Tube surfaces with type-2 Bishop frame of Weingarten types in E^3

Kızıltuğ, Sezai; Kaya, Seher; Tarakci, Ömer

doi:10.12988/ijma.2013.13002

Cited by 5 publications

(2 citation statements)

References 7 publications

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“…Many researches have been made about the formulation of a moving frame of a given trajectory, as recently in [16][17][18][19] and previously in [20,21]. However, the designing of the error functions of a moving frame is a difficulty because there is interdisciplinary knowledge involved such as the Lie group theory.…”

Section: Introductionmentioning

confidence: 99%

Some Discussions about the Error Functions on SO(3) and SE(3) for the Guidance of a UAV Using the Screw Algebra Theory

Zhu

Chen

2017

Advances in Mathematical Physics

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In this paper a new error function designed on 3-dimensional special Euclidean group SE(3) is proposed for the guidance of a UAV (Unmanned Aerial Vehicle). In the beginning, a detailed 6-DOF (Degree of Freedom) aircraft model is formulated including 12 nonlinear differential equations. Secondly the definitions of the adjoint representations are presented to establish the relationships of the Lie groups SO(3) and SE(3) and their Lie algebras so(3) and se(3). After that the general situation of the differential equations with matrices belonging to SO(3) and SE(3) is presented. According to these equations the features of the error function on SO(3) are discussed. Then an error function on SE(3) is devised which creates a new way of error functions constructing. In the simulation a trajectory tracking example is given with a target trajectory being a curve of elliptic cylinder helix. The result shows that a better tracking performance is obtained with the new devised error function.

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Section: Introductionmentioning

confidence: 99%

Some Discussions about the Error Functions on SO(3) and SE(3) for the Guidance of a UAV Using the Screw Algebra Theory

Zhu

Chen

2017

Advances in Mathematical Physics

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“…There are many ways to obtain a moving frame of a given curve [7,8]. The Bishop frame which is also called the parallel frame is the most famous one [9,10]. In recent years, papers tend to concentrate on the improvements of the Bishop frame [11,12].…”

Section: Introductionmentioning

confidence: 99%

A Moving Frame Trajectory Tracking Method of a Flying-Wing UAV Using the Differential Geometry

Zhu

Chen

2016

International Journal of Aerospace Engineering

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The problem of UAV trajectory tracking is a difficult issue for scholars and engineers, especially when the target curve is a complex curve in the three-dimensional space. In this paper, the coordinate frames during the tracking process are transformed to improve the tracking result. Firstly, the basic concepts of the moving frame are given. Secondly the transfer principles of various moving frames are formulated and the Bishop frame is selected as a final choice for its flexibility. Thirdly, the detailed dynamic equations of the moving frame tracking method are formulated. In simulation, a moving frame of an elliptic cylinder helix is formulated precisely. Then, the devised tracking method on the basis of the dynamic equations is tested in a complete flight control system with 6 DOF nonlinear equations of the UAV. The simulation result shows a satisfactory trajectory tracking performance so that the effectiveness and efficiency of the devised tracking method is proved.

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