GS-LIVM: Real-Time Photo-Realistic LiDAR-Inertial-Visual Mapping with Gaussian Splatting

In this paper, we introduce GS-LIVM, a real-time photo-realistic LiDAR-Inertial-Visual mapping framework with Gaussian Splatting tailored for outdoor scenes. Compared to existing methods based on Neural Radiance Fields (NeRF) and 3D Gaussian Splatting (3DGS), our approach enables real-time photo-realistic mapping while ensuring high-quality image rendering in large-scale unbounded outdoor environments. In this work, Gaussian Process Regression (GPR) is employed to mitigate the issues resulting from sparse and unevenly distributed LiDAR observations. The voxel-based 3D Gaussians map representation facilitates real-time dense mapping in large outdoor environments with acceleration governed by custom CUDA kernels. Moreover, the overall framework is designed in a covariance-centered manner, where the estimated covariance is used to initialize the scale and rotation of 3D Gaussians, as well as update the parameters of the GPR. We evaluate our algorithm on several outdoor datasets, and the results demonstrate that our method achieves state-of-the-art performance in terms of mapping efficiency and rendering quality. The source code is available on GitHub.

MCGMapper: Light-Weight Incremental Structure from Motion and Visual Localization With Planar Markers and Camera Groups

Structure from Motion (SfM) and visual localization in indoor texture-less scenes and industrial scenarios present prevalent yet challenging research topics. Existing SfM methods designed for natural scenes typically yield low accuracy or map-building failures due to insufficient robust feature extraction in such settings. Visual markers, with their artificially designed features, can effectively address these issues. Nonetheless, existing marker-assisted SfM methods encounter problems like slow running speed and difficulties in convergence; and also, they are governed by the strong assumption of unique marker size. In this paper, we propose a novel SfM framework that utilizes planar markers and multiple cameras with known extrinsics to capture the surrounding environment and reconstruct the marker map. In our algorithm, the initial poses of markers and cameras are calculated with Perspective-n-Points (PnP) in the front-end, while bundle adjustment methods customized for markers and camera groups are designed in the back-end to optimize the 6-DOF pose directly. Our algorithm facilitates the reconstruction of large scenes with different marker sizes, and its accuracy and speed of map building are shown to surpass existing methods. Our approach is suitable for a wide range of scenarios, including laboratories, basements, warehouses, and other industrial settings. Furthermore, we incorporate representative scenarios into simulations and also supply our datasets with pose labels to address the scarcity of quantitative ground-truth datasets in this research field. The datasets and source code are available on GitHub.

Collision-Free Trajectory Optimization in Cluttered Environments with Sums-of-Squares Programming

In this work, we propose a trajectory optimization approach for robot navigation in cluttered 3D environments. We represent the robot's geometry as a semialgebraic set defined by polynomial inequalities such that robots with general shapes can be suitably characterized. To address the robot navigation task in obstacle-dense environments, we exploit the free space directly to construct a sequence of free regions, and allocate each waypoint on the trajectory to a specific region. Then, we incorporate a uniform scaling factor for each free region, and formulate a Sums-of-Squares (SOS) optimization problem that renders the containment relationship between the robot and the free space computationally tractable. The SOS optimization problem is further reformulated to a semidefinite program (SDP), and the collision-free constraints are shown to be equivalent to limiting the scaling factor along the entire trajectory. In this context, the robot at a specific configuration is tailored to stay within the free region. Next, to solve the trajectory optimization problem with the proposed safety constraints (which are implicitly dependent on the robot configurations), we derive the analytical solution to the gradient of the minimum scaling factor with respect to the robot configuration. As a result, this seamlessly facilitates the use of gradient-based methods in efficient solving of the trajectory optimization problem. Through a series of simulations and real-world experiments, the proposed trajectory optimization approach is validated in various challenging scenarios, and the results demonstrate its effectiveness in generating collision-free trajectories in dense and intricate environments populated with obstacles.