JP2018132451A - Position measurement method and device - Google Patents
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Abstract
Description
本発明は、３Ｄスキャナを用いてトンネルなどの空間の位置を計測する位置計測方法および装置に関するものである。 The present invention relates to a position measurement method and apparatus for measuring the position of a space such as a tunnel using a 3D scanner.
従来、施工中の山岳トンネルの内空変位や沈下の計測等を、３Ｄスキャナを用いて行う方法が知られている。この方法に関連し、本願出願人は特許文献１において「トンネル内における３Ｄスキャナの自己位置推定方法」を既に提案している。これは、図９（１）に示すように、ｘ、ｙ、ｚの直交座標系をもとに施工が行われるトンネル内に、ξ、η、ζの直交座標系の３次元位置データを計測する３Ｄスキャナを、ξ、η軸が水平方向、ζ軸が鉛直方向となるように設置した後、この３Ｄスキャナでトンネル内の位置計測を実施して得られた点群データを特定の軸周りに回転させ、（２）に示すように、グリッドを設けた任意の１方向（例えばξ軸方向）の仮想の面に点群を投影し、（３）、（４）に示すように、そのグリッド内の累積数が最大となる回転角度や、累積したデータが特定の数を超えたグリッドの数が最大となる回転角度から、３Ｄスキャナのξ、η軸とトンネルのｘ、ｙ軸のずれを求め、求めたずれと、トンネル内の既知の座標値を利用して３Ｄスキャナの座標値を推定するものである。 2. Description of the Related Art Conventionally, a method is known in which a 3D scanner is used to measure internal displacement and settlement of a mountain tunnel under construction. In relation to this method, the applicant of the present application has already proposed a “self-position estimation method of a 3D scanner in a tunnel” in Patent Document 1. As shown in FIG. 9 (1), the three-dimensional position data of the orthogonal coordinate system of ξ, η, and ζ is measured in the tunnel where construction is performed based on the orthogonal coordinate system of x, y, and z. After installing the 3D scanner so that the ξ and η axes are in the horizontal direction and the ζ axis in the vertical direction, the point cloud data obtained by measuring the position in the tunnel with this 3D scanner is displayed around a specific axis. , And as shown in (2), a point cloud is projected onto a virtual plane in any one direction (for example, the ξ-axis direction) provided with a grid, and as shown in (3) and (4), 3D scanner ξ, η axis and tunnel x, y axis deviation from the rotation angle at which the cumulative number in the grid is the maximum or the rotation angle at which the number of grids where the accumulated data exceeds a specific number is the maximum 3D scanner coordinate value is estimated using the calculated deviation and the known coordinate value in the tunnel. Is shall.
しかしながら、上記の方法は３Ｄスキャナの座標系（ξηζ）のうち、ξ、η軸が水平方向を、ζ軸が鉛直方向を向いている必要があるという制限があった。 However, the above method has a limitation in the coordinate system (ξηζ) of the 3D scanner that the ξ and η axes need to be in the horizontal direction and the ζ axis needs to be in the vertical direction.
一方、本願出願人は、上記の技術に関連して「トンネル内における３Ｄスキャナの設置方法」を発明したところであり、これについての特許出願を現在検討中である。この方法では、図１０に示すように、３Ｄスキャナにより得られた点群データを任意の角度に回転させ、任意の１方向の仮想の面に点群データを投影した際に、投影された点群データを全て覆う長方形の面積Ａηζが最小となる場合の回転角度を用いて点群データを回転することにより、トンネルの進行方向（ｘ軸方向）の１軸と３Ｄスキャナの１軸の方向を一致させている。 On the other hand, the applicant of the present application has invented “a method for installing a 3D scanner in a tunnel” in relation to the above-described technique, and is currently considering a patent application on this. In this method, as shown in FIG. 10, when the point cloud data obtained by the 3D scanner is rotated to an arbitrary angle and the point cloud data is projected onto a virtual plane in any one direction, the projected points are projected. By rotating the point group data using the rotation angle when the area Aηζ of the rectangle covering all the group data is minimum, the direction of one axis of the tunnel traveling direction (x-axis direction) and the direction of one axis of the 3D scanner are changed. Match.
さらに、図１１に示すように、点群データをトンネルの進行方向の軸周りに任意の角度で回転させ、上記と同じ仮想の面に投影し、トンネルの断面を左右で２等分した際に、各点群を全て覆う長方形の面積の差の絶対値｜Ａηζ,h−Ａηζ,1｜が最小となる場合の回転角度を用いて、点群データをトンネルの進行方向の軸周りに回転することにより、トンネルの鉛直方向（ｚ軸方向）と側壁方向（ｙ軸方向）の２軸と３Ｄスキャナの２軸の方向を一致させている。 Furthermore, as shown in FIG. 11, when the point cloud data is rotated at an arbitrary angle around the axis of the tunnel traveling direction and projected onto the same virtual plane as described above, the tunnel cross section is divided into two equal parts on the left and right. The point cloud data is rotated around the axis in the tunnel traveling direction using the rotation angle when the absolute value | Aηζ , h− Aηζ , 1 | of the rectangular area covering all the point clouds is minimum. Thus, the two axes in the vertical direction (z-axis direction) and the side wall direction (y-axis direction) of the tunnel and the two axes of the 3D scanner are matched.
この方法は、上下非対称で左右対称の断面の空間（トンネル）では有効であるが、図１２に示すように、楕円や長方形のように上下左右対称の断面の空間では、任意の角度で空間の進行方向周りに点群データを回転させた場合、どの角度でも左右の長方形の面積の差｜Ａηζ,h−Ａηζ,1｜が０となり、空間の鉛直方向と側壁方向の２軸と３Ｄスキャナの２軸を一致させることができないという問題がある。 This method is effective in a space (tunnel) having a vertically symmetrical asymmetric cross section, but as shown in FIG. 12, in a space having a vertically symmetric cross section such as an ellipse or a rectangle, the space can be measured at an arbitrary angle. When the point cloud data is rotated around the traveling direction, the difference between the areas of the left and right rectangles | Aηζ , h− Aηζ , 1 | becomes 0 at any angle. There is a problem that the two axes cannot be matched.
このため、上下非対称で左右対称の内空断面のトンネルのみならず、上下左右対称の内空断面のトンネルであっても、トンネルの鉛直方向と側壁方向の２軸と３Ｄスキャナの２軸を一致させることができる技術が求められていた。 For this reason, not only a tunnel with an asymmetrical vertical cross section, but also a tunnel with a symmetrical vertical cross section, the vertical axis and side wall direction of the tunnel coincide with the two axes of the 3D scanner. There was a need for a technology that could be used.
本発明は、上記に鑑みてなされたものであって、上下左右対称の断面をもつ空間内に任意の姿勢で設置した３Ｄスキャナの座標軸を、空間の座標軸に合わせることのできる位置計測方法および装置を提供することを目的とする。 The present invention has been made in view of the above, and a position measuring method and apparatus capable of aligning the coordinate axis of a 3D scanner installed in an arbitrary posture in a space having a vertically and horizontally symmetrical cross section with the coordinate axis of the space. The purpose is to provide.
