NXP Semiconductors
AN5017
Aerospace Android and Windows Coordinate Systems
AN5017
All information provided in this document is subject to legal disclaimers.
© NXP B.V. 2016. All rights reserved.
Application note
Rev. 2.0 — 21 June 2016
6 of 28
the orientation reduces from three Euler angles to two. Any change in the first Euler
rotation angle can be offset by a cancelling change in the third Euler rotation angle with
the result that the two values oscillate unstably together.
Gimbal lock in strapdown navigation systems is, therefore, a mathematical instability that
results from the decomposition of the orientation matrix or quaternion into three individual
Euler angle rotations and is easily avoided by using orientation matrix or quaternion
representations which are completely stable at gimbal lock orientations.
The NXP Sensor Fusion Library uses orientation matrix and quaternion algebra
throughout and computes Euler angles for human use as an output from the algorithms.
The computed orientation is therefore just as stable at gimbal lock orientations as at
other orientations. Any software fundamentally based on Euler angle rotations in
preference to rotation matrix or quaternion will suffer from gimbal lock instability and
mathematical discontinuities.
Item
Aerospace (NED)
Android (ENU)
Windows 8 (ENU)
Gimbal Lock
±90° pitch (y-axis)
±90° roll (y-axis)
±90° pitch (x-axis)
Table 4. Gimbal lock defined by coordinate system
1.8 Euler Angle Discontinuities
Another problem with Euler angles representation of orientation is that, in addition to
there being an infinite number of Euler angle solutions at gimbal lock orientations, there
are, in general, two Euler angle solutions for every orientation. This forces one of the
Euler angles to be constrained with a reduced range of –90° to +90° to eliminate one of
the two solutions.
The presence of two solutions is easily demonstrated with the starting position of the
device laid flat on the table and then applying these two rotation sequences:
• rotation of 180° in pitch
• rotation of 180° in yaw followed by a rotation of 180° in pitch
Both rotation sequences result in the same physical orientation and the same orientation
matrix and quaternion.
The Aerospace coordinate system restricts the range of the pitch angle from –90° to +90°
and the Android and Windows 8 coordinate systems restrict the range of roll angle from
–90°to +90°. Although this restriction results in just one Euler angle solution at all
orientations except at gimbal lock, it creates the unfortunate mathematical side effect of
introducing discontinuities in the Euler angles.
The table below summarizes the Euler angle discontinuities in each coordinate system.
Sections 2 through 4 present more information on the meanings of the various table
entries.
Item
Aerospace (NED)
Android (ENU)
Windows 8 (ENU)
Ranges of Euler
angles
0°
≤ Yaw
ψ
(z) < 360°
–90° ≤ Pitch
θ
(y) < 90°
–180° ≤ Roll
φ
(x) < 180°
0° ≤ Yaw
ψ
(z) < 360°
–90° ≤ Roll
φ
(y) < 90°
–180° ≤ Pitch
θ
(x) < 180°
0° ≤ Yaw
ψ
(z) < 360°
–180° ≤ Pitch
θ
(x) < 180°
–90° ≤ Roll
φ
(y) < 90°
Equivalent
matrix
(
+
)
(
)
(
+
)
(
+
)
(
)
(
+
)
(
)
(
)
(
+
)
剩余27页未读，继续阅读
daidaiyijiu
- 粉丝: 17
- 资源: 322
我的内容管理
收起
- 我的资源
快来上传第一个资源
我的收益 登录查看自己的收益
我的积分
登录查看自己的积分
我的C币
登录后查看C币余额
我的收藏 
我的下载 
下载帮助
会员权益专享
最新资源
- 利用迪杰斯特拉算法的全国交通咨询系统设计与实现
- 全国交通咨询系统C++实现源码解析
- DFT与FFT应用：信号频谱分析实验
- MATLAB图论算法实现：最小费用最大流
- MATLAB常用命令完全指南
- 共创智慧灯杆数据运营公司——抢占5G市场
- 中山农情统计分析系统项目实施与管理策略
- XX省中小学智慧校园建设实施方案
- 中山农情统计分析系统项目实施方案
- MATLAB函数详解：从Text到Size的实用指南
- 考虑速度与加速度限制的工业机器人轨迹规划与实时补偿算法
- Matlab进行统计回归分析：从单因素到双因素方差分析
- 智慧灯杆数据运营公司策划书：抢占5G市场，打造智慧城市新载体
- Photoshop基础与色彩知识：信息时代的PS认证考试全攻略
- Photoshop技能测试：核心概念与操作
- Photoshop试题与答案详解
资源上传下载、课程学习等过程中有任何疑问或建议，欢迎提出宝贵意见哦~我们会及时处理！
点击此处反馈
