关于为不确定的平面位移构建信任区域
Zihan Yu1, Qiaode Jeffrey Ge1, Mark P Langer2
1Department of Mechanical Engineering, Stony Brook University, Stony Brook, NY 11794.
概括
这项研究引入了一种新方法,用于计算使用平面四次数的平面位移的置信区域. 与现有方法相比,这种方法提供了更紧和更有效的扫描体积,特别是与轴外旋转相比.
科学领域:
- 机器人技术 机器人技术 机器人技术
- 计算机视觉 计算机视觉
- 几何代数的几何代数
背景情况:
- 估计平面位移的不确定性对于机器人和计算机视觉至关重要.
- 使用移动坐标的传统方法通常是不理想的.
- 像指数坐标和平面四边形这样的表示更好地捕捉了SE(2) 组结构.
研究的目的:
- 开发一种统计学上可靠的方法来计算平面位移的置信区域.
- 为了比较不同表示平面位移的有效性.
- 在这种情况下,要突出平面四次数的优点.
主要方法:
- 对平面位移的三个表示方法进行比较:移动框架坐标,指数坐标和平面四边形.
- 开发使用平面四次数的信心区域计算方法.
- 主要组件分析 (PCA) 的应用,以确定主导的运动方向.
- 与旋转和转移置信限值 (RTCL) 方法进行比较分析.
主要成果:
- 用移动框架坐标表示的平面位移对于信心区域分析来说效果较差.
- 指数坐标和平面四边形同样捕获SE(2) 结构,平面四边形提供计算优势.
- 拟议的平面四边形方法比RTCL方法产生了比RTCL方法更紧和有效的扫描体积.
- 平面四边形方法表现出卓越的性能,特别是当有显著的离轴旋转时.
结论:
- 平面四次数为计算平面位移的置信区域提供了一个有利的框架.
- 开发的方法比RTCL等现有技术提供了更好的准确性和紧性.
- 这项研究有助于在平面运动分析中更可靠地量化不确定性.
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