上記した課題を解決し、目的を達成するために、本発明に係る位置計測方法は、ｘ軸、ｙ軸、ｚ軸の直交座標系により規定された空間内に設置され、この空間を区画形成する面の３次元位置データをξ軸、η軸、ζ軸の直交座標系の座標値で取得することによって空間の位置計測を行う３Ｄスキャナと、３Ｄスキャナの計測結果から所定の軸合わせを行うための演算を行う演算装置とを備えた位置計測装置を用いて空間の位置計測を行う方法であって、ｘ軸を軸方向とする空間内に３Ｄスキャナを設置した後、３Ｄスキャナで空間内を位置計測するステップと、３Ｄスキャナの位置計測結果である点群データを所定の仮想の面に投影した投影像に基づいて、空間のｘ軸と３Ｄスキャナのξ軸を一致させるための回転角度を求め、求めた回転角度でη軸、ζ軸周りにξ軸を回転させる第１の座標変換を行って、空間のｘ軸と３Ｄスキャナのξ軸を一致させるステップと、第１の座標変換後の点群データを所定の仮想の面に投影した投影像に基づいて、空間のｙ軸、ｚ軸と３Ｄスキャナのη軸、ζ軸をそれぞれ一致させるための回転角度を求め、求めた回転角度でξ軸周りにη軸、ζ軸を回転させる第２の座標変換を行って、空間のｙ軸、ｚ軸と３Ｄスキャナのη軸、ζ軸をそれぞれ一致させるステップと、第２の座標変換後の点群データを、空間の直交座標系における３Ｄスキャナの位置計測結果として推定するステップとを備えることを特徴とする。 In order to solve the above-described problems and achieve the object, the position measurement method according to the present invention is installed in a space defined by an orthogonal coordinate system of x-axis, y-axis, and z-axis, and this space is partitioned. The 3D position data of the surface to be acquired by the coordinate values of the orthogonal coordinate system of the ξ, η, and ζ axes, and a predetermined axis alignment is performed from the measurement result of the 3D scanner. A method for measuring the position of a space using a position measurement device including a calculation device for performing a calculation for the image, wherein the 3D scanner is installed in the space with the x-axis as the axial direction, and then the space is measured by the 3D scanner. And a rotation angle for matching the x-axis of the space and the ξ-axis of the 3D scanner based on a projection image obtained by projecting point cloud data as a position measurement result of the 3D scanner onto a predetermined virtual plane The rotation angle obtained performing a first coordinate transformation of rotating the ξ axis around the η axis and the ζ axis to match the x axis of the space with the ξ axis of the 3D scanner; Based on the projected image projected on the virtual plane, the rotation angle for matching the y-axis and z-axis of the space with the η-axis and ζ-axis of the 3D scanner is obtained, and the η-axis around the ξ axis at the calculated rotation angle , Performing a second coordinate transformation that rotates the ζ axis to match the y-axis and z-axis of the space with the η-axis and ζ-axis of the 3D scanner, and the point cloud data after the second coordinate transformation, And a step of estimating the position measurement result of the 3D scanner in the orthogonal coordinate system of the space.
また、本発明に係る他の位置計測方法は、上述した発明において、第１の座標変換は、３Ｄスキャナの位置計測結果である点群データをξ軸に垂直なηζ平面に投影した場合において、投影された点群データを包含して各辺がη軸とζ軸に平行で各辺の長さが最小となる長方形であって、この点群データをη軸、ζ軸周りにそれぞれ回転して得られる長方形の面積が最小となるときの回転角度θη、θζを求めた後、位置計測結果である点群データについて、求めた回転角度θη、θζでη軸、ζ軸周りにξ軸を回転させる座標変換であり、第２の座標変換は、第１の座標変換後の点群データをη軸に垂直なξζ平面に投影した場合において、投影された点群データを包含して各辺がξ軸とζ軸に平行で各辺の長さが最小となる長方形であって、この点群データをξ軸周りに回転して得られる長方形の面積が最小となるときの回転角度θξを求めた後、第１の座標変換後の点群データについて、求めた回転角度θξでξ軸周りにη軸、ζ軸を回転させる座標変換であることを特徴とする。 Further, in another position measurement method according to the present invention, in the above-described invention, the first coordinate conversion is performed when the point cloud data that is the position measurement result of the 3D scanner is projected onto the ηζ plane perpendicular to the ξ axis. A rectangle that includes the projected point cloud data, each side is parallel to the η axis and the ζ axis, and the length of each side is minimum, and the point cloud data is rotated around the η axis and the ζ axis, respectively. After obtaining the rotation angles θη and θζ when the area of the rectangle obtained in this way is minimum, the point cloud data as the position measurement result is obtained with the rotation angles θη and θζ as the η axis and the ξ axis around the ζ axis. The second coordinate transformation includes the projected point cloud data and includes each side when the point coordinate data after the first coordinate transformation is projected onto the ξζ plane perpendicular to the η axis. Is a rectangle that is parallel to the ξ and ζ axes and has the minimum length of each side. The rotation angle θξ when the area of the rectangle obtained by rotating the data about the ξ axis is minimum is obtained, and the point cloud data after the first coordinate conversion is obtained around the ξ axis at the obtained rotation angle θξ. The coordinate conversion is to rotate the η axis and ζ axis.
また、本発明に係る位置計測装置は、ｘ軸、ｙ軸、ｚ軸の直交座標系により規定された空間内に設置され、この空間を区画形成する面の３次元位置データをξ軸、η軸、ζ軸の直交座標系の座標値で取得することによって空間の位置計測を行う３Ｄスキャナと、３Ｄスキャナの計測結果から所定の軸合わせを行うための演算を行う演算装置とを備えた位置計測装置であって、演算装置は、ｘ軸を軸方向とする空間内に設置した３Ｄスキャナの位置計測結果である点群データを所定の仮想の面に投影した投影像に基づいて、空間のｘ軸と３Ｄスキャナのξ軸を一致させるための回転角度を求め、求めた回転角度でη軸、ζ軸周りにξ軸を回転させる第１の座標変換を行って、空間のｘ軸と３Ｄスキャナのξ軸を一致させる手段と、第１の座標変換後の点群データを所定の仮想の面に投影した投影像に基づいて、空間のｙ軸、ｚ軸と３Ｄスキャナのη軸、ζ軸をそれぞれ一致させるための回転角度を求め、求めた回転角度でξ軸周りにη軸、ζ軸を回転させる第２の座標変換を行って、空間のｙ軸、ｚ軸と３Ｄスキャナのη軸、ζ軸をそれぞれ一致させる手段と、第２の座標変換後の点群データを、空間の直交座標系における３Ｄスキャナの位置計測結果として推定する手段とを備えることを特徴とする。 In addition, the position measuring apparatus according to the present invention is installed in a space defined by an x-axis, y-axis, and z-axis orthogonal coordinate system, and the three-dimensional position data of a surface that defines the space is converted into ξ-axis, η A position provided with a 3D scanner that measures the position of the space by acquiring the coordinate values in the Cartesian coordinate system of the axis and the ζ axis, and an arithmetic device that performs a calculation for performing predetermined axis alignment from the measurement result of the 3D scanner A measurement device, the arithmetic device, based on a projection image obtained by projecting point cloud data, which is a position measurement result of a 3D scanner installed in a space having an x-axis as an axial direction, onto a predetermined virtual plane, A rotation angle for making the x axis coincide with the ξ axis of the 3D scanner is obtained, and the first coordinate transformation is performed by rotating the ξ axis around the η axis and the ζ axis at the obtained rotation angle, and the x axis of the space and the 3D Means for matching the ξ-axis of the scanner and after the first coordinate transformation Based on a projection image obtained by projecting point cloud data onto a predetermined virtual plane, a rotation angle for matching the y-axis and z-axis of the space with the η-axis and ζ-axis of the 3D scanner is obtained, and the calculated rotation angle is used. means for performing second coordinate transformation to rotate the η axis and ζ axis around the ξ axis so that the y axis and z axis of the space coincide with the η axis and ζ axis of the 3D scanner, and after the second coordinate transformation And a means for estimating the point cloud data as a position measurement result of the 3D scanner in the orthogonal coordinate system of the space.
また、本発明に係る他の位置計測装置は、上述した発明において、第１の座標変換は、３Ｄスキャナの位置計測結果である点群データをξ軸に垂直なηζ平面に投影した場合において、投影された点群データを包含して各辺がη軸とζ軸に平行で各辺の長さが最小となる長方形であって、この点群データをη軸、ζ軸周りにそれぞれ回転して得られる長方形の面積が最小となるときの回転角度θη、θζを求めた後、位置計測結果である点群データについて、求めた回転角度θη、θζでη軸、ζ軸周りにξ軸を回転させる座標変換であり、第２の座標変換は、第１の座標変換後の点群データをη軸に垂直なξζ平面に投影した場合において、投影された点群データを包含して各辺がξ軸とζ軸に平行で各辺の長さが最小となる長方形であって、この点群データをξ軸周りに回転して得られる長方形の面積が最小となるときの回転角度θξを求めた後、第１の座標変換後の点群データについて、求めた回転角度θξでξ軸周りにη軸、ζ軸を回転させる座標変換であることを特徴とする。 Further, in the position measurement apparatus according to the present invention, in the above-described invention, the first coordinate conversion is performed when the point cloud data that is the position measurement result of the 3D scanner is projected onto the ηζ plane perpendicular to the ξ axis. A rectangle that includes the projected point cloud data, each side is parallel to the η axis and the ζ axis, and the length of each side is minimum, and the point cloud data is rotated around the η axis and the ζ axis, respectively. After obtaining the rotation angles θη and θζ when the area of the rectangle obtained in this way is minimum, the point cloud data as the position measurement result is obtained with the rotation angles θη and θζ as the η axis and the ξ axis around the ζ axis. The second coordinate transformation includes the projected point cloud data and includes each side when the point coordinate data after the first coordinate transformation is projected onto the ξζ plane perpendicular to the η axis. Is a rectangle that is parallel to the ξ and ζ axes and has the minimum length of each side. The rotation angle θξ when the area of the rectangle obtained by rotating the data about the ξ axis is minimum is obtained, and the point cloud data after the first coordinate conversion is obtained around the ξ axis at the obtained rotation angle θξ. The coordinate conversion is to rotate the η axis and ζ axis.
