Bo Fu

Weijun Chen, Bo Fu, Yuxi Fu et al.

A VASS can be viewed as a finite-state automaton manipulating a fixed number (called its dimension) of counters holding non-negative values. The reachability problem, asking whether there is a run from one configuration, defined by a state and values of the counters, to another configuration, has been a long-standing algorithmic challenge in theoretical computer science. When the dimension is part of the input, the problem has been shown to be ACKERMANN-complete in 2021. For fixed dimension greater than 2, and in particular for dimension 3, the exact complexity of the reachability problem remains unclear. For a long time the known algorithms for the 3-dimensional VASS reachability problem had been non-elementary, while the best known lower bound is merely PSPACE hardness inherited from dimension 2. A recent breakthrough in (Czerwiński, Jecker, Lasota, Orlikowski, ICALP 2025) gave the first elementary upper bound for the problem, namely 2-EXPSPACE. In this paper it is shown that the reachability problem in 3-VASS belongs to EXPSPACE. The proof is based on a hierarchical pumpability analysis, yielding a doubly-exponential length bound on the shortest runs between two configurations.

Yanmei Jiao, Lilu Liu, Bo Fu et al.

Visual localization for planar moving robot is important to various indoor service robotic applications. To handle the textureless areas and frequent human activities in indoor environments, a novel robust visual localization algorithm which leverages dense correspondence and sparse depth for planar moving robot is proposed. The key component is a minimal solution which computes the absolute camera pose with one 3D-2D correspondence and one 2D-2D correspondence. The advantages are obvious in two aspects. First, the robustness is enhanced as the sample set for pose estimation is maximal by utilizing all correspondences with or without depth. Second, no extra effort for dense map construction is required to exploit dense correspondences for handling textureless and repetitive texture scenes. That is meaningful as building a dense map is computational expensive especially in large scale. Moreover, a probabilistic analysis among different solutions is presented and an automatic solution selection mechanism is designed to maximize the success rate by selecting appropriate solutions in different environmental characteristics. Finally, a complete visual localization pipeline considering situations from the perspective of correspondence and depth density is summarized and validated on both simulation and public real-world indoor localization dataset. The code is released on github.

Yanmei Jiao, Yue Wang, Bo Fu et al.

Map based visual inertial localization is a crucial step to reduce the drift in state estimation of mobile robots. The underlying problem for localization is to estimate the pose from a set of 3D-2D feature correspondences, of which the main challenge is the presence of outliers, especially in changing environment. In this paper, we propose a robust solution based on efficient global optimization of the consensus maximization problem, which is insensitive to high percentage of outliers. We first introduce translation invariant measurements (TIMs) for both points and lines to decouple the consensus maximization problem into rotation and translation subproblems, allowing for a two-stage solver with reduced solution dimensions. Then we show that (i) the rotation can be calculated by minimizing TIMs using only 1-dimensional branch-and-bound (BnB), (ii) the translation can be found by running 1-dimensional search for three times with prioritized progressive voting. Compared with the popular randomized solver, our solver achieves deterministic global convergence without depending on an initial value. While compared with existing BnB based methods, ours is exponentially faster. Finally, by evaluating the performance on both simulation and real-world datasets, our approach gives accurate pose even when there are 90\% outliers (only 2 inliers).

Bo Fu, Yue Wang, Xiaqing Ding et al.

LiDAR-camera calibration is a precondition for many heterogeneous systems that fuse data from LiDAR and camera. However, the constraint from common field of view and the requirement for strict time synchronization make the calibration a challenging problem. In this paper, we propose a novel LiDAR-camera calibration method aiming to eliminate these two constraints. Specifically, we capture a scan of 3D LiDAR when both the environment and the sensors are stationary, then move the camera to reconstruct the 3D environment using the sequentially obtained images. Finally, we align 3D visual points to the laser scan based on tightly couple graph optimization method to calculate the extrinsic parameters between LiDAR and camera. Under this design, the configuration of these two sensors are free from the common field of view constraint owing to the extended view from the moving camera. And we also eliminate the requirement for strict time synchronization as we only use the single scan of laser data when the sensors are stationary. We theoretically derive the conditions of minimal observability for our method and prove that the accuracy of calibration is improved by collecting more observations from multiple scattered calibration targets. We validate our method on both simulation platform and real-world datasets. Experiments show that our method achieves higher accuracy than other comparable methods, which is in accordance with our theoretical analysis. In addition, the proposed method is beneficial to not only plane measurement error based chessboard, but also other point measurement error based calibration targets, such as boxes and polygonal boards.

Yanmei Jiao, Yue Wang, Bo Fu et al.

Visual localization has attracted considerable attention due to its low-cost and stable sensor, which is desired in many applications, such as autonomous driving, inspection robots and unmanned aerial vehicles. However, current visual localization methods still struggle with environmental changes across weathers and seasons, as there is significant appearance variation between the map and the query image. The crucial challenge in this situation is that the percentage of outliers, i.e. incorrect feature matches, is high. In this paper, we derive minimal closed form solutions for 3D-2D localization with the aid of inertial measurements, using only 2 pairs of point matches or 1 pair of point match and 1 pair of line match. These solutions are further utilized in the proposed 2-entity RANSAC, which is more robust to outliers as both line and point features can be used simultaneously and the number of matches required for pose calculation is reduced. Furthermore, we introduce three feature sampling strategies with different advantages, enabling an automatic selection mechanism. With the mechanism, our 2-entity RANSAC can be adaptive to the environments with different distribution of feature types in different segments. Finally, we evaluate the method on both synthetic and real-world datasets, validating its performance and effectiveness in inter-session scenarios.