Strapdown Navigation Using Geometric Algebra: Screw Blade Algorithm

Wu, Dimin; Wang, Zhengzhi

doi:10.4236/pos.2012.32003

Cited by 4 publications

(5 citation statements)

References 15 publications

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“…By the integration of (23), (27) and (31), navigation parameters can all be obtained. Those differential equations can be solved by using geometric algebra screw blade algorithms [20]. The mechanism of the SDINS model using GA is shown in Fig.…”

Section: Strapdown Inertial Navigation Modelingmentioning

confidence: 99%

Strapdown navigation using geometric algebra: Modeling and error analysis

Wang

2013

2013 10th IEEE International Conference on Control and Automation (ICCA)

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A strapdown inertial navigation system (SDINS) model and two comparable error models are developed using geometric algebra (GA). GA is a powerful representational and computational system for geometry. Rigid body motions can be represented by versor products in GA framework. Therefore, the navigation equation can be recast using GA. It turns out that the principle of strapdown navigation can be expressed in three continuous motor kinematic equations, which share a unitary form. Two error models, i.e. the additive and multiplicative GA error models, are developed. The SDINS and error models presented in this paper are supposed to benefit the prospective integrated navigation filter in terms of GA.

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Section: Strapdown Inertial Navigation Modelingmentioning

confidence: 99%

Strapdown navigation using geometric algebra: Modeling and error analysis

Wang

2013

2013 10th IEEE International Conference on Control and Automation (ICCA)

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“…where ω is the angular rate. Similarly, the kinematic equation of the motor can be written as [2] 1 2…”

Section: Rigid Body Motion In Geometric Algebramentioning

confidence: 99%

“…GA is found to be eminently suitable to robotics, computer vision, computer graphics, biological vision, physics etc. [2]. As Lasenby stated in [3], GA could be considered as "a unified mathematical language for physics and engineering in the 21st century".…”

Section: Introductionmentioning

confidence: 99%

Position and Attitude Tracking Control Law Design Using Geometric Algebra

et al. 2014

AMM

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A position and attitude tracking control law is developed using geometric algebra (GA). The rigid body motion can be represented by the screw versor (or motor) in GA. Using the kinematics of the motor, the tracking control law of the rigid body motion can be formulated similar to the proportional control law. This paper provides a GA-based position and attitude tracking control law by using the negative feedback of the motor logarithm. The stability of the control law is validated by the numerical simulation.

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“…= ω , where ω is the angular rate. Similarly, the kinematic equation of the motor can be written as [4,8] / 2 M M…”

Section: Rigid Body Motionmentioning

confidence: 99%

“…Actually, DQ should be considered as a subset of GA. GA is found to be eminently suitable to robotics, computer vision, computer graphics, biological vision, physics etc. [4]. As Lasenby stated in [5], GA could be considered as "a unified mathematical language for physics and engineering in the 21st century".…”

Section: Introductionmentioning

confidence: 99%

Control Law Design Based on Geometric Algebra

Liu

et al. 2013

AMM

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A position and attitude control law is developed using geometric algebra (GA). GA is a powerful representational and computational system for geometry. The rigid body motion can be represented by the versor product in GA framework. Using the kinematics of the motor (the versor which represents the rigid body motion in GA), the control law of the rigid body motion can be developed. This paper provides a GA-based position and attitude control law by using the negative feedback of the motor. The stability of the control law is validated by the Lyapunov theorem and the numerical simulation.

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Strapdown Navigation Using Geometric Algebra: Screw Blade Algorithm

Cited by 4 publications

References 15 publications

Strapdown navigation using geometric algebra: Modeling and error analysis

Strapdown navigation using geometric algebra: Modeling and error analysis

Position and Attitude Tracking Control Law Design Using Geometric Algebra

Control Law Design Based on Geometric Algebra

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