The classical formulation of PCA, dating back to Carl F. Gauss, is based on minimizing the sum of

Wheeled bipedal robots have garnered increasing attention in exploration and inspection. However, most research simplifies calculations by ignoring leg dynamics, thereby restricting the robot's full motion potential. Additionally, robots face challenges when traversing uneven terrain. To address the aforementioned issue, we develop a complete dynamics model and design a whole-body control framework with terrain estimation for a novel 6 degrees of freedom wheeled bipedal robot. This model incorporates the closed-loop dynamics of the robot and a ground contact model based on the estimated ground normal vector. We use a LiDAR inertial odometry framework and improved Principal Component Analysis for terrain estimation. Task controllers, including PD control law and LQR, are employed for pose control and centroidal dynamics-based balance control, respectively. Furthermore, a hierarchical optimization approach is used to solve the whole-body control problem. We validate the performance of the terrain estimation algorithm and demonstrate the algorithm's robustness and ability to traverse uneven terrain through both simulation and real-world experiments.

Despite years of research, real-time diverse grasp synthesis for dexterous hands remains an unsolved core challenge in robotics and computer graphics. We present Lightning Grasp, a novel high-performance procedural grasp synthesis algorithm that achieves orders-of-magnitude speedups over state-of-the-art approaches, while enabling unsupervised grasp generation for irregular, tool-like objects. The method avoids many limitations of prior approaches, such as the need for carefully tuned energy functions and sensitive initialization. This breakthrough is driven by a key insight: decoupling complex geometric computation from the search process via a simple, efficient data structure - the Contact Field. This abstraction collapses the problem complexity, enabling a procedural search at unprecedented speeds. We open-source our system to propel further innovation in robotic manipulation.

Recent studies in 3D object detection for autonomous vehicles aim to enrich features through the utilization of multi-modal setups or the extraction of local patterns within LiDAR point clouds. However, multi-modal methods face significant challenges in feature alignment, and gaining features locally can be oversimplified for complex 3D object detection tasks. In this paper, we propose a novel model, NV3D, which utilizes local features acquired from voxel neighbors, as normal vectors computed per voxel basis using K-nearest neighbors (KNN) and principal component analysis (PCA). This informative feature enables NV3D to determine the relationship between the surface and pertinent target entities, including cars, pedestrians, or cyclists. During the normal vector extraction process, NV3D offers two distinct sampling strategies: normal vector density-based sampling and FOV-aware bin-based sampling, allowing elimination of up to 55% of data while maintaining performance. In addition, we applied element-wise attention fusion, which accepts voxel features as the query and value and normal vector features as the key, similar to the attention mechanism. Our method is trained on the KITTI dataset and has demonstrated superior performance in car and cyclist detection owing to their spatial shapes. In the validation set, NV3D without sampling achieves 86.60% and 80.18% mean Average Precision (mAP), greater than the baseline Voxel R-CNN by 2.61% and 4.23% mAP, respectively. With both samplings, NV3D achieves 85.54% mAP in car detection, exceeding the baseline by 1.56% mAP, despite roughly 55% of voxels being filtered out.