Although 3D Gaussian Splatting has been widely studied because of its realistic and efficient novel-view synthesis, it is still challenging to extract a high-quality surface from the point-based representation. Previous works improve the surface by incorporating geometric priors from the off-the-shelf normal estimator. However, there are two main limitations: 1) Supervising normal rendered from 3D Gaussians updates only the rotation parameter while neglecting other geometric parameters; 2) The inconsistency of predicted normal maps across multiple views may lead to severe reconstruction artifacts. In this paper, we propose a Depth-Normal regularizer that directly couples normal with other geometric parameters, leading to full updates of the geometric parameters from normal regularization. We further propose a confidence term to mitigate inconsistencies of normal predictions across multiple views. Moreover, we also introduce a densification and splitting strategy to regularize the size and distribution of 3D Gaussians for more accurate surface modeling. Compared with Gaussian-based baselines, experiments show that our approach obtains better reconstruction quality and maintains competitive appearance quality at faster training speed and 100+ FPS rendering. Our code will be made open-source upon paper acceptance.

Sphere packing, Hilbert's eighteenth problem, asks for the densest arrangement of congruent spheres in n-dimensional Euclidean space. Although relevant to areas such as cryptography, crystallography, and medical imaging, the problem remains unresolved: beyond a few special dimensions, neither optimal packings nor tight upper bounds are known. Even a major breakthrough in dimension $n=8$, later recognised with a Fields Medal, underscores its difficulty. A leading technique for upper bounds, the three-point method, reduces the problem to solving large, high-precision semidefinite programs (SDPs). Because each candidate SDP may take days to evaluate, standard data-intensive AI approaches are infeasible. We address this challenge by formulating SDP construction as a sequential decision process, the SDP game, in which a policy assembles SDP formulations from a set of admissible components. Using a sample-efficient model-based framework that combines Bayesian optimisation with Monte Carlo Tree Search, we obtain new state-of-the-art upper bounds in dimensions $4-16$, showing that model-based search can advance computational progress in longstanding geometric problems. Together, these results demonstrate that sample-efficient, model-based search can make tangible progress on mathematically rigid, evaluation limited problems, pointing towards a complementary direction for AI-assisted discovery beyond large-scale LLM-driven exploration.

The design of the humanoid ankle is critical for safe and efficient ground interaction. Key factors such as mechanical compliance and motor mass distribution have driven the adoption of parallel mechanism architectures. However, selecting the optimal configuration depends on both actuator availability and task requirements. We propose a unified methodology for the design and evaluation of parallel ankle mechanisms. A multi-objective optimization synthesizes the mechanism geometry, the resulting solutions are evaluated using a scalar cost function that aggregates key performance metrics for cross-architecture comparison. We focus on two representative architectures: the Spherical-Prismatic-Universal (SPU) and the Revolute-Spherical-Universal (RSU). For both, we resolve the kinematics, and for the RSU, introduce a parameterization that ensures workspace feasibility and accelerates optimization. We validate our approach by redesigning the ankle of an existing humanoid robot. The optimized RSU consistently outperforms both the original serial design and a conventionally engineered RSU, reducing the cost function by up to 41% and 14%, respectively.

The microphysical properties of ice crystals are important because they significantly alter the radiative properties and spatiotemporal distributions of clouds, which in turn strongly affect Earth's climate. However, it is challenging to measure key properties of ice crystals, such as mass or morphological features. Here, we present a framework for predicting three-dimensional (3D) microphysical properties of ice crystals from in situ two-dimensional (2D) imagery. First, we computationally generate synthetic ice crystals using 3D modeling software along with geometric parameters estimated from the 2021 Ice Cryo-Encapsulation Balloon (ICEBall) field campaign. Then, we use synthetic crystals to train machine learning (ML) models to predict effective density ($ρ_{e}$), effective surface area ($A_e$), and number of bullets ($N_b$) from synthetic rosette imagery. When tested on unseen synthetic images, we find that our ML models can predict microphysical properties with high accuracy. For $ρ_{e}$ and $A_e$, respectively, our best-performing single view models achieved $R^2$ values of 0.99 and 0.98. For $N_b$, our best single view model achieved a balanced accuracy and F1 score of 0.91. We also quantify the marginal prediction improvements from incorporating a second view. A stereo view ResNet-18 model reduced RMSE by 40% for both $ρ_e$ and $A_e$, relative to a single view ResNet-18 model. For $N_b$, we find that a stereo view ResNet-18 model improved the F1 score by 8%. This work provides a novel ML-driven framework for estimating ice microphysical properties from in situ imagery, which will allow for downstream constraints on microphysical parameterizations, such as the mass-size relationship.

