Summary: Estimating the robot state within a known map is an essential problem for mobile robot; it is also referred to “localization”. Even LiDAR-based localization is practical in many applications, it is difficult to achieve global localization with LiDAR only for its low-dimension feedback, especially in environments with repetitive geometric features. A sensor-fusion-based localization system is introduced in this paper, which has the capability of addressing the global localization problem. Both LiDAR and vision sensors are integrated, making use of the rich information introduced by vision sensor and the robustness from LiDAR. A hybrid grid-map is built for global localization, and a visual global descriptor is applied to speed up the localization convergence, combined with a pose refining pipeline for improving the localization accuracy. Also, a trigger mechanism is introduced to solve kidnapped problem and verify the relocalization result. The experiments under different conditions are designed to evaluate the performance of the proposed approach, as well as a comparison with the existing localization systems. According to the experimental results, our system is able to solve the global localization problem, and the sensor-fusion mechanism in our system has an improved performance.

This article aims to extend the theory of Lie subgroups and symmetric subspaces for studying an important class of submanifolds of the special Euclidean group $\text{SE}(3)$ whose tangent space at each point on the submanifold relates to that at the identity by an adjoint map. These submanifolds, which we call adjoint-invariant submanifolds in this article, are known in the literature as persistent submanifolds, since they are strictly related to the concept of persistent screw systems. The difference is that in this article, just as Lie subgroups and symmetric subspaces, we put forward adjoint-invariant submanifolds as independent geometric objects from mechanisms and their associated local screw systems. Adjoint invariance relaxes the strict left and right invariance of Lie subgroups and the reflective invariance of symmetric subspaces by allowing generic moving reference frame in the aforementioned adjoint map. It turns out such adjoint invariance can be studied under the framework of distributions on manifolds, which allows us to explore global geometric properties of adjoint-invariant submanifolds. We classify adjoint-invariant submanifolds into reflective-type and product-type submanifolds and derive the conditions for their adjoint invariance. We then propose geometric methods and algorithms for synthesizing the kinematic generators for reflective-type submanifolds, as demonstrated with a number of examples.

This paper investigates the motion planning problem of planar m-link ( $m \geq 4$ ) closed chains among point obstacles with extension to arbitrary convex 2-D obstacles. The configuration space (C-space) of closed chains is embedded into two copies of m-3 dimensional tori. Two structural sets, the C-boundaries and the C-obstacles, are analyzed based upon the C-spaces of recursively constructed lower-dimensional closed chains. They contain essential structural information about the connectivity of the collision-free portion (C-free) of the C-space. By approximating each workspace obstacle by a set of points on the boundary after dilation, its corresponding C-obstacle is guaranteed to be covered by the C-obstacle of the convex hull of the point set. This permits a resolution-complete roadmap algorithm that puts specific bias for sampling the structural sets. Several benchmark examples are presented that compare the performance between our algorithm and the traditional algorithms. Animation videos and source codes are also provided which demonstrate the effectiveness of our method for closed chains of up to 20 links.

Narrow passages in free space pose great challenges to many sampling-based motion planners. In problems with high-dimensional configuration spaces (C-spaces), narrow passages in free space (C-free) can be hard to find and navigate and, sometimes, even counterintuitive. In this article, we present an algorithm to construct cones of available instantaneous velocities (“free velocity cones” or, briefly, “free cones”) on the boundary of C-free to facilitate finding and navigating narrow passages. This is accomplished by first developing free cones and associated measures of local C-space narrowness for a single rigid link. These results are then extended to kinematic chains (open and closed) of arbitrary degrees of freedom. It turns out that the degeneracy of the free cones dictates the existence of C-space narrow passages, and the locations and orientations of the links in the workspace relate intimately to the corresponding connected component of C-free. This observation leads us to a modified probabilistic roadmap (M-PRM) algorithm and a modified rapidly exploring random vine (M-RRV) algorithm of combining the enumeration of topological components and random sampling of the free cones. Experimental results from applying our algorithms to several challenging examples show that our new algorithms are more efficient than some variants of the PRM algorithms, and several variants of the rapidly exploring random tree (RRT) algorithms, such as RRT-CONNECT and RRV.

This paper aims to analyze and compare the performances of several representative machine (deep) learning algorithms in global climate forecasting. We choose the benchmark problem that predicts the distribution of average temperatures along the globe in the near future given historical records. Notice the similarity between a graph of the spatial temperatures and a 2D image, many deep neural network models, originally targeted for image classification, can now be adopted to learn the models for global temperature forecasting. We also examine batch optimization techniques to reduce the uncertainties of these algorithms due to their inherent drawbacks such as overfitting. Experiments are carried out that compare the accuracies and mean bias of these three models in predicting the average temperature between 2015 and 2017. These experimental results demonstrate the advantages and disadvantages of each individual deep learning model, providing insights into further research in global climate forecasting.