, aiding decision-making and advancing knowledge. Currently, this task relies on complex, human-designed workflows comprising iterative steps such as denoising, spatial sampling, keypoint detection, feature generation, clustering, dimensionality reduction, and physics-based deconvolutions. The introduction of machine learning over the past decade has accelerated tasks like image segmentation and object detection via supervised learning, and dimensionality reduction via unsupervised methods. However, both classical and NN-based approaches still require human input, whether for hyperparameter tuning, data labeling, or both. The growing use of automated imaging tools, from atomically resolved imaging to biological applications, demands unsupervised methods that optimize data representation for human decision-making or autonomous experimentation. Here, we discuss advances in reward-based workflows, which adopt expert decision-making principles and demonstrate strong transfer learning across diverse tasks. We represent image analysis as a decision-making process over possible operations and identify desiderata and their mappings to classical decision-making frameworks. Reward-driven workflows enable a shift from supervised, black-box models sensitive to distribution shifts to explainable, unsupervised, and robust optimization in image analysis. They can function as wrappers over classical and DCNN-based methods, making them applicable to both unsupervised and supervised workflows (e.g., classification, regression for structure-property mapping) across imaging and hyperspectral data.

Asteroid shape inversion using photometric data has been a key area of study in planetary science and astronomical research.However, the current methods for asteroid shape inversion require extensive iterative calculations, making the process time-consuming and prone to becoming stuck in local optima. We directly established a mapping between photometric data and shape distribution through deep neural networks. In addition, we used 3D point clouds to represent asteroid shapes and utilized the deviation between the light curves of non-convex asteroids and their convex hulls to predict the concave areas of non-convex asteroids. We compared the results of different shape models using the Chamfer distance between traditional methods and ours and found that our method performs better, especially when handling special shapes. For the detection of concave areas on the convex hull, the intersection over union (IoU) of our predictions reached 0.89. We further validated this method using observational data from the Lowell Observatory to predict the convex shapes of the asteroids 3337 Milo and 1289 Kuta, and conducted light curve fitting experiments. The experimental results demonstrated the robustness and adaptability of the method

Gaussian process (GP) regression is a popular surrogate modeling tool for computer simulations in engineering and scientific domains. However, it often struggles with high computational costs and low prediction accuracy when the simulation involves too many input variables. For some simulation models, the outputs may only be significantly influenced by a small subset of the input variables, referred to as the ``active variables''. We propose an optimal kernel learning approach to identify these active variables, thereby overcoming GP model limitations and enhancing system understanding. Our method approximates the original GP model's covariance function through a convex combination of kernel functions, each utilizing low-dimensional subsets of input variables. Inspired by the Fedorov-Wynn algorithm from optimal design literature, we develop an optimal kernel learning algorithm to determine this approximation. We incorporate the effect heredity principle, a concept borrowed from the field of ``design and analysis of experiments'', to ensure sparsity in active variable selection. Through several examples, we demonstrate that the proposed method outperforms alternative approaches in correctly identifying active input variables and improving prediction accuracy. It is an effective solution for interpreting the surrogate GP regression and simplifying the complex underlying system.