The state estimation on$SE_{2}(3)$Lie Group has been proven to have the ability to improve the consistency of the estimated results. They are called invariant state estimation approaches, including filter-based ones and optimization-based ones. Precise Point Positioning (PPP) is a Global Navigation Satellite System (GNSS) positioning technology which can achieve high-precision positioning without commercial base stations. Visual-Inertial Odometry (VIO) combines Visual-SLAM and IMU, realizing a more robust local pose estimation than either of the two. In this paper, the invariant optimization approach has been applied to fuse PPP/INS/Visual-SLAM. The proposed positioning system in our paper is called In-P3VINS. All raw data of the In-P3VINS is modeled and optimized under an invariant factor graph framework. In particular, the carrier phase measurement is utilized by adding the phase ambiguity into the estimated states. Finally, In-P3VINS is evaluated in both simulation experiments and real-world experiments. In the simulation experiments, the accuracy and consistency of In-P3VINS are superior to the other compared methods. In the real-world experiments, In-P3VINS has the most accurate results.

This paper presents FAST-LIVO2, a fast and direct LiDAR-inertial-visual odometry framework designed for accurate and robust state estimation in SLAM tasks, enabling real-time robotic applications. FAST-LIVO2 integrates IMU, LiDAR, and image data through an efficient error-state iterated Kalman filter (ESIKF). To address the dimensional mismatch between LiDAR and image measurements, we adopt a sequential update strategy. Efficiency is further enhanced using direct methods for LiDAR and visual data fusion: the LiDAR module registers raw points without extracting features, while the visual module minimizes photometric errors without relying on feature extraction. Both LiDAR and visual measurements are fused into a unified voxel map. The LiDAR module constructs the geometric structure, while the visual module links image patches to LiDAR points, enabling precise image alignment. Plane priors from LiDAR points improve alignment accuracy and are refined dynamically during the process. Additionally, an on-demand raycast operation and real-time image exposure estimation enhance robustness. Extensive experiments on benchmark and custom datasets demonstrate that FAST-LIVO2 outperforms state-of-the-art systems in accuracy, robustness, and efficiency. Key modules are validated, and we showcase three applications: UAV navigation highlighting real-time capabilities, airborne mapping demonstrating high accuracy, and 3D model rendering (mesh-based and NeRF-based) showcasing suitability for dense mapping. Code and datasets are open-sourced on GitHub to benefit the robotics community.

This article investigates the robust output regulation of linear uncertain singularly perturbed systems by output-feedback control. Due to the presence of extremely small perturbation parameters, numerical issues will arise when applying conventional robust regulator design techniques to the regular system. To handle the problem, a continuous-time output-feedback controller adopting the forwarding design technique is proposed by combining the internal model approach with singularly perturbed theory. In this manner, the circumvention of numerical issues and the resolution of robustness problems can be achieved. Additionally, the sampling of the transmissions between the plant and the controller is taken into account, leading to the proposed implementation of a dynamic output-based event-triggered strategy. As a result, the output regulation property becomes practical. To avoid Zeno behavior, the implementation ensures the existence of a strictly positive minimum intertime for the triggering instant sequence. The validity of the results is demonstrated through the presentation of a numerical example.

Invariant Extended Kalman Filter (IEKF) has been successfully applied in Visual-inertial Odometry (VIO) as an advanced achievement of Kalman filter, showing great potential in sensor fusion. In this paper, we propose partial IEKF (PIEKF), which only incorporates rotation-velocity state into the Lie group structure and apply it for Visual-Inertial-Wheel Odometry (VIWO) to improve positioning accuracy and consistency. Specifically, we derive the rotation-velocity measurement model, which combines wheel measurements with kinematic constraints. The model circumvents the wheel odometer's 3D integration and covariance propagation, which is essential for filter consistency. And a plane constraint is also introduced to enhance the position accuracy. A dynamic outlier detection method is adopted, leveraging the velocity state output. Through the simulation and real-world test, we validate the effectiveness of our approach, which outperforms the standard Multi-State Constraint Kalman Filter (MSCKF) based VIWO in consistency and accuracy.