本発明に係る位置計測方法によれば、ｘ軸、ｙ軸、ｚ軸の直交座標系により規定された空間内に設置され、この空間を区画形成する面の３次元位置データをξ軸、η軸、ζ軸の直交座標系の座標値で取得することによって空間の位置計測を行う３Ｄスキャナと、３Ｄスキャナの計測結果から所定の軸合わせを行うための演算を行う演算装置とを備えた位置計測装置を用いて空間の位置計測を行う方法であって、ｘ軸を軸方向とする空間内に３Ｄスキャナを設置した後、３Ｄスキャナで空間内を位置計測するステップと、３Ｄスキャナの位置計測結果である点群データを所定の仮想の面に投影した投影像に基づいて、空間のｘ軸と３Ｄスキャナのξ軸を一致させるための回転角度を求め、求めた回転角度でη軸、ζ軸周りにξ軸を回転させる第１の座標変換を行って、空間のｘ軸と３Ｄスキャナのξ軸を一致させるステップと、第１の座標変換後の点群データを所定の仮想の面に投影した投影像に基づいて、空間のｙ軸、ｚ軸と３Ｄスキャナのη軸、ζ軸をそれぞれ一致させるための回転角度を求め、求めた回転角度でξ軸周りにη軸、ζ軸を回転させる第２の座標変換を行って、空間のｙ軸、ｚ軸と３Ｄスキャナのη軸、ζ軸をそれぞれ一致させるステップと、第２の座標変換後の点群データを、空間の直交座標系における３Ｄスキャナの位置計測結果として推定するステップとを備えるので、空間の断面形状が上下非対称で左右対称の場合のみならず、上下左右対称の場合であっても、この空間内に任意の姿勢で設置した３Ｄスキャナの座標軸を、空間の座標軸に合わせることが可能となる。このため、位置計測を効率よく実施することができるという効果を奏する。 According to the position measuring method according to the present invention, the three-dimensional position data of the plane that is installed in the space defined by the orthogonal coordinate system of the x-axis, y-axis, and z-axis and that defines the space is converted into the ξ-axis, η A position provided with a 3D scanner that measures the position of the space by acquiring the coordinate values in the Cartesian coordinate system of the axis and the ζ axis, and an arithmetic device that performs a calculation for performing predetermined axis alignment from the measurement result of the 3D scanner A method for measuring the position of a space using a measuring device, the step of measuring the position in the space with a 3D scanner after the 3D scanner is installed in a space having the x-axis as an axial direction, and the position measurement of the 3D scanner Based on a projection image obtained by projecting the resulting point cloud data on a predetermined virtual plane, a rotation angle for matching the x-axis of the space with the ξ axis of the 3D scanner is obtained, and the η-axis, ζ A first rotating ξ axis around the axis Based on the projected image obtained by projecting the point group data after the first coordinate transformation on the predetermined virtual plane, the target transformation is performed to match the x axis of the space with the ξ axis of the 3D scanner. A rotation angle for making the axis, the z-axis and the η-axis and ζ-axis of the 3D scanner coincide with each other, and performing a second coordinate transformation that rotates the η-axis and the ζ-axis around the ξ-axis at the obtained rotation angle, The step of matching the y-axis and z-axis of the space with the η-axis and ζ-axis of the 3D scanner, respectively, and the point cloud data after the second coordinate conversion are estimated as the position measurement result of the 3D scanner in the space orthogonal coordinate system. Steps, the coordinate axis of the 3D scanner installed in an arbitrary posture in this space can be used not only when the cross-sectional shape of the space is vertically asymmetric and left-right symmetric but also when it is vertically and horizontally symmetric. It becomes possible to match the coordinate axisFor this reason, there exists an effect that position measurement can be implemented efficiently.
また、本発明に係る他の位置計測方法によれば、第１の座標変換は、３Ｄスキャナの位置計測結果である点群データをξ軸に垂直なηζ平面に投影した場合において、投影された点群データを包含して各辺がη軸とζ軸に平行で各辺の長さが最小となる長方形であって、この点群データをη軸、ζ軸周りにそれぞれ回転して得られる長方形の面積が最小となるときの回転角度θη、θζを求めた後、位置計測結果である点群データについて、求めた回転角度θη、θζでη軸、ζ軸周りにξ軸を回転させる座標変換であり、第２の座標変換は、第１の座標変換後の点群データをη軸に垂直なξζ平面に投影した場合において、投影された点群データを包含して各辺がξ軸とζ軸に平行で各辺の長さが最小となる長方形であって、この点群データをξ軸周りに回転して得られる長方形の面積が最小となるときの回転角度θξを求めた後、第１の座標変換後の点群データについて、求めた回転角度θξでξ軸周りにη軸、ζ軸を回転させる座標変換であるので、位置計測処理の効率を上げることができるという効果を奏する。 According to another position measurement method according to the present invention, the first coordinate transformation is projected when the point cloud data that is the position measurement result of the 3D scanner is projected onto the ηζ plane perpendicular to the ξ axis. A rectangle that includes point cloud data, each side is parallel to the η axis and ζ axis, and the length of each side is minimum, and is obtained by rotating the point cloud data around the η axis and the ζ axis, respectively. Coordinates for rotating the ξ axis around the η axis and the ζ axis at the obtained rotation angles θη and θζ for the point cloud data as the position measurement result after calculating the rotation angles θη and θζ when the rectangular area is minimized In the second coordinate transformation, when the point group data after the first coordinate transformation is projected onto the ξζ plane perpendicular to the η axis, each side includes the projected point group data and the ξ axis The rectangle is parallel to the ζ axis and the length of each side is minimum, and this point cloud data is rotated around the ξ axis. Rotate the η and ζ axes around the ξ axis with the calculated rotation angle θξ for the point group data after the first coordinate transformation. Therefore, the position conversion processing efficiency can be increased.
また、本発明に係る位置計測装置によれば、ｘ軸、ｙ軸、ｚ軸の直交座標系により規定された空間内に設置され、この空間を区画形成する面の３次元位置データをξ軸、η軸、ζ軸の直交座標系の座標値で取得することによって空間の位置計測を行う３Ｄスキャナと、３Ｄスキャナの計測結果から所定の軸合わせを行うための演算を行う演算装置とを備えた位置計測装置であって、演算装置は、ｘ軸を軸方向とする空間内に設置した３Ｄスキャナの位置計測結果である点群データを所定の仮想の面に投影した投影像に基づいて、空間のｘ軸と３Ｄスキャナのξ軸を一致させるための回転角度を求め、求めた回転角度でη軸、ζ軸周りにξ軸を回転させる第１の座標変換を行って、空間のｘ軸と３Ｄスキャナのξ軸を一致させる手段と、第１の座標変換後の点群データを所定の仮想の面に投影した投影像に基づいて、空間のｙ軸、ｚ軸と３Ｄスキャナのη軸、ζ軸をそれぞれ一致させるための回転角度を求め、求めた回転角度でξ軸周りにη軸、ζ軸を回転させる第２の座標変換を行って、空間のｙ軸、ｚ軸と３Ｄスキャナのη軸、ζ軸をそれぞれ一致させる手段と、第２の座標変換後の点群データを、空間の直交座標系における３Ｄスキャナの位置計測結果として推定する手段とを備えるので、空間の断面形状が上下非対称で左右対称の場合のみならず、上下左右対称の場合であっても、この空間内に任意の姿勢で設置した３Ｄスキャナの座標軸を、空間の座標軸に合わせることが可能となる。このため、位置計測を効率よく実施することができるという効果を奏する。 Further, according to the position measuring apparatus of the present invention, the three-dimensional position data of the surface that is installed in the space defined by the orthogonal coordinate system of the x-axis, y-axis, and z-axis and forms the space is converted to the ξ-axis. , Η-axis, and ζ-axis orthogonal coordinate system to obtain a 3D scanner that measures the position of the space, and an arithmetic unit that performs a calculation for performing predetermined axis alignment from the measurement result of the 3D scanner The position measurement device is a computing device based on a projection image obtained by projecting point cloud data, which is a position measurement result of a 3D scanner installed in a space having the x-axis as an axial direction, onto a predetermined virtual plane. A rotation angle for matching the x-axis of the space with the ξ-axis of the 3D scanner is obtained, and the first coordinate conversion is performed by rotating the ξ-axis around the η-axis and the ζ-axis at the obtained rotation angle. Means for matching the ξ axis of the 3D scanner and the first coordinate change Based on the projection image obtained by projecting the converted point cloud data onto a predetermined virtual plane, the rotation angles for matching the y-axis and z-axis of the space with the η-axis and ζ-axis of the 3D scanner are obtained and obtained. A second coordinate transformation for rotating the η-axis and the ζ-axis around the ξ-axis at a rotation angle so as to match the y-axis and z-axis of the space with the η-axis and ζ-axis of the 3D scanner, respectively, Means for estimating the point group data after coordinate transformation as a position measurement result of the 3D scanner in the space's orthogonal coordinate system. Even in this case, the coordinate axis of the 3D scanner installed in an arbitrary posture in this space can be matched with the coordinate axis of the space. For this reason, there exists an effect that position measurement can be implemented efficiently.
