On the Comparisons of Unit Dual Quaternion and Homogeneous Transformation Matrix

Wang, Xiangke; Zhu, Huayong

doi:10.1007/s00006-013-0436-y

Cited by 46 publications

(32 citation statements)

References 22 publications

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“…It is worth emphasizing that in generating the variable ε k there is no need for the true inertia matrix parameters; only the regressor matrix R k , the estimated dual inertia, and the applied dual force are needed as in Eq. (16).…”

Section: Concurrent Learningmentioning

confidence: 99%

“…Dual quaternions have been shown to have better computational efficiency and lower memory requirements than other conventional methods for kinematic modeling. [13][14][15][16] Since computational power is often limited in space-related tasks, this makes quaternions and dual quaternions more appropriate than, say, working directly with the more natural spaces SO(3) (for attitude) or SE(3) (for pose).…”

Section: Introductionmentioning

confidence: 99%

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Spacecraft Trajectory Tracking with Identification of Mass Properties Using Dual Quaternions

Valverde

Tsiotras

2018

2018 AIAA Guidance, Navigation, and Control Conference

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The problem of estimating the mass properties of a spacecraft while tracking a 6-DOF reference is addressed using dual quaternions. Dual quaternions provide a position and attitude (pose) representation, which has proven to be advantageous over other, more conventional, parameterizations. An adaptive controller for 6-DOF tracking is proposed using concepts from the concurrent learning framework. The latter is a recently proposed methodology to incorporate current and recorded system data from measurements into the update of an adaptive controller's parameters. Asymptotic convergence of the parameters is ensured through an easily verifiable rank condition of the matrix formed from a finite set of collected data, contrary to the rather stringent, but more common requirement of persistency of excitation. Simulation results for the tracking of a non-persistently exciting, 6-DOF reference are provided and compared to the baseline adaptive controller.

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Section: Concurrent Learningmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Spacecraft Trajectory Tracking with Identification of Mass Properties Using Dual Quaternions

Valverde

Tsiotras

2018

2018 AIAA Guidance, Navigation, and Control Conference

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“…The trajectory of the closed-loop system exhibits chattering in the neighborhood of the discontinuity-that lies in η = 0-as a result of the measurement noise. The performance degradation stems from infinitely fast switches in (6). Furthermore, the chattering influence over the system is not restricted to the attitude error and may also impact on the resulting trajectory of the translation, as shown in Fig.…”

Section: Prior Work On Pose Stabilizationmentioning

confidence: 99%

“…Although it is usual to design attitude and rigid motion controllers for mechanical systems respectively using rotation matrices and homogeneous transformation matrices (HTM) [3], it has been noted by some authors that a non-singular representation, namely the unit quaternion group Spin(3) for rotations and the unit dual quaternions Spin(3) R 3 for rigid motions can bring computational advantages [4,5,6].…”

Section: Introductionmentioning

confidence: 99%

Hybrid kinematic control for rigid body pose stabilization using dual quaternions

Kussaba

Figueredo

Ishihara

et al. 2017

Journal of the Franklin Institute

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In this paper, we address the rigid body pose stabilization problem using dual quaternion formalism. We propose a hybrid control strategy to design a switching control law with hysteresis in such a way that the global asymptotic stability of the closed-loop system is guaranteed and such that the global attractivity of the stabilization pose does not exhibit chattering, a problem that is present in all discontinuous-based feedback controllers. Using numerical simulations, we illustrate the problems that arise from existing results in the literature-as unwinding and chattering-and verify the effectiveness of the proposed controller to solve the robust global pose stability problem.

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“…There exists a unique mapping between HTM's and DQ's [20]. Let c Q i be the curve parametric DQ of the i th continuum section.…”

Section: B Modal Dual Quaternions For Continuum Sectionsmentioning

confidence: 99%

Dual Quaternion based modal kinematics for multisection continuum arms

Godage

Walker

2015

2015 IEEE International Conference on Robotics and Automation (ICRA)

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This paper presents general modal dual Quaternion (DQ) kinematics for multisection continuum arms. DQ's produce higher accuracy than homogeneous transformation matrices (HTM) when transformed to modal shape functions (MSF) of similar order and are numerically stable. Thus, the model is compact, more accurate and computationally efficient than the modal kinematics proposed by the author based on HTM's. Also, DQ kinematics does not suffer from singularity related limitations of Euler angle based inverse orientation kinematics. Recursive schemes for deriving DQ's and DQ Jacobians are also presented and can be extended arbitrarily. Both modal HTM and modal DQ kinematics are then applied to solve illustrative spatial inverse position and orientation tracking problems. Based on the results, this paper quantitatively compares both methods and highlights the advantages of modal DQ kinematics. The proposed DQ kinematics are easily extensible to variable length multisection continuum arm with general actuator configurations.

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On the Comparisons of Unit Dual Quaternion and Homogeneous Transformation Matrix

Cited by 46 publications

References 22 publications

Spacecraft Trajectory Tracking with Identification of Mass Properties Using Dual Quaternions

Spacecraft Trajectory Tracking with Identification of Mass Properties Using Dual Quaternions

Hybrid kinematic control for rigid body pose stabilization using dual quaternions

Dual Quaternion based modal kinematics for multisection continuum arms

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