arXiv subjects

Yijun Yuan

Publications and source records attributed to Yijun Yuan.

31 records · Page 2Linked to original sources

arXiv2023

Truncated expansion of $ζ_{p^n}$ in the $p$-adic Mal'cev-Neumann field

Fix an odd prime $p$. In this article, we provide a $\mathrm{mod}\ p$ harmonic number identity, which appears naturally in the canonical expansion of a root $ζ_{p^n}$ of the $p^n$-th cyclotomic polynomial $Φ_{p^n}(T)$ in the $p$-adic Mal'cev-Neumann field $\mathbb{L}_p$. We establish a $\frac{2}{(p-1)p^{n-2}}$-truncated expansion of $ζ_{p^n}$ via a variant of the transfinite Newton algorithm, which gives the first $\aleph_0^2$ terms of the canonical expansion of $ζ_{p^n}$. The harmonic number identity simplifies the expression of this expansion.

math.NT↗

arXiv2022

An Algorithm for the SE(3)-Transformation on Neural Implicit Maps for Remapping Functions

Implicit representations are widely used for object reconstruction due to their efficiency and flexibility. In 2021, a novel structure named neural implicit map has been invented for incremental reconstruction. A neural implicit map alleviates the problem of inefficient memory cost of previous online 3D dense reconstruction while producing better quality. % However, the neural implicit map suffers the limitation that it does not support remapping as the frames of scans are encoded into a deep prior after generating the neural implicit map. This means, that neither this generation process is invertible, nor a deep prior is transformable. The non-remappable property makes it not possible to apply loop-closure techniques. % We present a neural implicit map based transformation algorithm to fill this gap. As our neural implicit map is transformable, our model supports remapping for this special map of latent features. % Experiments show that our remapping module is capable to well-transform neural implicit maps to new poses. Embedded into a SLAM framework, our mapping model is able to tackle the remapping of loop closures and demonstrates high-quality surface reconstruction. % Our implementation is available at github\footnote{\url{https://github.com/Jarrome/IMT_Mapping}} for the research community.

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arXiv2022

Indirect Point Cloud Registration: Aligning Distance Fields using a Pseudo Third Point Ses

In recent years, implicit functions have drawn attention in the field of 3D reconstruction and have successfully been applied with Deep Learning. However, for incremental reconstruction, implicit function-based registrations have been rarely explored. Inspired by the high precision of deep learning global feature registration, we propose to combine this with distance fields. We generalize the algorithm to a non-Deep Learning setting while retaining the accuracy. Our algorithm is more accurate than conventional models while, without any training, it achieves a competitive performance and faster speed, compared to Deep Learning-based registration models. The implementation is available on github for the research community.

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arXiv2021

Uniformizer of the False Tate Curve Extension of $\mathbb{Q}_p$

Let $p\geq 3$ be a prime number. In this article, we study the canonical expansion of the primitive $p^n$-th root of unity $ζ_{p^n}$ in $p$-adic Mal'cev-Neumann field $\mathbb{L}_p$ for $n\geq 1$. More precisely, we give the explicit formula for the first $\aleph_0$ terms of the expansion of $ζ_{p^n}$ and as an application, we use it to construct a uniformizer of $K_{2,m}=\mathbb{Q}_p\left(ζ_{p^2},p^{1/p^m}\right)$ with $m\geq 1$.

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arXiv2020

Improved Visual-Inertial Localization for Low-cost Rescue Robots

This paper improves visual-inertial systems to boost the localization accuracy for low-cost rescue robots. When robots traverse on rugged terrain, the performance of pose estimation suffers from big noise on the measurements of the inertial sensors due to ground contact forces, especially for low-cost sensors. Therefore, we propose \textit{Threshold}-based and \textit{Dynamic Time Warping}-based methods to detect abnormal measurements and mitigate such faults. The two methods are embedded into the popular VINS-Mono system to evaluate their performance. Experiments are performed on simulation and real robot data, which show that both methods increase the pose estimation accuracy. Moreover, the \textit{Threshold}-based method performs better when the noise is small and the \textit{Dynamic Time Warping}-based one shows greater potential on large noise.

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arXiv2020

Non-iterative One-step Solution for Point Set Registration Problem on Pose Estimation without Correspondence

In this work, we propose to directly find the one-step solution for the point set registration problem without correspondences. Inspired by the Kernel Correlation method, we consider the fully connected objective function between two point sets, thus avoiding the computation of correspondences. By utilizing least square minimization, the transformed objective function is directly solved with existing well-known closed-form solutions, e.g., singular value decomposition, that is usually used for given correspondences. However, using equal weights of costs for each connection will degenerate the solution due to the large influence of distant pairs. Thus, we additionally set a scale on each term to avoid high costs on non-important pairs. As in feature-based registration methods, the similarity between descriptors of points determines the scaling weight. Given the weights, we get a one step solution. As the runtime is in $\mathcal O (n^2)$, we also propose a variant with keypoints that strongly reduces the cost. The experiments show that the proposed method gives a one-step solution without an initial guess. Our method exhibits competitive outlier robustness and accuracy, compared to various other methods, and it is more stable in case of large rotations. Additionally, our one-step solution achieves a performance on-par with the state-of-the-art feature based method TEASER.