また、本発明に係る他の位置計測装置によれば、第１の座標変換は、３Ｄスキャナの位置計測結果である点群データをξ軸に垂直なηζ平面に投影した場合において、投影された点群データを包含して各辺がη軸とζ軸に平行で各辺の長さが最小となる長方形であって、この点群データをη軸、ζ軸周りにそれぞれ回転して得られる長方形の面積が最小となるときの回転角度θη、θζを求めた後、位置計測結果である点群データについて、求めた回転角度θη、θζでη軸、ζ軸周りにξ軸を回転させる座標変換であり、第２の座標変換は、第１の座標変換後の点群データをη軸に垂直なξζ平面に投影した場合において、投影された点群データを包含して各辺がξ軸とζ軸に平行で各辺の長さが最小となる長方形であって、この点群データをξ軸周りに回転して得られる長方形の面積が最小となるときの回転角度θξを求めた後、第１の座標変換後の点群データについて、求めた回転角度θξでξ軸周りにη軸、ζ軸を回転させる座標変換であるので、位置計測処理の効率を上げることができるという効果を奏する。 According to another position measurement apparatus of the present invention, the first coordinate transformation is projected when the point cloud data that is the position measurement result of the 3D scanner is projected onto the ηζ plane perpendicular to the ξ axis. A rectangle that includes point cloud data, each side is parallel to the η axis and ζ axis, and the length of each side is minimum, and is obtained by rotating the point cloud data around the η axis and the ζ axis, respectively. Coordinates for rotating the ξ axis around the η axis and the ζ axis at the obtained rotation angles θη and θζ for the point cloud data as the position measurement result after calculating the rotation angles θη and θζ when the rectangular area is minimized In the second coordinate transformation, when the point group data after the first coordinate transformation is projected onto the ξζ plane perpendicular to the η axis, each side includes the projected point group data and the ξ axis The rectangle is parallel to the ζ axis and the length of each side is minimum, and this point cloud data is rotated around the ξ axis. Rotate the η and ζ axes around the ξ axis with the calculated rotation angle θξ for the point group data after the first coordinate transformation. Therefore, the position conversion processing efficiency can be increased.
上述したように、本願出願人が特許出願を検討中の「トンネル内における３Ｄスキャナの設置方法」の発明では、３Ｄスキャナにより得られた位置計測結果の点群データを投影する仮想の面が１種類であった。これに対し、本発明では、空間（トンネル）の内部に任意の姿勢で設置した３Ｄスキャナにより得られる位置計測結果の点群データを、２種類の仮想の面に投影する。そして、２種類の仮想の面に投影された点群データを全て覆う長方形の面積が最小となる場合の回転角度を用いて、点群データを回転する。これにより、上記の従来の方法では不可能であった、上下左右対称の断面をもつ空間と３Ｄスキャナの３軸の方向を一致させることが可能となる。これにより、上下左右対称の断面をもつ空間内での３Ｄスキャナの軸合わせができる。また、本発明による方法は特許出願を検討中の上記の方法を包含するものなので、従来の方法で軸を一致させることが可能であった、上下非対称で左右対称の断面をもつ空間でも、空間と３Ｄスキャナの３軸の方向を一致させることが可能となる。 As described above, in the invention of the “method of installing a 3D scanner in a tunnel” that the applicant of the present application is considering a patent application, there is one virtual plane on which point cloud data of the position measurement result obtained by the 3D scanner is projected. It was a kind. On the other hand, in the present invention, point cloud data of a position measurement result obtained by a 3D scanner installed in an arbitrary posture inside a space (tunnel) is projected onto two types of virtual surfaces. Then, the point cloud data is rotated using the rotation angle when the area of the rectangle covering all the point cloud data projected on the two types of virtual surfaces is minimized. As a result, it is possible to make the three-axis directions of the 3D scanner coincide with the space having a vertically and horizontally symmetrical cross section, which is impossible with the above-described conventional method. Thereby, the axis alignment of the 3D scanner can be performed in a space having a symmetrical cross section. In addition, since the method according to the present invention includes the above-mentioned method under consideration of patent applications, even in a space having a vertically asymmetrical and left-right symmetric cross-section, the axes can be matched by the conventional method. And the 3 axis directions of the 3D scanner can be matched.
以下に、本発明に係る位置計測方法および装置の実施の形態について、施工中のトンネルを模した上下左右対称の長方形断面の空間に位置計測装置を設置した場合を例にとり、図面に基づいて詳細に説明する。なお、この実施の形態によりこの発明が限定されるものではない。 Hereinafter, the embodiment of the position measuring method and apparatus according to the present invention will be described in detail with reference to the drawings, taking as an example the case where the position measuring apparatus is installed in a space of a rectangular cross section that is vertically and horizontally symmetrical to simulate a tunnel under construction. Explained. Note that the present invention is not limited to the embodiments.
図１に示すように、本発明に係る位置計測装置１００は、掘削面の３次元位置データを取得して施工中のトンネル（空間）の位置計測を行う３Ｄスキャナ１と、３Ｄスキャナ１の計測結果から座標軸合わせを行い、この軸合わせに基づいて自己位置を推定するための演算装置２と、位置計測センサー３と、三脚４とを備える。 As shown in FIG. 1, a position measuring apparatus 100 according to the present invention acquires a three-dimensional position data of an excavation surface and measures a position of a tunnel (space) under construction, and a measurement by the 3D scanner 1 Coordinate axes are aligned from the results, and an arithmetic device 2, a position measurement sensor 3, and a tripod 4 for estimating the self-position based on the axis alignment are provided.
３Ｄスキャナ１は対象物の位置計測を行った際に、３次元の位置情報を持った点群データを取得できる。これは３Ｄスキャナ１の位置計測センサー３の中心を原点Ｏとし、Ｏを通るξ、η、ζ軸からなる直交座標系をもとにした情報である。 The 3D scanner 1 can acquire point cloud data having three-dimensional position information when measuring the position of the object. This is information based on an orthogonal coordinate system including the center of the position measurement sensor 3 of the 3D scanner 1 as the origin O and passing through O and the ξ, η, and ζ axes.
図２に示すように、３Ｄスキャナ１は三脚４を用いて長方形断面のトンネル内に任意の姿勢で設置する。ここで、トンネルはｘ軸、ｙ軸、ｚ軸の直交座標系をもとに施工され、ｘ軸をトンネル軸方向としている。 As shown in FIG. 2, the 3D scanner 1 is installed in an arbitrary posture in a tunnel having a rectangular cross section using a tripod 4. Here, the tunnel is constructed based on the orthogonal coordinate system of the x-axis, y-axis, and z-axis, and the x-axis is the tunnel axis direction.
演算装置２は、第１手段と第２手段と第３手段とを有している。 The computing device 2 has first means, second means, and third means.
第１手段は、３Ｄスキャナ１の位置計測結果である点群データを所定の仮想の面に投影した投影像に基づいて、トンネルのｘ軸と３Ｄスキャナ１のξ軸を一致させるための回転角度を求め、求めた回転角度でη軸、ζ軸周りにξ軸を回転させる第１の座標変換を行って、トンネルのｘ軸と３Ｄスキャナ１のξ軸を一致させるものである。 The first means is a rotation angle for matching the x-axis of the tunnel and the ξ-axis of the 3D scanner 1 based on a projection image obtained by projecting point cloud data as a position measurement result of the 3D scanner 1 onto a predetermined virtual plane. The first coordinate transformation is performed by rotating the ξ axis about the η axis and the ζ axis at the determined rotation angle, and the x axis of the tunnel and the ξ axis of the 3D scanner 1 are made to coincide.
