GB2204689A - Measurement of a position - Google Patents

Abstract

Position measurement apparatus comprises a theodolite, eg at point O, and at least three targets A, B, C, eg on a staff, to permit the unique determination of their spatial position and that of any point F in known relation to them. The three targets need not be in a linear array. <IMAGE>

Description

METHOD AND APPARATUS FOR THE MEASUREMENT OF POSITION This invention relates to methods and apparatus for the measurement of distance.

Before the widespread use of electronic methods for distance measurement, much large-scale surveying employed extended linear scales for position measurements. The techniques generally were classified as 'fixed base', such as those using a subtense bar, or 'fixed angle' which covered the variety of stadia tacheometric methods. In addition there were some specialised instruments which constituted hybrids of the two broad classes. The measurements made were essentially horizontal directions and zenith angles from a single instrument station and for accurate results it was essential that the linear scale, or target array, as it may be considered, was oriented with respect to the vertical, the survey point and often the sight line.

With the advent of infrared electronic distance measurement apparatus and, more particularly, the almost orientation insensitive retroprism, the target array reduced to a single target and was no longer needed to provide a length scale. There was one negative aspect however in the transition to electronic distance measurement in respect of vertical staff tacheometry, and that arose from the need to measure independently the height above the survey point of the prism target before relative three-dimensional position could be determined. It is still necessary moreover to accurately plumb the retroprism target over the survey station.

More recently demand has arisen for high accuracy three-dimensional position measurements to be made at short ranges, sometimes as a time-scheduled series of measures as in structural deformation monitoring. The polar fixation techniques of large-scale surveying have been applied in this area but the +5mum accuracy of most electronic distance measurements is inadequate for much of this work and specialised instruments such as the Mekometer and Geomensor have had to be used.

Such refined electronic distance measurement equipment is expensive and the expense is exacerbated by the restricted application of the apparatus in other types of survey work.

Moreover, in order to realise the O.lmm accuracy offered by these instruments the locating of the target and its spatial orientation (particularly if mounted on a rod or stalk) is critical.

Another technique for three-dimensional fixation which is becoming universally adopted is that where observations are made to a common target from two theodolites separated by a "baseline". A theodolite can be used with a smaller and hence better defined target than is the case with an electronic distance measurement instrument. Further, theodolites are more 'universal' instruments than high-accuracy electronic distance measurements, and with the advent of the electronic theodolite the horizontal and vertical angle scales of the instrument can be read automatically and even faster than an electronic distance measurement measurement can be performed.

There are of course many advantages of the 'baseline' method, the choice of baseline is virtually unrestricted, the theodolites do not have to be set up at a common height, and repeated observations to good quality targets provide one of the most accurate measurements which can be made using the human eye. On the negative side it is sometimes difficult to present the same image of a common target to two observers in different positions around it - the so-called 'phase' error of the target. Also the method requires at least two fixed theodolites for accurate results and preferably two observers.Somewhat ironically, the 'scale' of the measurements is usually produced from simultaneous observations to a form of 'subtense' bar In accordance with the present invention there is provided apparatus for the measurement of position comprising position sensing apparatus and target means therefore, wherein at least three of said target means are provided to permit the unique determination of their spatial position and tbat of any point in known relation to them.

The invention will now be described, by way of example, with reference to the accompanying drawings in which: Figure 1 is an illustration of distance measuring apparatus incorporating a vertical staff arrangement (tangent tacheometry), Figure 2 shows alternative apparatus incorporating a tilted staff arrangement, Figure 3 is an explanatory diagram used in relation to the embodiment of Figure 2, and Figure 4 is an illustration of an embodiment of the present invention depicting an unconstrained attitude of a staff.

Referring now to the drawings, Figure 1 illustrates a theodolite at 0 which is used to measure the zenith angles wA and wB respectively to two fixed targets A and B at a known separation 'a' on a vertical staff. Target B is a known distance 'L' from the foot of the staff F. 'R' is the horizontal reduced range of the staff from 0.

Using plane trigonometry: tan wA = a + L + z : tan wB = L + z R R rearranging gives: z = (a + L) . tan R - L . tan (tan wA - tan wB) and R = a (tan wA - tan wB) Thus the polar coordinates of F can be deduced from the angle measurements: the horizontal direction would be determined by the appropriate reference object.

The prime geometrical constraint in using this arrangement is the need for verticality of the staff. Considerable practical benefit can be obtained by incorporating a 'sight' into the staff which allows the staff to be tilted sideways if required. The constraint has now changed its character.

