Motivated by the latest research on feasible space monitoring of multiple control barrier functions (CBFs) as well as polytopic collision avoidance, this paper studies the Polytope Volume Monitoring (PVM) problem, whose goal is to design a control law for inputs of nonlinear systems to prevent the volume of some state-dependent polytope from decreasing to zero. Recent studies have explored the idea of applying Chebyshev ball method in optimization theory to solve the case study of PVM; however, the underlying difficulties caused by nonsmoothness have not been addressed. This paper continues the study on this topic, where our main contribution is to establish the relationship between nonsmooth CBF and parametric optimization theory through directional derivatives for the first time, so as to solve PVM problems more conveniently. In detail, inspired by Chebyshev ball approach, a parametric linear program (PLP) based nonsmooth barrier function candidate is established for PVM, and then, sufficient conditions for it to be a nonsmooth CBF are proposed, based on which a quadratic program (QP) based safety filter with guaranteed feasibility is proposed to address PVM problems. Finally, a numerical simulation example is given to show the efficiency of the proposed safety filter.

The low-level spatial detail information and high-level semantic abstract information are both essential to the semantic segmentation task. The features extracted by the deep network can obtain rich semantic information, while a lot of spatial information is lost. However, how to recover spatial detail information effectively and fuse it with high-level semantics has not been well addressed so far. In this paper, we propose a new architecture based on Bilateral Segmentation Network (BiseNet) called Multi-scale Covariance Feature Fusion Network (MCFNet). Specifically, this network introduces a new feature refinement module and a new feature fusion module. Furthermore, a gating unit named L-Gate is proposed to filter out invalid information and fuse multi-scale features. We evaluate our proposed model on Cityscapes, CamVid datasets and compare it with the state-of-the-art methods. Extensive experiments show that our method achieves competitive success. On Cityscapes, we achieve 75.5% mIOU with a speed of 151.3 FPS.

PyPose is an open-source library for robot learning. It combines a learning-based approach with physics-based optimization, which enables seamless end-to-end robot learning. It has been used in many tasks due to its meticulously designed application programming interface (API) and efficient implementation. From its initial launch in early 2022, PyPose has experienced significant enhancements, incorporating a wide variety of new features into its platform. To satisfy the growing demand for understanding and utilizing the library and reduce the learning curve of new users, we present the fundamental design principle of the imperative programming interface, and showcase the flexible usage of diverse functionalities and modules using an extremely simple Dubins car example. We also demonstrate that the PyPose can be easily used to navigate a real quadruped robot with a few lines of code.