Rotation Identification in Geometric Algebra: Theory and Application to the Navigation of Underwater Robots in the Field

Stanway, M. Jordan; Kinsey, James C.

doi:10.1002/rob.21572

Cited by 11 publications

(7 citation statements)

References 68 publications

(133 reference statements)

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“…This fact is supported by Euler's rotation theorem 44 . Although its existence in matrix algebra has been known since Euler's time, its realization is really tedious and is not free of several inconveniences, 37,45,46 although some optimized implementations exist, such as those of Rodrigues 47 . Obtaining the plane and angle of rotation in GA for 3D is determined in a much simpler and more intuitive way, by simply calculating the associated GA rotor 36 …”

Section: Clarke Transformation As a Geometric Manipulation Of Electri...mentioning

confidence: 99%

Formulating the geometric foundation of Clarke, Park, and FBD transformations by means of Clifford's geometric algebra

Montoya

Eid

2021

Math Methods in App Sciences

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Several of the most fundamental transformations widely used by the power engineering community are strongly based on geometrical considerations. Clifford's geometric algebra (GA) is the natural language for describing concepts in Euclidean geometry. In this work, we show how Clarke, Park, and Depenbrock's FBD transformations can be derived by imposing orthogonality on the voltage and current vectors defined in a Euclidean space by using GA. This paper presents these transformations as spatial‐like rotations and projections by means of the use of special algebraic objects named GA rotors. We prove that there is no need to use complex numbers nor matrices to perform the mentioned transformations and to provide geometrical intuition for electrical quantities and their transformations. Furthermore, power properties can be described using GA terminology by means of the proposed geometric power. The manipulation of the geometric power allows a useful current decomposition for a variety of applications such active filtering, frequency estimation, or electrical machinery. We provide in this paper an alternative approach focused on power systems under the paradigm of GA.

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Section: Clarke Transformation As a Geometric Manipulation Of Electri...mentioning

confidence: 99%

Formulating the geometric foundation of Clarke, Park, and FBD transformations by means of Clifford's geometric algebra

Montoya

Eid

2021

Math Methods in App Sciences

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“…Stanway and Kinsey [221] presented the formulation of a stable adaptive identifier to estimate rigid body rotations using rotors in GA. The authors showed an experimental evaluation of this technique, which reduces dead reckoning navigation errors on these platforms and provides comparable performance to previously reported SO(3) constrained Linear Algebra (LA) approaches.…”

Section: Estimation Pose Hand-eye Relocalization Kalman Filtermentioning

confidence: 99%

A Survey on Quaternion Algebra and Geometric Algebra Applications in Engineering and Computer Science 1995–2020

Bayro–Corrochano

2021

IEEE Access

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Geometric Algebra (GA) has proven to be an advanced language for mathematics, physics, computer science, and engineering. This review presents a comprehensive study of works on Quaternion Algebra and GA applications in computer science and engineering from 1995 to 2020. After a brief introduction of GA, the applications of GA are reviewed across many fields. We discuss the characteristics of the applications of GA to various problems of computer science and engineering. In addition, the challenges and prospects of various applications proposed by many researchers are analyzed. We analyze the developments using GA in image processing, computer vision, neurocomputing, quantum computing, robot modeling, control, and tracking, as well as improvement of computer hardware performance. We believe that up to now GA has proven to be a powerful geometric language for a variety of applications. Furthermore, there is evidence that this is the appropriate geometric language to tackle a variety of existing problems and that consequently, step-by-step GA-based algorithms should continue to be further developed. We also believe that this extensive review will guide and encourage researchers to continue the advancement of geometric computing for intelligent machines.INDEX TERMS Geometric algebra, Clifford algebra, quaternion algebra, screw theory, signal processing, electrical engineering and power systems, geometric and quantum computing, image processing, computer vision, graphic engineering, artificial intelligence, machine learning, neural networks, control engineering, robotics, biomedical engineering, and biotechnology.

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“…Sound speed, installation error and ocean currents are the main DVL error factors, and most of the DVL errors caused by these factors can be calculated and compensated before DVL velocity output. However, not all DVL velocity errors can be compensated, which means that there is a residual error as the component of DVL velocity output and influence the DVL accuracy [ 36 , 37 , 50 , 51 , 52 ]. It means that the components of DVL output includes the vehicle’s real velocity and the DVL residue error, and the DVL residue error is unclear where it comes from.…”

Section: Principle Of the Integration Subsystem And Error Analysismentioning

confidence: 99%

Performance Enhancement of a USV INS/CNS/DVL Integration Navigation System Based on an Adaptive Information Sharing Factor Federated Filter

Wang

Cui

et al. 2017

Sensors

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Abstract:To improve the ability of autonomous navigation for Unmanned Surface Vehicles (USVs), multi-sensor integrated navigation based on Inertial Navigation System (INS), Celestial Navigation System (CNS) and Doppler Velocity Log (DVL) is proposed. The CNS position and the DVL velocity are introduced as the reference information to correct the INS divergence error. The autonomy of the integrated system based on INS/CNS/DVL is much better compared with the integration based on INS/GNSS alone. However, the accuracy of DVL velocity and CNS position are decreased by the measurement noise of DVL and bad weather, respectively. Hence, the INS divergence error cannot be estimated and corrected by the reference information. To resolve the problem, the Adaptive Information Sharing Factor Federated Filter (AISFF) is introduced to fuse data. The information sharing factor of the Federated Filter is adaptively adjusted to maintaining multiple component solutions usable as back-ups, which can improve the reliability of overall system. The effectiveness of this approach is demonstrated by simulation and experiment, the results show that for the INS/CNS/DVL integrated system, when the DVL velocity accuracy is decreased and the CNS cannot work under bad weather conditions, the INS/CNS/DVL integrated system can operate stably based on the AISFF method.

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Rotation Identification in Geometric Algebra: Theory and Application to the Navigation of Underwater Robots in the Field

Cited by 11 publications

References 68 publications

Formulating the geometric foundation of Clarke, Park, and FBD transformations by means of Clifford's geometric algebra

Formulating the geometric foundation of Clarke, Park, and FBD transformations by means of Clifford's geometric algebra

A Survey on Quaternion Algebra and Geometric Algebra Applications in Engineering and Computer Science 1995–2020

Performance Enhancement of a USV INS/CNS/DVL Integration Navigation System Based on an Adaptive Information Sharing Factor Federated Filter

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