Relative pose (position and orientation) estimation is an essential component of many robotics applications. Fiducial markers, such as the AprilTag visual fiducial system, yield a relative pose measurement from a single marker detection and provide a powerful tool for pose estimation. In this paper, we perform a Lie algebraic nonlinear observability analysis on a nonlinear dual quaternion system that is composed of a relative pose measurement model and a relative motion model. We prove that many common dual quaternion expressions yield Jacobian matrices with advantageous block structures and rank properties that are beneficial for analysis. We show that using a dual quaternion representation yields an observability matrix with a simple block triangular structure and satisfies the necessary full rank condition.

In this paper, we address the problem of relative localization of two mobile agents. Specifically, we consider the Dual-IMU system, where each agent is equipped with one IMU, and employs relative pose observations between them. Previous works, however, typically assumed known ego motion and ignored biases of the IMUs. Instead, we study the most general case of unknown biases for both IMUs. Besides the derivation of dynamic model equations of the proposed system, we focus on the observability analysis, for the observability under general motion and the unobservable directions arising from various special motions. Through numerical simulations, we validate our key observability findings and examine their impact on the estimation accuracy and consistency. Finally, the system is implemented to achieve effective relative localization of an HMD with respect to a vehicle moving in the real world.

In robotics, motion capture systems have been widely used to measure the accuracy of localization algorithms. Moreover, this infrastructure can also be used for other computer vision tasks, such as the evaluation of Visual (-Inertial) SLAM dynamic initialization, multi-object tracking, or automatic annotation. Yet, to work optimally, these functionalities require having accurate and reliable spatial-temporal calibration parameters between the camera and the global pose sensor. In this study, we provide two novel solutions to estimate these calibration parameters. Firstly, we design an offline target-based method with high accuracy and consistency. Spatial-temporal parameters, camera intrinsic, and trajectory are optimized simultaneously. Then, we propose an online target-less method, eliminating the need for a calibration target and enabling the estimation of time-varying spatial-temporal parameters. Additionally, we perform detailed observability analysis for the target-less method. Our theoretical findings regarding observability are validated by simulation experiments and provide explainable guidelines for calibration. Finally, the accuracy and consistency of two proposed methods are evaluated with hand-held real-world datasets where traditional hand-eye calibration method do not work.

In this study, we address multi-robot localization issues, with a specific focus on cooperative localization and observability analysis of relative pose estimation. Cooperative localization involves enhancing each robot's information through a communication network and message passing. If odometry data from a target robot can be transmitted to the ego robot, observability of their relative pose estimation can be achieved through range-only or bearing-only measurements, provided both robots have non-zero linear velocities. In cases where odometry data from a target robot are not directly transmitted but estimated by the ego robot, both range and bearing measurements are necessary to ensure observability of relative pose estimation. For ROS/Gazebo simulations, we explore four sensing and communication structures. We compare extended Kalman filtering (EKF) and pose graph optimization (PGO) estimation using different robust loss functions (filtering and smoothing with varying batch sizes of sliding windows) in terms of estimation accuracy. In hardware experiments, two Turtlebot3 equipped with UWB modules are used for real-world inter-robot relative pose estimation, applying both EKF and PGO and comparing their performance.

Accurate global localization is crucial for autonomous navigation and planning. To this end, GPS-aided Visual-Inertial Odometry (GPS-VIO) fusion algorithms are proposed in the literature. This paper presents a novel GPS-VIO system that is able to significantly benefit from the online adaptive calibration of the rotational extrinsic parameter between the GPS reference frame and the VIO reference frame. The behind reason is this parameter is observable. This paper provides novel proof through nonlinear observability analysis. We also evaluate the proposed algorithm extensively on diverse platforms, including flying UAV and driving vehicle. The experimental results support the observability analysis and show increased localization accuracy in comparison to state-of-the-art (SOTA) tightly-coupled algorithms.

In this paper, we propose a novel performance metric for articulated robotic mechanisms called the sensor observability analysis and the resulting sensor observability index. The goal is to analyse and evaluate the performance of robot-mounted distributed directional or axial-based sensors to observe specific axes in task space as a function of joint configuration. For example, joint torque sensors are often used in serial robot manipulators and assumed to be perfectly capable of estimating end effector forces, but certain joint configurations may cause one or more task-space axes to be unobservable as a result of how the joint torque sensors are aligned. The proposed sensor observability analysis provides a method to analyse the cumulative quality of a robot configuration to observe the task space, akin to forward kinematics for sensors. The resultant metrics can then be used in optimization and in null-space control to avoid sensor observability singular configurations or to maximize sensor observability in particular directions. Parallels are drawn between sensor observability and the traditional kinematic Jacobian for the particular case of joint torque sensors in serial robot manipulators. Compared to kinematic analysis using the Jacobian in serial manipulators, sensor observability analysis is shown to be more generalizable in terms of analysing non-joint-mounted sensors and can potentially be applied to sensor types other than for force sensing, e.g., link-mounted proximity sensors. Simulations and experiments using a custom 3-DOF robot and the Baxter robot demonstrate the utility and importance of sensor observability in physical interactions.

Multiple microphone arrays have many applications in robot audition, including sound source localization, audio scene perception and analysis, etc. However, accurate calibration of multiple microphone arrays remains a challenge because there are many unknown parameters to be identified, including the Euler angles, geometry, asynchronous factors between the microphone arrays. This paper is concerned with joint calibration of multiple microphone arrays and sound source localization using graph simultaneous localization and mapping (SLAM). By using a Fisher information matrix (FIM) approach, we focus on the observability analysis of the graph SLAM framework for the above-mentioned calibration problem. We thoroughly investigate the identifiability of the unknown parameters, including the Euler angles, geometry, asynchronous effects between the microphone arrays, and the sound source locations. We establish necessary/sufficient conditions under which the FIM and the Jacobian matrix have full column rank, which implies the identifiability of the unknown parameters. These conditions are closely related to the variation in the motion of the sound source and the configuration of microphone arrays, and have intuitive and physical interpretations. We also discover several scenarios where the unknown parameters are not uniquely identifiable. All theoretical findings are demonstrated using simulation data.

This paper presents Lidar-based Simultaneous Localization and Mapping (SLAM) for autonomous driving vehicles. Fusing data from landmark sensors and a strap-down Inertial Measurement Unit (IMU) in an adaptive Kalman filter (KF) plus the observability of the system are investigated. In addition to the vehicle's states and landmark positions, a self-tuning filter estimates the IMU calibration parameters as well as the covariance of the measurement noise. The discrete-time covariance matrix of the process noise, the state transition matrix, and the observation sensitivity matrix are derived in closed-form making them suitable for real-time implementation. Examining the observability of the 3D SLAM system leads to the conclusion that the system remains observable upon a geometrical condition on the alignment of the landmarks.