Relative State Estimation perform mutually localization between two mobile agents undergoing six-degree-of-freedom motion. Based on the principle of circular motion, the estimation accuracy is sensitive to nonlinear rotations of the reference platform, particularly under large inter-platform distances. This phenomenon is even obvious for linearized kinematics, because cumulative linearization errors significantly degrade precision. In virtual reality (VR) applications, this manifests as substantial positional errors in 6-DoF controller tracking during rapid rotations of the head-mounted display. The linearization errors introduce drift in the estimate and render the estimator inconsistent. In the field of odometry, IMU preintegration is proposed as a kinematic observation to enable efficient relinearization, thus mitigate linearized error. Building on this theory, we propose dual preintegration, a novel observation integrating IMU preintegration from both platforms. This method serves as kinematic constraints for consecutive relative state and supports efficient relinearization. We also perform observability analysis of the state and analytically formulate the accordingly null space. Algorithm evaluation encompasses both simulations and real-world experiments. Multiple nonlinear rotations on the reference platform are simulated to compare the precision of the proposed method with that of other state-of-the-art (SOTA) algorithms. The field test compares the proposed method and SOTA algorithms in the application of VR controller tracking from the perspectives of bias observability, nonlinear rotation, and background texture. The results demonstrate that the proposed method is more precise and robust than the SOTA algorithms.

Radar ensures robust sensing capabilities in adverse weather conditions, yet challenges remain due to its high inherent noise level. Existing radar odometry has overcome these challenges with strategies such as filtering spurious points, exploiting Doppler velocity, or integrating with inertial measurements. This paper presents two novel improvements beyond the existing radar-inertial odometry: ground-optimized noise filtering and continuous velocity preintegration. Despite the widespread use of ground planes in LiDAR odometry, imprecise ground point distributions of radar measurements cause naive plane fitting to fail. Unlike plane fitting in LiDAR, we introduce a zone-based uncertainty-aware ground modeling specifically designed for radar. Secondly, we note that radar velocity measurements can be better combined with IMU for a more accurate preintegration in radar-inertial odometry. Existing methods often ignore temporal discrepancies between radar and IMU by simplifying the complexities of asynchronous data streams with discretized propagation models. Tackling this issue, we leverage GP and formulate a continuous preintegration method for tightly integrating 3-DOF linear velocity with IMU, facilitating full 6-DOF motion directly from the raw measurements. Our approach demonstrates remarkable performance (less than 1% vertical drift) in public datasets with meticulous conditions, illustrating substantial improvement in elevation accuracy. The code will be released as open source for the community: https://github.com/wooseongY/Go-RIO.

Event cameras, as bio-inspired sensors, are asynchronously triggered with high-temporal resolution compared to intensity cameras. Recent work has focused on fusing the event measurements with inertial measurements to enable ego-motion estimation in high-speed and HDR environments. However, existing methods predominantly rely on IMU preintegration designed mainly for synchronous sensors and discrete-time frameworks. In this paper, we propose a continuous-time preintegration method based on the Temporal Gaussian Process (TGP) called GPO. Concretely, we model the preintegration as a time-indexed motion trajectory and leverage an efficient two-step optimization to initialize the precision preintegration pseudo-measurements. Our method realizes a linear and constant time cost for initialization and query, respectively. To further validate the proposal, we leverage the GPO to design an asynchronous event-inertial odometry and compare with other asynchronous fusion schemes within the same odometry system. Experiments conducted on both public and own-collected datasets demonstrate that the proposed GPO offers significant advantages in terms of precision and efficiency, outperforming existing approaches in handling asynchronous sensor fusion.

Recent works have combined monocular event camera and inertial measurement unit to estimate the $SE(3)$ trajectory. However, the asynchronicity of event cameras brings a great challenge to conventional fusion algorithms. In this paper, we present an asynchronous event-inertial odometry under a unified Gaussian Process (GP) regression framework to naturally fuse asynchronous data associations and inertial measurements. A GP latent variable model is leveraged to build data-driven motion prior and acquire the analytical integration capacity. Then, asynchronous event-based feature associations and integral pseudo measurements are tightly coupled using the same GP framework. Subsequently, this fusion estimation problem is solved by underlying factor graph in a sliding-window manner. With consideration of sparsity, those historical states are marginalized orderly. A twin system is also designed for comparison, where the traditional inertial preintegration scheme is embedded in the GP-based framework to replace the GP latent variable model. Evaluations on public event-inertial datasets demonstrate the validity of both systems. Comparison experiments show competitive precision compared to the state-of-the-art synchronous scheme.