Whole-body geometric calibration of humanoid robots using classical robot calibration methods is a timeconsuming and experimentally burdensome task. However, despite its significance for accurate control and simulation, it is often overlooked in the humanoid robotics community. To address this issue, we propose a novel practical method that utilizes a single plane, embedded force sensors, and an admittance controller to calibrate the whole-body kinematics of humanoids without requiring manual intervention. Given the complexity of humanoid robots, it is crucial to generate and determine a minimal set of optimal calibration postures. To do so, we propose a new algorithm called IROC (Information Ranking algorithm for selecting Optimal Calibration postures). IROC requires a pool of feasible candidate postures to build a normalized weighted information matrix for each posture. Then, contrary to other algorithms from the literature, IROC will determine the minimal number of optimal postures that are to be played onto a robot for its calibration. Both IROC and the single-plane calibration method were experimentally validated on a TALOS humanoid robot. The total whole-body kinematics chain was calibrated using solely 31 optimal postures with 3-point contacts on a table by the robot gripper. In a cross-validation experiment, the average root-mean-square (RMS) error was reduced by a factor of 2.3 compared to the manufacturer's model.

Although 3D Gaussian Splatting has been widely studied because of its realistic and efficient novel-view synthesis, it is still challenging to extract a high-quality surface from the point-based representation. Previous works improve the surface by incorporating geometric priors from the off-the-shelf normal estimator. However, there are two main limitations: 1) Supervising normal rendered from 3D Gaussians updates only the rotation parameter while neglecting other geometric parameters; 2) The inconsistency of predicted normal maps across multiple views may lead to severe reconstruction artifacts. In this paper, we propose a Depth-Normal regularizer that directly couples normal with other geometric parameters, leading to full updates of the geometric parameters from normal regularization. We further propose a confidence term to mitigate inconsistencies of normal predictions across multiple views.

Sim-to-real transfer remains a significant challenge in soft robotics due to the unpredictability introduced by common manufacturing processes such as 3D printing and molding. These processes often result in deviations from simulated designs, requiring multiple prototypes before achieving a functional system. In this study, we propose a novel methodology to address these limitations by combining advanced rapid prototyping techniques and an efficient optimization strategy. Firstly, we employ rapid prototyping methods typically used for rigid structures, leveraging their precision to fabricate compliant components with reduced manufacturing errors. Secondly, our optimization framework minimizes the need for extensive prototyping, significantly reducing the iterative design process. The methodology enables the identification of stiffness parameters that are more practical and achievable within current manufacturing capabilities. The proposed approach demonstrates a substantial improvement in the efficiency of prototype development while maintaining the desired performance characteristics. This work represents a step forward in bridging the sim-to-real gap in soft robotics, paving the way towards a faster and more reliable deployment of soft robotic systems.

A main challenge in mechanical design is to efficiently explore the design space while satisfying engineering constraints. This work explores the use of 3D generative models to explore the design space in the context of vehicle development, while estimating and enforcing engineering constraints. Specifically, we generate diverse 3D models of cars that meet a given set of geometric specifications, while also obtaining quick estimates of performance parameters such as aerodynamic drag. For this, we employ a data-driven approach (using the ShapeNet dataset) to train VehicleSDF, a DeepSDF based model that represents potential designs in a latent space witch can be decoded into a 3D model. We then train surrogate models to estimate engineering parameters from this latent space representation, enabling us to efficiently optimize latent vectors to match specifications. Our experiments show that we can generate diverse 3D models while matching the specified geometric parameters. Finally, we demonstrate that other performance parameters such as aerodynamic drag can be estimated in a differentiable pipeline.

From serving a cup of coffee to carefully rearranging delicate items, stable object placement is a crucial skill for future robots. This skill is challenging due to the required accuracy, which is difficult to achieve under geometric uncertainty. We leverage differentiable contact dynamics to develop a principled method for stable object placement under geometric uncertainty. We estimate the geometric uncertainty by minimizing the discrepancy between the force-torque sensor readings and the model predictions through gradient descent. We further keep track of a belief over multiple possible geometric parameters to mitigate the gradient-based method's sensitivity to the initialization. We verify our approach in the real world on various geometric uncertainties, including the in-hand pose uncertainty of the grasped object, the object's shape uncertainty, and the environment's shape uncertainty.

When objects are packed in a cluster, physical interactions are unavoidable. Such interactions emerge because of the objects geometric features; some of these features promote entanglement, while others create repulsion. When entanglement occurs, the cluster exhibits a global, complex behaviour, which arises from the stochastic interactions between objects. We hereby refer to such a cluster as an entangled granular metamaterial. We investigate the geometrical features of the objects which make up the cluster, henceforth referred to as grains, that maximise entanglement. We hypothesise that a cluster composed from grains with high propensity to tangle, will also show propensity to interact with a second cluster of tangled objects. To demonstrate this, we use the entangled granular metamaterials to perform complex robotic picking tasks, where conventional grippers struggle. We employ an electromagnet to attract the metamaterial (ferromagnetic) and drop it onto a second cluster of objects (targets, non-ferromagnetic). When the electromagnet is re-activated, the entanglement ensures that both the metamaterial and the targets are picked, with varying degrees of physical engagement that strongly depend on geometric features. Interestingly, although the metamaterials structural arrangement is random, it creates repeatable and consistent interactions with a second tangled media, enabling robust picking of the latter.