第２手段は、第１の座標変換後の点群データを所定の仮想の面に投影した投影像に基づいて、トンネルのｙ軸、ｚ軸と３Ｄスキャナ１のη軸、ζ軸をそれぞれ一致させるための回転角度を求め、求めた回転角度でξ軸周りにη軸、ζ軸を回転させる第２の座標変換を行って、トンネルのｙ軸、ｚ軸と３Ｄスキャナ１のη軸、ζ軸をそれぞれ一致させるものである。 The second means matches the y-axis and z-axis of the tunnel with the η-axis and ζ-axis of the 3D scanner 1 based on the projection image obtained by projecting the point group data after the first coordinate conversion onto a predetermined virtual surface. The second rotation is performed by rotating the η-axis and the ζ-axis around the ξ axis at the calculated rotation angle, and the tunnel y-axis and z-axis and the η-axis of the 3D scanner 1 and ζ. Each axis is matched.
第３手段は、第２の座標変換後の点群データを、トンネルの直交座標系における３Ｄスキャナ１の位置計測結果として推定するものである。これにより、３Ｄスキャナ１の位置計測結果は、トンネルの直交座標系で表現される。 The third means estimates the point group data after the second coordinate conversion as a position measurement result of the 3D scanner 1 in the orthogonal coordinate system of the tunnel. Thereby, the position measurement result of the 3D scanner 1 is expressed in the orthogonal coordinate system of the tunnel.
ここで、第１の座標変換は、３Ｄスキャナ１の位置計測結果である点群データをξ軸に垂直なηζ平面に投影した場合において、投影された点群データを包含して各辺がη軸とζ軸に平行で各辺の長さが最小となる長方形であって、この点群データをη軸、ζ軸周りにそれぞれ回転して得られる長方形の面積が最小となるときの回転角度θη、θζを求めた後、位置計測結果である点群データについて、求めた回転角度θη、θζでη軸、ζ軸周りにξ軸を回転させる座標変換である。 Here, in the first coordinate transformation, when the point cloud data that is the position measurement result of the 3D scanner 1 is projected onto the ηζ plane perpendicular to the ξ axis, each side includes the projected point cloud data and η A rotation angle when the area of the rectangle obtained by rotating the point cloud data around the η axis and the ζ axis is the minimum, which is parallel to the axis and the ζ axis and the length of each side is minimum. After obtaining θη and θζ, coordinate conversion is performed by rotating the ξ axis around the η axis and the ζ axis at the obtained rotation angles θη and θζ with respect to the point cloud data as the position measurement result.
また、第２の座標変換は、第１の座標変換後の点群データをη軸に垂直なξζ平面に投影した場合において、投影された点群データを包含して各辺がξ軸とζ軸に平行で各辺の長さが最小となる長方形であって、この点群データをξ軸周りに回転して得られる長方形の面積が最小となるときの回転角度θξを求めた後、第１の座標変換後の点群データについて、求めた回転角度θξでξ軸周りにη軸、ζ軸を回転させる座標変換である。 Further, the second coordinate transformation includes the projected point group data when each point group data after the first coordinate transformation is projected onto the ξζ plane perpendicular to the η axis, and each side has the ξ axis and ζ After obtaining the rotation angle θξ when the area of the rectangle obtained by rotating the point cloud data around the ξ axis is the minimum, the rotation angle θξ is obtained by calculating the rotation angle θξ. This is a coordinate transformation in which the η axis and the ζ axis are rotated around the ξ axis at the obtained rotation angle θξ with respect to the point group data after one coordinate transformation.
本実施の形態によれば、トンネルの内空断面の形状が上下非対称で左右対称の場合のみならず、上下左右対称の場合であっても、３Ｄスキャナ１の座標軸とトンネルの座標軸の軸合わせが可能である。 According to the present embodiment, the alignment of the coordinate axis of the 3D scanner 1 and the coordinate axis of the tunnel is performed not only in the case where the shape of the inner cross section of the tunnel is vertically asymmetric and left-right symmetric but also in the case of vertical and left-right symmetric. Is possible.
次に、本発明による３Ｄスキャナ１の軸合わせ方法の具体的な手順について、図３Ａ、図３Ｂのフローチャートを参照しながら説明する。図３Ａに示される前半のフロー（ステップＳ１００）が上記の従来の方法に相当する基本的なフロー、図３Ｂに示される後半のフロー（ステップＳ２００）が本発明の特徴的なフローである。 Next, a specific procedure of the axis alignment method of the 3D scanner 1 according to the present invention will be described with reference to the flowcharts of FIGS. 3A and 3B. The first half flow (step S100) shown in FIG. 3A is a basic flow corresponding to the above-described conventional method, and the second half flow (step S200) shown in FIG. 3B is a characteristic flow of the present invention.
（基本的なフロー）
まず、前半の基本的なフロー（ステップＳ１００）を説明する。このフローは、長方形断面の空間のｘ軸と３Ｄスキャナのξ軸を一致させるためのものである。
(Basic flow)
First, the basic flow of the first half (step S100) will be described. This flow is for making the x-axis of the rectangular cross-section space coincide with the ξ-axis of the 3D scanner.
図３Ａに示すように、最初に、３Ｄスキャナ１を長方形断面の空間内に任意の姿勢で設置する（ステップＳ１）。図４に、長方形断面の空間内への３Ｄスキャナ１の設置例を示す。長方形断面の空間は進行方向（トンネル軸方向）がｘ軸、側面方向がｙ軸、鉛直方向がｚ軸方向である直交座標系をもつと仮定する。 As shown in FIG. 3A, first, the 3D scanner 1 is installed in an arbitrary posture in a rectangular cross-section space (step S1). FIG. 4 shows an installation example of the 3D scanner 1 in a space having a rectangular cross section. The space of the rectangular cross section is assumed to have an orthogonal coordinate system in which the traveling direction (tunnel axis direction) is the x axis, the side surface direction is the y axis, and the vertical direction is the z axis direction.
続いて、３Ｄスキャナ１を用いて長方形断面の空間内の位置計測を実施する（ステップＳ２）。これにより、図５に示すような点群データが得られる。 Subsequently, position measurement in a rectangular cross-section space is performed using the 3D scanner 1 (step S2). Thereby, point cloud data as shown in FIG. 5 is obtained.
次に、以下のステップＳ３〜Ｓ１０の処理により、長方形断面の空間のｘ軸と３Ｄスキャナのξ軸を一致させるための回転角度θη、θζ（°）を求める。 Next, rotation angles θη and θζ (°) for matching the x-axis of the rectangular cross-section space and the ξ-axis of the 3D scanner are obtained by the following steps S3 to S10.
まず、図６（ａ）に示すように、位置計測結果をηζ平面に投影し、η軸、ζ軸方向の最大値、最小値であるηmax、ηmin、ζmax、ζminを求める（ステップＳ３）。求めたηmax、ηmin、ζmax、ζminで囲まれた長方形の面積Ａηζを求める（ステップＳ４）。 First, as shown in FIG. 6A, the position measurement result is projected onto the ηζ plane, and the maximum value and minimum value η max , η min , ζ max , ζ min that are the η axis and the ζ axis direction are obtained ( Step S3). A rectangular area Aηζ surrounded by the obtained η max , η min , ζ max , ζ min is obtained (step S4).
次に、図６（ｂ）に示すように、点群データを例えばη軸周りに任意の回転角θ（°）で回転させる（ステップＳ５でＹｅｓ）。そして、上記の回転と、Ａηζの導出を任意の角度θで実施後（ステップＳ５、Ｓ６）、Ａηζが最小となるときのθを回転角θη（°）として求める（ステップＳ７）。続いて、求めた回転角θηを用いてη軸周りに位置計測結果である点群データを回転させて座標変換を行う（ステップＳ８）。 Next, as shown in FIG. 6B, the point cloud data is rotated, for example, around the η axis at an arbitrary rotation angle θ (°) (Yes in step S5). Then, after the rotation and the derivation of Aηζ are performed at an arbitrary angle θ (steps S5 and S6), θ when Aηζ is minimized is obtained as a rotation angle θη (°) (step S7). Subsequently, using the obtained rotation angle θη, the point cloud data as the position measurement result is rotated around the η axis to perform coordinate conversion (step S8).
次に、図６（ｃ）に示すように、例えばステップＳ８で座標変換したη軸ではない方のζ軸周りに任意の回転角θで回転させる（ステップＳ９でＹｅｓ）。そして、上記の回転と、Ａηζの導出を任意の角度θで実施後（ステップＳ９、Ｓ６）、Ａηζが最小となるときのθを回転角θζとして求める（ステップＳ１０）。 Next, as shown in FIG. 6C, for example, the rotation is performed at an arbitrary rotation angle θ around the ζ axis that is not the η axis coordinate-converted in step S8 (Yes in step S9). Then, after the rotation and the derivation of Aηζ are performed at an arbitrary angle θ (steps S9 and S6), θ at which Aηζ is minimized is obtained as the rotation angle θζ (step S10).