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arXiv2020

Configuration-Space Flipper Planning on 3D Terrain

Flippers are essential components of tracked robot locomotion systems for unstructured terrain, especially within a rescue scenario. Achieving full and semi-autonomy for such rescue robots is the goal of many research efforts. In this work, we propose an algorithm to plan the morphologies of a small rescue robot with four flippers over 3D ground without any extra sensor, such as pressure sensor. To achieve the goal, we simplify the rescue robot as a skeleton on inflated terrain. Its morphology can be represented by configurations of several parameters. Then we plan the mobile movement on 3D terrain with four individually manipulated flippers. We perform real robot experiments on three different obstacles. The results show that we move the flippers very effectively and are thus able to tackle those terrains very well.

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arXiv2020

Self-supervised Point Set Local Descriptors for Point Cloud Registration

In this work, we propose to learn local descriptors for point clouds in a self-supervised manner. In each iteration of the training, the input of the network is merely one unlabeled point cloud. On top of our previous work, that directly solves the transformation between two point sets in one step without correspondences, the proposed method is able to train from one point cloud, by supervising its self-rotation, that we randomly generate. The whole training requires no manual annotation. In several experiments we evaluate the performance of our method on various datasets and compare to other state of the art algorithms. The results show, that our self-supervised learned descriptor achieves equivalent or even better performance than the supervised learned model, while being easier to train and not requiring labeled data.

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arXiv2019

Area Graph: Generation of Topological Maps using the Voronoi Diagram

Representing a scanned map of the real environment as a topological structure is an important research topic in robotics. Since topological representations of maps save a huge amount of map storage space and online computing time, they are widely used in fields such as path planning, map matching, and semantic mapping. We use a topological map representation, the Area Graph, in which the vertices represent areas and edges represent passages. The Area Graph is developed from a pruned Voronoi Graph, the Topology Graph. We also employ a simple room detection algorithm to compensate the fact that the Voronoi Graph gets unstable in open areas. We claim that our area segmentation method is superior to state-of-the-art approaches in complex indoor environments and support this claim with a number of experiments.

cs.RO↗

arXiv2019

Incrementally Building Topology Graphs via Distance Maps

Mapping is an essential task for mobile robots and topological representation often works as a basis for the various applications. In this paper, a novel framework that can build topological maps incrementally is proposed. The algorithm is using a distance map, and in our framework the topological map can grow as we append more sensor data to the map. To demonstrate our algorithm, we show the result of the distance map based method on several popular maps and run the incremental framework with raw sensor data to have a growing topological map, as an example of a robot exploring the environment.

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arXiv2019

Configuration-Space Flipper Planning for Rescue Robots

For rescue robots, flipper endows the robot with additional ability to pass through various terrain. Autonomous motion becomes more important. In recent work autonomy is done by either planning with several special states or based on collected data. We are considering if it is possible to find a way to build continues states without collecting old trail data. In this paper, we first model the possible states as a global planning path with parameter configuration of the scene. Then, we follows the path to achieve the autonomous run. We plot the morphology of each path points to show the correctness of the path and implement a simple path following on real robot to demonstrate the performance of our algorithm.

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arXiv2018

Fast Gaussian Process Occupancy Maps

In this paper, we demonstrate our work on Gaussian Process Occupancy Mapping (GPOM). We concentrate on the inefficiency of the frame computation of the classical GPOM approaches. In robotics, most of the algorithms are required to run in real time. However, the high cost of computation makes the classical GPOM less useful. In this paper we dont try to optimize the Gaussian Process itself, instead, we focus on the application. By analyzing the time cost of each step of the algorithm, we find a way that to reduce the cost while maintaining a good performance compared to the general GPOM framework. From our experiments, we can find that our model enables GPOM to run online and achieve a relatively better quality than the classical GPOM.

cs.RO↗

arXiv2018

Topological Area Graph Generation and its Application to Path Planning

Representing a scanned map of the real environment as a topological structure is an important research in robotics. %is currently an important research. Since topological representations of maps save a huge amount of map storage space and online computing time, they are widely used in fields such as path planning, map matching, and semantic mapping. We propose a novel topological map representation, the Area Graph, in which the vertices represent areas and edges represent passages. The Area Graph is developed from a pruned Voronoi Graph, the Topology Graph. The paper also presents path planning as one application for the Area Graph. For that, we derive a so-called Passage Graph from the Area Graph. Because our algorithm segments the map as a set of areas, the first experiment compares the results of the Area Graph with that of state-of-the-art segmentation approaches, which proved that our method effectively prevented over-segmentation. Then the second experiment shows the superiority of our method over the traditional A* planning algorithm.

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