Clifford Algebra-Based Iterated Extended Kalman Filter with Application to Low-Cost INS/GNSS Navigation

The traditional GNSS-aided inertial navigation system (INS) usually exploits the extended Kalman filter (EKF) for state estimation, and the initial attitude accuracy is key to the filtering performance. To spare the reliance on the initial attitude, this work generalizes the previously proposed trident quaternion within the framework of Clifford algebra to represent the extended pose, IMU biases and lever arms on the Lie group. Consequently, a quasi-group-affine system is established for the low-cost INS/GNSS integrated navigation system, and the right-error Clifford algebra-based EKF (Clifford-RQEKF) is accordingly developed. The iterated filtering approach is further applied to significantly improve the performances of the Clifford-RQEKF and the previously proposed trident quaternion-based EKFs. Numerical simulations and experiments show that all iterated filtering approaches fulfill the fast and global convergence without the prior attitude information, whereas the iterated Clifford-RQEKF performs much better than the others under especially large IMU biases

Visual Position Tracking using Dual Quaternions with Hand-Eye Motion Constraints

In this paper a method for contour-based rigid body tracking with simultaneouscamera calibration is developed. The method works for a singleeye-in-hand camera with unknown hand-eye transformation,viewing a stationary object with unknown position. The method usesdual quaternions to express the relationship between the camera- andend-effector screws. It is shown how using the measured motion of therobot end-effector can improve the accuracy of theestimation, even if the relative position and orientation between sensorand actuator is completely unknown.The method is evaluated in simulations on images from a real-time 3D renderingsystem. The system is shown to be able to track the pose of rigid objects and changes in intrinsic camera parameters, using only rough initial values for the parameters. The method is finally validated in anexperiment using real images from a camera mounted on an industrial robot

Single and multiple stereo view navigation for planetary rovers

© Cranfield UniversityThis thesis deals with the challenge of autonomous navigation of the ExoMars rover. The absence of global positioning systems (GPS) in space, added to the limitations of wheel odometry makes autonomous navigation based on these two techniques - as done in the literature - an inviable solution and necessitates the use of other approaches. That, among other reasons, motivates this work to use solely visual data to solve the robot’s Egomotion problem. The homogeneity of Mars’ terrain makes the robustness of the low level image processing technique a critical requirement. In the first part of the thesis, novel solutions are presented to tackle this specific problem. Detection of robust features against illumination changes and unique matching and association of features is a sought after capability. A solution for robustness of features against illumination variation is proposed combining Harris corner detection together with moment image representation. Whereas the first provides a technique for efficient feature detection, the moment images add the necessary brightness invariance. Moreover, a bucketing strategy is used to guarantee that features are homogeneously distributed within the images. Then, the addition of local feature descriptors guarantees the unique identification of image cues. In the second part, reliable and precise motion estimation for the Mars’s robot is studied. A number of successful approaches are thoroughly analysed. Visual Simultaneous Localisation And Mapping (VSLAM) is investigated, proposing enhancements and integrating it with the robust feature methodology. Then, linear and nonlinear optimisation techniques are explored. Alternative photogrammetry reprojection concepts are tested. Lastly, data fusion techniques are proposed to deal with the integration of multiple stereo view data. Our robust visual scheme allows good feature repeatability. Because of this, dimensionality reduction of the feature data can be used without compromising the overall performance of the proposed solutions for motion estimation. Also, the developed Egomotion techniques have been extensively validated using both simulated and real data collected at ESA-ESTEC facilities. Multiple stereo view solutions for robot motion estimation are introduced, presenting interesting benefits. The obtained results prove the innovative methods presented here to be accurate and reliable approaches capable to solve the Egomotion problem in a Mars environment

A Survey on Dual-Quaternions

Over the past few years, the applications of dual-quaternions have not only developed in many different directions but has also evolved in exciting ways in several areas. As dual-quaternions offer an efficient and compact symbolic form with unique mathematical properties. While dual-quaternions are now common place in many aspects of research and implementation, such as, robotics and engineering through to computer graphics and animation, there are still a large number of avenues for exploration with huge potential benefits. This article is the first to provide a comprehensive review of the dual-quaternion landscape. In this survey, we present a review of dual-quaternion techniques and applications developed over the years while providing insights into current and future directions. The article starts with the definition of dual-quaternions, their mathematical formulation, while explaining key aspects of importance (e.g., compression and ambiguities). The literature review in this article is divided into categories to help manage and visualize the application of dual-quaternions for solving specific problems. A timeline illustrating key methods is presented, explaining how dual-quaternion approaches have progressed over the years. The most popular dual-quaternion methods are discussed with regard to their impact in the literature, performance, computational cost and their real-world results (compared to associated models). Finally, we indicate the limitations of dual-quaternion methodologies and propose future research directions.Comment: arXiv admin note: text overlap with arXiv:2303.1339

Dual Quaternion Sample Reduction for SE(2) Estimation

We present a novel sample reduction scheme for random variables belonging to the SE(2) group by means of Dirac mixture approximation. For this, dual quaternions are employed to represent uncertain planar transformations. The Cramér–von Mises distance is modified as a smooth metric to measure the statistical distance between Dirac mixtures on the manifold of planar dual quaternions. Samples of reduced size are then obtained by minimizing the probability divergence via Riemannian optimization while interpreting the correlation between rotation and translation. We further deploy the proposed scheme for nonparametric modeling of estimates for nonlinear SE(2) estimation. Simulations show superior tracking performance of the sample reduction-based filter compared with Monte Carlo-based as well as parametric model-based planar dual quaternion filters