次に、上記で求めた回転角θηおよびθζを用いてη軸およびζ軸周りに位置計測結果である点群データを回転させて、長方形断面の空間のｘ軸と３Ｄスキャナのξ軸を一致させる第１の座標変換を行う（ステップＳ１１）。 Next, using the rotation angles θη and θζ obtained above, the point cloud data, which is the position measurement result, is rotated around the η axis and the ζ axis, so that the x-axis of the rectangular cross section space coincides with the ξ axis of the 3D scanner First coordinate conversion is performed (step S11).
（特徴的なフロー）
次に、後半の特徴的なフロー（ステップＳ２００）を説明する。このフローは、長方形断面の空間のｙ、ｚ軸と３Ｄスキャナ１のη、ζ軸を一致させるためのものである。
(Characteristic flow)
Next, a characteristic flow in the latter half (step S200) will be described. This flow is for making the y and z axes of the space of the rectangular cross section coincide with the η and ζ axes of the 3D scanner 1.
図３Ｂに示すように、まず、上記のステップＳ１００の第１の座標変換により得られた点群データを、図７（ａ）に示すようなξζ平面上に投影し、ξ、ζ軸方向の最大値、最小値であるξmax、ξmin、ζmax、ζminを求める（ステップＳ１２）。求めたξmax、ξmin、ζmax、ζminで囲まれた長方形の面積Ａξζを求める（ステップＳ１３）。 As shown in FIG. 3B, first, the point cloud data obtained by the first coordinate transformation in step S100 is projected on the ξζ plane as shown in FIG. The maximum value and the minimum value ξ max , ξ min , ζ max , and ζ min are obtained (step S12). Obtained ξ max, ξ min, ζ max , determining the rectangular areas Aξζ surrounded by zeta min (step S13).
次に、図７（ｂ）に示すように、点群データの座標（Ξi，Ηi，Ζi）を、ξ軸周りに任意の回転角θで回転し、点（ξi,ξ，ηi,ξ，ζi,ξ）に変換を行い、Ａξζを求める（ステップＳ１４、Ｓ１５）。 Next, as shown in FIG. 7B, the coordinates (Ξ i , Η i , Ζ i ) of the point cloud data are rotated around the ξ axis at an arbitrary rotation angle θ, and the points (ξ i, ξ, ([eta] i, [xi], [ zeta] i, [xi] ) is converted into A [xi] [zeta] (steps S14 and S15).
上記の回転と、Ａξζの導出を任意の角度θで実施後、Ａξζが最小となるξ軸周りの回転角θξを求める（ステップＳ１６）。 After performing the above rotation and derivation of Aξζ at an arbitrary angle θ, a rotation angle θξ around the ξ axis that minimizes Aξζ is obtained (step S16).
次に、図７（ｂ）に示すように、求めたθξを用いて上記のステップＳ１００の第１の座標変換により得られた点群データをξ軸周りに回転させて、長方形断面の空間のｙ、ｚ軸と３Ｄスキャナ１のη、ζ軸を一致させる第２の座標変換を行う（ステップＳ１７）。 Next, as shown in FIG. 7B, the point cloud data obtained by the first coordinate transformation in the above step S100 is rotated around the ξ axis using the obtained θξ, and the rectangular cross section space is obtained. Second coordinate transformation is performed to match the y and z axes with the η and ζ axes of the 3D scanner 1 (step S17).
θξを用いて点群データをξ軸周りに回転させると、図８に示すような点群データが得られ、長方形断面の空間のｙ、ｚ軸と３Ｄスキャナのη、ζ軸が一致することになる。 When the point cloud data is rotated around the ξ axis using θξ, the point cloud data as shown in FIG. 8 is obtained, and the y and z axes of the rectangular cross-section space coincide with the η and ζ axes of the 3D scanner. become.
以上の方法により、上下左右対称の長方形断面の空間内に３Ｄスキャナ１を任意の姿勢で設置した場合、３Ｄスキャナ１の計測結果から、上下左右対称の断面の空間の直交座標系（ｘｙｚ）と３Ｄスキャナ１のセンサー３の直交座標系（ξηζ）の座標軸の方向を一致させることができる。 When the 3D scanner 1 is installed in an arbitrary posture in a rectangular cross-section space that is vertically and horizontally symmetrical by the above method, the orthogonal coordinate system (xyz) of the space of the vertically and horizontally symmetric cross-section is determined from the measurement result of the 3D scanner 1. The directions of the coordinate axes of the orthogonal coordinate system (ξηζ) of the sensor 3 of the 3D scanner 1 can be matched.
なお、上記の実施の形態では、長方形断面の空間に適用する場合を例にとり説明したが、本発明は長方形断面の空間に限定するものではなく、例えば上下左右対称の楕円形などの上下左右対称の形状の断面に対しても適用可能である。また、本発明は、本願出願人が特許出願を検討中の上記の従来の方法も包含したものであることから、上下非対称で左右対称の断面の空間（例えば馬蹄形断面の空間）に対しても適用可能であることはいうまでもない。 In the above embodiment, the case where the present invention is applied to a rectangular cross-section space has been described as an example. However, the present invention is not limited to a rectangular cross-section space. The present invention can also be applied to a cross section of the shape. In addition, since the present invention includes the above-described conventional method for which the applicant of the present application is considering a patent application, the present invention is also applicable to a space with a vertically asymmetric and left-right cross section (for example, a space with a horseshoe cross section). Needless to say, this is applicable.
以上説明したように、本発明に係る位置計測方法によれば、ｘ軸、ｙ軸、ｚ軸の直交座標系により規定された空間内に設置され、この空間を区画形成する面の３次元位置データをξ軸、η軸、ζ軸の直交座標系の座標値で取得することによって空間の位置計測を行う３Ｄスキャナと、３Ｄスキャナの計測結果から所定の軸合わせを行うための演算を行う演算装置とを備えた位置計測装置を用いて空間の位置計測を行う方法であって、ｘ軸を軸方向とする空間内に３Ｄスキャナを設置した後、３Ｄスキャナで空間内を位置計測するステップと、３Ｄスキャナの位置計測結果である点群データを所定の仮想の面に投影した投影像に基づいて、空間のｘ軸と３Ｄスキャナのξ軸を一致させるための回転角度を求め、求めた回転角度でη軸、ζ軸周りにξ軸を回転させる第１の座標変換を行って、空間のｘ軸と３Ｄスキャナのξ軸を一致させるステップと、第１の座標変換後の点群データを所定の仮想の面に投影した投影像に基づいて、空間のｙ軸、ｚ軸と３Ｄスキャナのη軸、ζ軸をそれぞれ一致させるための回転角度を求め、求めた回転角度でξ軸周りにη軸、ζ軸を回転させる第２の座標変換を行って、空間のｙ軸、ｚ軸と３Ｄスキャナのη軸、ζ軸をそれぞれ一致させるステップと、第２の座標変換後の点群データを、空間の直交座標系における３Ｄスキャナの位置計測結果として推定するステップとを備えるので、空間の断面形状が上下非対称で左右対称の場合のみならず、上下左右対称の場合であっても、この空間内に任意の姿勢で設置した３Ｄスキャナの座標軸を、空間の座標軸に合わせることが可能となる。このため、位置計測を効率よく実施することができる。 As described above, according to the position measuring method according to the present invention, the three-dimensional position of the surface that is installed in the space defined by the orthogonal coordinate system of the x-axis, y-axis, and z-axis and that defines the space. A 3D scanner that performs spatial position measurement by acquiring data with coordinate values in the orthogonal coordinate system of the ξ, η, and ζ axes, and an operation that performs an operation for performing predetermined axis alignment from the measurement results of the 3D scanner A position measurement device comprising a device, and a step of measuring the position in the space with the 3D scanner after the 3D scanner is installed in the space having the x-axis as the axial direction; Based on a projected image obtained by projecting point cloud data, which is a position measurement result of the 3D scanner, onto a predetermined virtual plane, a rotation angle for matching the x axis of the space with the ξ axis of the 3D scanner is obtained, and the obtained rotation is obtained. Ξ around η axis and ζ axis The first coordinate transformation is performed to rotate, and the x-axis of the space and the ξ-axis of the 3D scanner are made to coincide with each other, and the point cloud data after the first coordinate transformation is projected onto a predetermined virtual plane. Based on this, the rotation angles for matching the y-axis and z-axis of the space with the η-axis and ζ-axis of the 3D scanner are obtained, and the η-axis and ζ-axis are rotated around the ξ-axis by the obtained rotation angle. Performing coordinate transformation to match the y-axis and z-axis of the space with the η-axis and ζ-axis of the 3D scanner, respectively, and the point group data after the second coordinate transformation are converted to the 3D scanner in the space orthogonal coordinate system. 3D scanner installed in an arbitrary posture in this space not only when the cross-sectional shape of the space is vertically asymmetric and left-right symmetric but also when it is vertically and horizontally symmetric Align the coordinate axis of with the coordinate axis of the space. Rukoto is possible. For this reason, position measurement can be implemented efficiently.
