三旋转自由度激光经纬仪的扫描数学模型

The Scanning Mathematical Models of a Laser-theodolite with Three Freedoms of Rotation

首先给出二旋转自由度激光经纬仪的铅垂面扫描方程和圆锥面扫描方程的推演结果 ,然后着重推演三旋转自由度激光经纬仪的扫描方程 ,其中包括绕竖轴 (主轴 )旋转生成的单叶双曲面扫描方程、绕横轴 (副轴 )旋转的单叶双曲面扫描方程以及绕视准轴 (第三轴 )旋转的给定方位的平面扫描方程。

The structured light industrial surveying with high accuracy (e.g.±1mm) based on laser theodolite with three freedoms of rotation is particularly applicable for texture_lacking objects,such as capacity of oil tanker,external form of airplane and ship etc.As we know that certain instrument (such as Leica Profiler 4000) can not be used for this kind of objects,because its standard error(±5mm,even more) does not satisfy the accuracy reguirement.In this paper the scanning equation of plumb plane and the scanning equation of circular cone are firstly deduced when the laser theodolite with two freedoms of rotation is used.Then some scanning equations are briefly deduced when the instrument with three freedoms of rotation is used.These equations include the scanning equation of huperbolid of one sheet generated by rotating around the vertical axis(host axis),the scanning equation of huperbolid of one sheet generated by rotating around the horizotal axis(countershaft axis),and the scanning equation of plane for given orientation generated by rotating around the third axis.According to these planes and surfaces of known position and orientation in space,the space coordinates of unknown points could be determinates,and just one angle_measured instrument (or one CCD camera ) is needed.The accuracy obtained by using this system(through the intersection) is much better than the accuracy by using the total station without reflector,(such as TCR,Leica).Furthermore,the system consists of a laser_theodolite,an angle_measured instrument and a portable computer,so it belongs to'toy bricks type'and it is quite cheap.It is also emphasized that the mathematical models in this paper could be used as designing model of certain laser scanning system.