This letter proposes a new approach for Inertial Measurement Unit (IMU) preintegration, a fundamental building block that can be leveraged in different optimization-based Inertial Navigation System (INS) localization solutions. Inspired by recent advances in equivariant theory applied to biased INSs, we derive a discrete-time formulation of the IMU preintegration on ${\mathbf{Gal}(3) \ltimes \mathfrak{gal}(3)}$, the left-trivialization of the tangent group of the Galilean group $\mathbf{Gal}(3)$. We define a novel preintegration error that geometrically couples the navigation states and the bias leading to lower linearization error. Our method improves in consistency compared to existing preintegration approaches which treat IMU biases as a separate state-space. Extensive validation against state-of-the-art methods, both in simulation and with real-world IMU data, implementation in the Lie++ library, and open-source code are provided.

Event cameras, when combined with inertial sensors, show significant potential for motion estimation in challenging scenarios, such as high-speed maneuvers and low-light environments. There are many methods for producing such estimations, but most boil down to a synchronous discrete-time fusion problem. However, the asynchronous nature of event cameras and their unique fusion mechanism with inertial sensors remain underexplored. In this paper, we introduce a monocular event-inertial odometry method called AsynEIO, designed to fuse asynchronous event and inertial data within a unified Gaussian Process (GP) regression framework. Our approach incorporates an event-driven frontend that tracks feature trajectories directly from raw event streams at a high temporal resolution. These tracked feature trajectories, along with various inertial factors, are integrated into the same GP regression framework to enable asynchronous fusion. With deriving analytical residual Jacobians and noise models, our method constructs a factor graph that is iteratively optimized and pruned using a sliding-window optimizer. Comparative assessments highlight the performance of different inertial fusion strategies, suggesting optimal choices for varying conditions. Experimental results on both public datasets and our own event-inertial sequences indicate that AsynEIO outperforms existing methods, especially in high-speed and low-illumination scenarios.

The special Galilean group, usually denoted SGal(3), is a 10-dimensional Lie group whose important subgroups include the special orthogonal group, the special Euclidean group, and the group of extended poses. We briefly describe SGal(3) and its Lie algebra and show how the group structure supports a unified representation of uncertainty in space and time. Our aim is to highlight the potential usefulness of this group for several robotics problems.

Cooperative localization and target tracking are essential for multi-robot systems to implement high-level tasks. To this end, we propose a distributed invariant Kalman filter based on covariance intersection for effective multi-robot pose estimation. The paper utilizes the object-level measurement models, which have condensed information further reducing the communication burden. Besides, by modeling states on special Lie groups, the better linearity and consistency of the invariant Kalman filter structure can be stressed. We also use a combination of CI and KF to avoid overly confident or conservative estimates in multi-robot systems with intricate and unknown correlations, and some level of robot degradation is acceptable through multi-robot collaboration. The simulation and real data experiment validate the practicability and superiority of the proposed algorithm.

Accurate disturbance estimation is crucial for reliable robotic physical interaction. To estimate environmental interference in a low-cost and sensorless way (without force sensor), a variety of tightly-coupled visual inertial external force estimators are proposed in the literature. However, existing solutions may suffer from relatively low-frequency preintegration. In this paper, a novel estimator is designed to overcome this issue via high-frequency instantaneous accelerometer update.

Significant work has been done on advancing localization and mapping in underwater environments. Still, state-of-the-art methods are challenged by low-texture environments, which is common for underwater settings. This makes it difficult to use existing methods in diverse, real-world scenes. In this paper, we present TURTLMap, a novel solution that focuses on textureless underwater environments through a real-time localization and mapping method. We show that this method is low-cost, and capable of tracking the robot accurately, while constructing a dense map of a low-textured environment in real-time. We evaluate the proposed method using real-world data collected in an indoor water tank with a motion capture system and ground truth reference map. Qualitative and quantitative results validate the proposed system achieves accurate and robust localization and precise dense mapping, even when subject to wave conditions. The project page for TURTLMap is https://umfieldrobotics.github.io/TURTLMap.