また、本発明に係る他の位置計測方法によれば、第１の座標変換は、３Ｄスキャナの位置計測結果である点群データをξ軸に垂直なηζ平面に投影した場合において、投影された点群データを包含して各辺がη軸とζ軸に平行で各辺の長さが最小となる長方形であって、この点群データをη軸、ζ軸周りにそれぞれ回転して得られる長方形の面積が最小となるときの回転角度θη、θζを求めた後、位置計測結果である点群データについて、求めた回転角度θη、θζでη軸、ζ軸周りにξ軸を回転させる座標変換であり、第２の座標変換は、第１の座標変換後の点群データをη軸に垂直なξζ平面に投影した場合において、投影された点群データを包含して各辺がξ軸とζ軸に平行で各辺の長さが最小となる長方形であって、この点群データをξ軸周りに回転して得られる長方形の面積が最小となるときの回転角度θξを求めた後、第１の座標変換後の点群データについて、求めた回転角度θξでξ軸周りにη軸、ζ軸を回転させる座標変換であるので、位置計測処理の効率を上げることができる。 According to another position measurement method according to the present invention, the first coordinate transformation is projected when the point cloud data that is the position measurement result of the 3D scanner is projected onto the ηζ plane perpendicular to the ξ axis. A rectangle that includes point cloud data, each side is parallel to the η axis and ζ axis, and the length of each side is minimum, and is obtained by rotating the point cloud data around the η axis and the ζ axis, respectively. Coordinates for rotating the ξ axis around the η axis and the ζ axis at the obtained rotation angles θη and θζ for the point cloud data as the position measurement results after obtaining the rotation angles θη and θζ when the rectangular area is minimized In the second coordinate transformation, when the point group data after the first coordinate transformation is projected onto the ξζ plane perpendicular to the η axis, each side includes the projected point group data and the ξ axis The rectangle is parallel to the ζ axis and the length of each side is minimum, and this point cloud data is rotated around the ξ axis. Rotate the η and ζ axes around the ξ axis with the calculated rotation angle θξ for the point group data after the first coordinate transformation. Therefore, the position measurement processing efficiency can be increased.
また、本発明に係る位置計測装置によれば、ｘ軸、ｙ軸、ｚ軸の直交座標系により規定された空間内に設置され、この空間を区画形成する面の３次元位置データをξ軸、η軸、ζ軸の直交座標系の座標値で取得することによって空間の位置計測を行う３Ｄスキャナと、３Ｄスキャナの計測結果から所定の軸合わせを行うための演算を行う演算装置とを備えた位置計測装置であって、演算装置は、ｘ軸を軸方向とする空間内に設置した３Ｄスキャナの位置計測結果である点群データを所定の仮想の面に投影した投影像に基づいて、空間のｘ軸と３Ｄスキャナのξ軸を一致させるための回転角度を求め、求めた回転角度でη軸、ζ軸周りにξ軸を回転させる第１の座標変換を行って、空間のｘ軸と３Ｄスキャナのξ軸を一致させる手段と、第１の座標変換後の点群データを所定の仮想の面に投影した投影像に基づいて、空間のｙ軸、ｚ軸と３Ｄスキャナのη軸、ζ軸をそれぞれ一致させるための回転角度を求め、求めた回転角度でξ軸周りにη軸、ζ軸を回転させる第２の座標変換を行って、空間のｙ軸、ｚ軸と３Ｄスキャナのη軸、ζ軸をそれぞれ一致させる手段と、第２の座標変換後の点群データを、空間の直交座標系における３Ｄスキャナの位置計測結果として推定する手段とを備えるので、空間の断面形状が上下非対称で左右対称の場合のみならず、上下左右対称の場合であっても、この空間内に任意の姿勢で設置した３Ｄスキャナの座標軸を、空間の座標軸に合わせることが可能となる。このため、位置計測を効率よく実施することができる。 Further, according to the position measuring apparatus of the present invention, the three-dimensional position data of the surface that is installed in the space defined by the orthogonal coordinate system of the x-axis, y-axis, and z-axis and forms the space is converted to the ξ-axis. , Η-axis, and ζ-axis orthogonal coordinate system to obtain a 3D scanner that measures the position of the space, and an arithmetic unit that performs a calculation for performing predetermined axis alignment from the measurement result of the 3D scanner The position measurement device is a computing device based on a projection image obtained by projecting point cloud data, which is a position measurement result of a 3D scanner installed in a space having the x-axis as an axial direction, onto a predetermined virtual plane. A rotation angle for matching the x-axis of the space with the ξ-axis of the 3D scanner is obtained, and the first coordinate conversion is performed by rotating the ξ-axis around the η-axis and the ζ-axis at the obtained rotation angle. Means for matching the ξ axis of the 3D scanner and the first coordinate change Based on the projection image obtained by projecting the converted point cloud data onto a predetermined virtual plane, the rotation angles for matching the y-axis and z-axis of the space with the η-axis and ζ-axis of the 3D scanner are obtained and obtained. A second coordinate transformation for rotating the η-axis and the ζ-axis around the ξ-axis at a rotation angle so as to match the y-axis and z-axis of the space with the η-axis and ζ-axis of the 3D scanner, respectively, Means for estimating the point group data after coordinate transformation as a position measurement result of the 3D scanner in the space's orthogonal coordinate system. Even in this case, the coordinate axis of the 3D scanner installed in an arbitrary posture in this space can be matched with the coordinate axis of the space. For this reason, position measurement can be implemented efficiently.
また、本発明に係る他の位置計測装置によれば、第１の座標変換は、３Ｄスキャナの位置計測結果である点群データをξ軸に垂直なηζ平面に投影した場合において、投影された点群データを包含して各辺がη軸とζ軸に平行で各辺の長さが最小となる長方形であって、この点群データをη軸、ζ軸周りにそれぞれ回転して得られる長方形の面積が最小となるときの回転角度θη、θζを求めた後、位置計測結果である点群データについて、求めた回転角度θη、θζでη軸、ζ軸周りにξ軸を回転させる座標変換であり、第２の座標変換は、第１の座標変換後の点群データをη軸に垂直なξζ平面に投影した場合において、投影された点群データを包含して各辺がξ軸とζ軸に平行で各辺の長さが最小となる長方形であって、この点群データをξ軸周りに回転して得られる長方形の面積が最小となるときの回転角度θξを求めた後、第１の座標変換後の点群データについて、求めた回転角度θξでξ軸周りにη軸、ζ軸を回転させる座標変換であるので、位置計測処理の効率を上げることができる。 According to another position measurement apparatus of the present invention, the first coordinate transformation is projected when the point cloud data that is the position measurement result of the 3D scanner is projected onto the ηζ plane perpendicular to the ξ axis. A rectangle that includes point cloud data, each side is parallel to the η axis and ζ axis, and the length of each side is minimum, and is obtained by rotating the point cloud data around the η axis and the ζ axis, respectively. Coordinates for rotating the ξ axis around the η axis and the ζ axis at the obtained rotation angles θη and θζ for the point cloud data as the position measurement result after calculating the rotation angles θη and θζ when the rectangular area is minimized In the second coordinate transformation, when the point group data after the first coordinate transformation is projected onto the ξζ plane perpendicular to the η axis, each side includes the projected point group data and the ξ axis The rectangle is parallel to the ζ axis and the length of each side is minimum, and this point cloud data is rotated around the ξ axis. Rotate the η and ζ axes around the ξ axis with the calculated rotation angle θξ for the point group data after the first coordinate transformation. Therefore, the position measurement processing efficiency can be increased.
以上のように、本発明に係る位置計測方法および装置は、３Ｄスキャナを用いたトンネル掘削の管理に有用であり、特に、上下左右対称の断面をもつ空間内に任意の姿勢で設置した３Ｄスキャナの座標軸を、空間の座標軸に合わせるのに適している。 As described above, the position measuring method and apparatus according to the present invention are useful for managing tunnel excavation using a 3D scanner, and in particular, a 3D scanner installed in an arbitrary posture in a space having a vertically and horizontally symmetrical cross section. It is suitable for aligning the coordinate axis of with the coordinate axis of the space.