Referring now to Figure 2, this shows a two-target staff which has a 'sight' S located midway between the targets A and B. In operation, whatever the sideways tilt of the staff' the angle OSF is maintained a right-angle. Analysis of this arrangement may be made as follows: (i) Unit vectors in the directions OA and OB are computed from the measured horizontal angles (a) from a given reference direction, and zenith angles (cup) for the targets A and B; ii) the slope angle AOB in the plane of the staff is computed using the cosine rule of spherical trigonometry and using the measured values of a and cp for the two targets;; iii) since AB forms a 'subtense' bar subtending an angle AOB, found in (ii), the lengths OA and 08 are found and together with the unit vectors (direction vectors) from (i) provide full position vectors for A and B: and finally, iv) the x,y and z coordinates of position for A and B are extended along the same straight line of the staff to generate appropriate coordinates for the staff foot F.

The components of a unit vector in x,y and z directions may be seen from Fig. 3 where a particular vector OP of unit length is in a direction which makes an angle a in the x-y plane from some reference direction (y=O, z=O), and makes a zenith angle with the x-y plane of w. From the figure, OQ = cosw and cosw = OX/OQ, thus OX = cosa . COS. Similarly OY = sina . cosw and OZ = sin.

The unit vector in the direction of target A is therefore coswA . cosA . i + sinwA . coswA . j + sinwA .k. where i,j,k are respectively unit vectors along the component axes Ox' Oy' Oz. A similar expression applies to target B.

The slope angle AOB is obtained from the cosine rule of spherical trigonometry.

cos(AOB) = sin#A . sin#B + cos#A . cos#B . cosCB-aA) From the right-angled triangle AOS: OA = (a/2). cosecY2(AOB) and OB = OA in this instance.

Thus XA = OA . cosaA . coseA ; YA = OA . sinaÁ . coswA ZA = OA . sinwAX and similarly for B.

The coordinates of F are found by extending the line AB in the following manner: XF - XB FB = XF - XA FA similarly for YF and ZF.

Once the directions in space of the two lines OA and OB are determined, some further geometrical constraint is needed in order that the position of F is unique. However, if three targets are used, and consequently three directions in space are defined, there is one, and only one, attitude and position for the staff which places the three targets on the three determined lines.

Referring now to Figure 4, the analysis for this more general case follows closely that described above, and the main departure arises from the plane triangles AOB and BOC in Fig. 4 generally not containing a right angle. In the figure a and ss are the angles within the generally sloping plane of the staff and computed from spherical trigonometry as described earlier.

For triangle OBC : OC b sin(OBC) = sinp For triangle OBA : OA a OA sin(OBA) - sina - sin(OBC) OC = (b.sina) . OA ~ K.OA (a.sinp) Using the cosine rule for the plane triangle OAC: (a+b)2 = OA 2 + OC - 2.OA.DC.cos(a+ss) = (K2 + 1) OA2 - 2K.cos(a+ss).OA2 or OA (a+b) (K2=2K.cos(a+13)+l )% Once the magnitude of the vectors OA and OC are found the x'y'z coordinates of A and C are calculated and the coordinates of the staff foot F produced as before.

On the basis of this analysis, it will be apparent to one skilled in the art that, by the use of a fixed target array containing at least three targets, the three-dimensional position of a point on a known extension of the line of the array may be determined by observations from a single theodolite. The accuracy limitations set by the 'quality' of the targets are not significantly different from those which arise in the scaling exercise of the 'baseline' technique, but 'phase' errors produced by different points of observation are eliminated.

Preferably, the target separation is known or maintained and the staff is either constructed of almost zero expansion coefficient material or alternatively made from one which has a linear coefficient at normal operating temperatures and incorporates embedded thermistors from which may be derived the necessary software scale correction.

It is necessary to maintain the spatial attitude of the staff during the measurements although the attitude does not need to be known. In one embodiment, the monitored point is a hemispherical cup having a threaded outer rim and the staff has a spherical ball foot carrying a captured locking ring. The ball foot is placed in the cup and the locking ring tightened rather like a locking ball-joint.

An analysis of accuracy for this technique is close to that which applies to the subtense bar, and in terms of errors in the target separation distances has an identical form.

The method herein described is not restricted to a linear array of the three targets. Any fixed configuration of three points will define a plane, and this plane is oriented uniquely by measurement of the respective azimuth and zenith directions to the three points.

Claims (6)

1. Apparatus for the measurement of position comprising position sensing apparatus and target means therefore, wherein at least three of said target means are provided to permit the unique determination of their spatial position and that of any point in known relation to them.

2. Apparatus for the measurement of position as claimed in claaim 1 wherein the sensing apparatus is a theodolite.

3. Apparatus as claimed in either claim 1 or claim 2 wherein there is provided at said point a hemispherical receptacle adapted to receive a cooperating locating member fixedly attached to a surveying staff

4. Apparatus as claimed in claim 3 wherein said receptacle is provided with retaining means to retain said locating member.

5. Apparatus as claimed in claim 4 wherein said retaining means comprises a screw thread adapted to cooperate with a complementary locking ring on said locating member.

6. Apparatus for the measurement of position substantially as herein described with reference to and as shown in the accompanying drawings.