In order to expand the polynomial surface fitting in 3D dimensional space into the high dimensional feature space using a neural network with parameter Θ, we define f1(gω):= g and f2(cυ):= c, where f means MLP layer. Then, the multiplication of real numbers gω cυ in the polynomial function is represented as g c, i.e., gω cυ:= g c, and the orders ω,υ [0,1,...,τ]. Then, the final bivariate function used in our hyper surface fitting is Nθ,τ(G,C) = Θ(G C), where Gand C are high dimensional features of the 3D point clouds extracted by the two different modules, which are introduced in Sec.3.3 and Sec.3.4 of the paper, respectively. The other terms except the principal terms in the polynomial equation are not used in the estimation of the normal. Based on this, we use the max-pooling over all features from the hyper surface fitting 2 Figure 1: Visualization of the contribution of each 3D point to estimate the normal of the query point (black).

However, fitting surfaces explicitly from raw point clouds suffers from overfitting or underfitting issues caused by inappropriatepolynomial orders andoutliers, which significantly limits theperformance of existing methods.

Automating bone micro-milling using a robotic system presents challenges due to the uncertainties in both the external and internal features of bone tissue. For example, during a mouse cranial window creation, a circular path with a radius of 2 to 4 mm needs to be milled on the mouse skull using a microdrill. The uneven surface and non-uniform thickness of the mouse skull make it difficult to fully automate this process, requiring the system to possess advanced perceptual and adaptive capabilities. In this study, we propose an automatic calibration and 3D surface fitting method and integrate it into an autonomous robotic bone micro-milling system, enabling it to quickly, in real-time, and accurately perceive and adapt to the uneven surface and non-uniform thickness of the target without human assistance. Validation experiments on euthanized mice demonstrate that the improved system achieves a success rate of 85.7 % and an average milling time of 2.1 minutes, showing not only significant performance improvements over the previous system but also exceptional accuracy, speed, and stability compared to human operators.

In computational fluid dynamics, it often takes days or weeks to simulate the aerodynamic behavior of designs such as jets, spacecraft, or gas turbine engines. One of the biggest open problems in the field is how to simulate such systems much more quickly with sufficient accuracy. Many approaches have been tried; some involve models of the underlying physics, while others are model-free and make predictions based only on existing simulation data. However, all previous approaches have severe shortcomings or limitations. We present a novel approach: we reformulate the prediction problem to effectively increase the size of the otherwise tiny datasets, and we introduce a new neural network architecture (called a cluster network) with an inductive bias well-suited to fluid dynamics problems. Compared to state-of-the-art model-based approximations, we show that our approach is nearly as accurate, an order of magnitude faster and vastly easier to apply. Moreover, our method outperforms previous model-free approaches.

Abstract-- Customized grippers have specifically designed fingers to increase the contact area with the workpieces and improve the grasp robustness. However, grasp planning for customized grippers is challenging due to the object variations, surface contacts and structural constraints of the grippers. In this paper, we propose a learning framework to plan robust grasps for customized grippers in real-time. The learning framework contains a low-level optimization-based planner to search for optimal grasps locally under object shape variations, and a high-level learning-based explorer to learn the grasp exploration based on previous grasp experience. The optimization-based planner uses an iterative surface fitting (ISF) to simultaneously search for optimal gripper transformation and finger displacement by minimizing the surface fitting error. The high-level learning-based explorer trains a regionbased convolutional neural network (R-CNN) to propose good optimization regions, which avoids ISF getting stuck in bad local optima and improves the collision avoidance performance. The proposed learning framework with RCNN-ISF is able to consider the structural constraints of the gripper, learn grasp exploration strategy from previous experience, and plan optimal grasps in clutter environment in real-time. The effectiveness of the algorithm is verified by experiments. Customized grippers have been broadly applied in industry to execute complex tasks such as assembly and packaging.