１ ３Ｄスキャナ
２ 演算装置
３ センサー
４ 三脚
１００ 位置計測装置
DESCRIPTION OF SYMBOLS 1 3D scanner 2 Arithmetic device 3 Sensor 4 Tripod 100 Position measuring device
Claims (4)
ｘ軸を軸方向とする空間内に３Ｄスキャナを設置した後、３Ｄスキャナで空間内を位置計測するステップと、
３Ｄスキャナの位置計測結果である点群データを所定の仮想の面に投影した投影像に基づいて、空間のｘ軸と３Ｄスキャナのξ軸を一致させるための回転角度を求め、求めた回転角度でη軸、ζ軸周りにξ軸を回転させる第１の座標変換を行って、空間のｘ軸と３Ｄスキャナのξ軸を一致させるステップと、
第１の座標変換後の点群データを所定の仮想の面に投影した投影像に基づいて、空間のｙ軸、ｚ軸と３Ｄスキャナのη軸、ζ軸をそれぞれ一致させるための回転角度を求め、求めた回転角度でξ軸周りにη軸、ζ軸を回転させる第２の座標変換を行って、空間のｙ軸、ｚ軸と３Ｄスキャナのη軸、ζ軸をそれぞれ一致させるステップと、
第２の座標変換後の点群データを、空間の直交座標系における３Ｄスキャナの位置計測結果として推定するステップとを備えることを特徴とする位置計測方法。 Installed in a space defined by the x-axis, y-axis, and z-axis Cartesian coordinate systems, and the coordinate values of the ξ-axis, η-axis, and ζ-axis Cartesian coordinate systems for the three-dimensional position data of the plane that defines this space The position of the space is measured using a position measuring device that includes a 3D scanner that measures the position of the space by acquiring the image and a calculation device that performs a calculation for performing predetermined axis alignment from the measurement result of the 3D scanner. A method,
a step of measuring the position in the space with the 3D scanner after installing the 3D scanner in the space with the x-axis as the axial direction;
Based on a projection image obtained by projecting point cloud data as a position measurement result of the 3D scanner onto a predetermined virtual plane, a rotation angle for matching the x-axis of the space with the ξ axis of the 3D scanner is obtained, and the obtained rotation angle Performing a first coordinate transformation of rotating the ξ axis around the η axis and the ζ axis to match the x axis of the space with the ξ axis of the 3D scanner;
Based on the projection image obtained by projecting the point group data after the first coordinate conversion onto a predetermined virtual plane, the rotation angles for matching the y-axis and z-axis of the space with the η-axis and ζ-axis of the 3D scanner are set. Performing a second coordinate transformation to rotate the η and ζ axes around the ξ axis at the determined rotation angle so that the y axis and z axis of the space coincide with the η axis and ζ axis of the 3D scanner, respectively ,
And a step of estimating the point group data after the second coordinate conversion as a position measurement result of the 3D scanner in the orthogonal coordinate system of the space.
第２の座標変換は、第１の座標変換後の点群データをη軸に垂直なξζ平面に投影した場合において、投影された点群データを包含して各辺がξ軸とζ軸に平行で各辺の長さが最小となる長方形であって、この点群データをξ軸周りに回転して得られる長方形の面積が最小となるときの回転角度θξを求めた後、第１の座標変換後の点群データについて、求めた回転角度θξでξ軸周りにη軸、ζ軸を回転させる座標変換であることを特徴とする請求項１に記載の位置計測方法。 In the first coordinate transformation, when point cloud data, which is a position measurement result of the 3D scanner, is projected onto the ηζ plane perpendicular to the ξ axis, each side includes the projected point cloud data and the η axis and the ζ axis. Rotation angles θη and θζ when the area of the rectangle obtained by rotating the point cloud data around the η axis and the ζ axis, respectively, is minimum. After obtaining, for the point cloud data which is the position measurement result, the transformation angle θη, θζ at the obtained rotation angle, the coordinate transformation to rotate the ξ axis around the ζ axis,
In the second coordinate transformation, when the point cloud data after the first coordinate transformation is projected onto the ξζ plane perpendicular to the η axis, each side includes the projected point cloud data on the ξ axis and the ζ axis. After obtaining the rotation angle θξ when the area of the rectangle which is parallel and has the minimum length of each side and which is obtained by rotating this point cloud data around the ξ axis is minimum, the first 2. The position measurement method according to claim 1, wherein the point group data after coordinate conversion is coordinate conversion in which the η axis and the ζ axis are rotated around the ξ axis at the obtained rotation angle θξ.
演算装置は、ｘ軸を軸方向とする空間内に設置した３Ｄスキャナの位置計測結果である点群データを所定の仮想の面に投影した投影像に基づいて、空間のｘ軸と３Ｄスキャナのξ軸を一致させるための回転角度を求め、求めた回転角度でη軸、ζ軸周りにξ軸を回転させる第１の座標変換を行って、空間のｘ軸と３Ｄスキャナのξ軸を一致させる手段と、
第１の座標変換後の点群データを所定の仮想の面に投影した投影像に基づいて、空間のｙ軸、ｚ軸と３Ｄスキャナのη軸、ζ軸をそれぞれ一致させるための回転角度を求め、求めた回転角度でξ軸周りにη軸、ζ軸を回転させる第２の座標変換を行って、空間のｙ軸、ｚ軸と３Ｄスキャナのη軸、ζ軸をそれぞれ一致させる手段と、
第２の座標変換後の点群データを、空間の直交座標系における３Ｄスキャナの位置計測結果として推定する手段とを備えることを特徴とする位置計測装置。 Installed in a space defined by the x-axis, y-axis, and z-axis Cartesian coordinate systems, and the coordinate values of the ξ-axis, η-axis, and ζ-axis Cartesian coordinate systems for the three-dimensional position data of the plane that defines this space A position measurement device comprising a 3D scanner that measures the position of a space by acquiring the data and a calculation device that performs a calculation for performing predetermined axis alignment from the measurement result of the 3D scanner,
The arithmetic device uses the x-axis of the space and the 3D scanner based on a projection image obtained by projecting point cloud data, which is a position measurement result of the 3D scanner installed in the space with the x-axis as the axial direction, onto a predetermined virtual plane. Obtain the rotation angle for matching the ξ axis, perform the first coordinate transformation that rotates the ξ axis around the η axis and the ζ axis at the calculated rotation angle, and match the x axis of the space with the ξ axis of the 3D scanner Means to
Based on the projection image obtained by projecting the point group data after the first coordinate conversion onto a predetermined virtual plane, the rotation angles for matching the y-axis and z-axis of the space with the η-axis and ζ-axis of the 3D scanner are set. A second coordinate transformation for rotating the η axis and the ζ axis around the ξ axis at the determined rotation angle to match the y axis and z axis of the space with the η axis and ζ axis of the 3D scanner, respectively; ,
A position measuring apparatus comprising: means for estimating the point group data after the second coordinate conversion as a position measurement result of a 3D scanner in a space orthogonal coordinate system.
第２の座標変換は、第１の座標変換後の点群データをη軸に垂直なξζ平面に投影した場合において、投影された点群データを包含して各辺がξ軸とζ軸に平行で各辺の長さが最小となる長方形であって、この点群データをξ軸周りに回転して得られる長方形の面積が最小となるときの回転角度θξを求めた後、第１の座標変換後の点群データについて、求めた回転角度θξでξ軸周りにη軸、ζ軸を回転させる座標変換であることを特徴とする請求項３に記載の位置計測装置。 In the first coordinate transformation, when point cloud data, which is a position measurement result of the 3D scanner, is projected onto the ηζ plane perpendicular to the ξ axis, each side includes the projected point cloud data and the η axis and the ζ axis. Rotation angles θη and θζ when the area of the rectangle obtained by rotating the point cloud data around the η axis and the ζ axis, respectively, is minimum. After obtaining, for the point cloud data which is the position measurement result, the transformation angle θη, θζ at the obtained rotation angle, the coordinate transformation to rotate the ξ axis around the ζ axis,
In the second coordinate transformation, when the point cloud data after the first coordinate transformation is projected onto the ξζ plane perpendicular to the η axis, each side includes the projected point cloud data on the ξ axis and the ζ axis. After obtaining the rotation angle θξ when the area of the rectangle which is parallel and has the minimum length of each side and which is obtained by rotating this point cloud data around the ξ axis is minimum, the first 4. The position measuring apparatus according to claim 3, wherein the point group data after coordinate conversion is coordinate conversion for rotating the η axis and the ζ axis around the ξ axis at the obtained rotation angle θξ.
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