GB2213673A - Optical position finding - Google Patents

Abstract

Optical apparatus for the measurement of spatial position comprises a laser source rotatable about an axis for generating radiation in the form of a divergent beam having a cross-sectional shape in the form of a "v" or an "x", a sensor or retroreflector for sensing the presence of the beam, means for determining the angular position of said beam about said axis and means for computing the direction in space of said sensor or retroreflector means relative to a reference point at the source of the radiation. Use of two beams allows correction of mounting and beam orientation errors. <IMAGE>

Description

OPTICAL APPARATUS AND METHOD This invention relates to the measurement of spatial position by means of a regular movement of a beam or beams of electromagnetic radiation. It finds application in many areas of non-contact measurement, and specifically those of surveying; computer-controlled robot position calibration; the monitoring of attitude and position of agricultural and earth-moving machinery and also in the field of tunnelling-machine guidance.

According to the present invention there is provided optical apparatus for the measurement of spatial position comprising generating means for generating radiation in the form of a divergent beam having a sectional shape with a leading edge and a trailing edge that are straight and diverge from one another, means for rotating said beam of radiation about an axis, sensor means for sensing the presence of said beam, means for determining the angular position of said beam about said axis and means for computing the direction in space of said sensor means relative to a reference point at the source of the radiation.

A basic configuration for a system which operates according to the present invention would comprise an unattended unit emitting electromagnetic radiation which is shaped according to a predetermined pattern; a receiver unit which comprises a radiation sensor or array of sensors for detecting incident radiation from the source unit. and means for computing therefrom direction or.directions in space from a reference point on the source unit to the centre of each sensor.

An embodiment of the invention will now be described by way of example with reference to the accompanying drawings, in which: Figure 1 shows in schematic form the beam arrangement of one form of surveying device Figure 2 shows different arrangements of a laser beam in a vertical plane Figure 3 illustrates the arrangement of a suitable detector Figures 4 to 6 show alternative laser beam geometries Figure 7 shows another detector arrangement Figure 8 to 10 are explanatory diagrams relating to this detector arrangement Figure 11 is diagrammatic view of apparatus in accordance with one embodiment of the invention Figure 12 is an illustration of a staff suitable for use with the apparatus of Figure 11 Figure 13 illustrates the generation of sloping beams, and Figure 14 is a diagrammatic view of an optical unit for use with an embodiment of the invention Referring now to the drawings, an unattended source of a protected laser beam together with remote detection of the beam are characteristic features of the rotary beam laser level.

For levelling operations the rotary laser level provides elevation measurements over a large area and with a system accuracy of the order of Smm up 100 metres from the unattended laser source. In such instruments, the appropriately focussed beam and of the appropriate diameter for the range of measurement, is projected vertically upwards into a pentagonal prism which rotates about the vertical axis of the laser beam.

The resulting sweeping beam defines a horizontal plane against which relative elevation measurements. can be performed.

Electronic detection of a stationary beam is normally achieved by use of a 'balanced' photodetector such as a quadrant sensor QS whose sensitive area usually exceeds that of the incoming beam IB. This form of detector is shown in Figure 1 together with a linear strip form applicable to rotary laser level beams. In this latter detector the two strips of silicon photocell PC are mounted in line and separated by a small gap G of 1 or 2 millimetres. As the beam sweeps past the detector unit the output from the two electrically separate cells is compared. These outputs will only balance when the beam centre passes through the middle of the gap between the strips and any off-centre condition can be translated into a visual or audible indication.

Laser levelling operations are concerned with single dimension measurements normal to a fixed reference plans defined by the laser beam. If it is required to measure directions within a plane using a laser beam, then a plane of laser light must itself be rotated about one of its diameters. Figure 2a illustrates a laser beam LB which has been fanned out to form a sector of a vertical plane and its rotation about a vertical axis through the source S is continuously monitored by some kind of electronic angle encoder incorporated within the source.The width of the fan beam would be determined in a similar manner to that for an alignment operation i.e., e function only of range, whereas the vector plane angle of the beam would be determined by the required horizontal range of the measurements, the vertical plane angular coverage, the power of the laser source and sensitivity of the electronic detector target. A version for measuring vertical angles is also shown. (Figure 2b) A suitable form of detector for such arrangements is shown in Figure 3 with square photocells PC where the passage of the fan beam produces an output "signature" SIG resulting from the cell outputs being connected in opposition. Thus the zero-crossing point of the output corresponds to that position of the beam which produced equal illumination of the two cells.

This is efficient for detecting the beam centre and has the added advantage of being virtually insensitive to extraneous light which illuminates both cells simultaneously (so called common-mode rejection).

However, there are considerable practical advantages to be gained by combining these two laser beam geometries so that simultaneous measurements of both horizontal and vertical plane directions ray be determined in a single sweep of the composite beam. In this new arrangement, Figure 4 two laser beams are generated, each fanned out into a sector shape, with their central rays separated by a fixed angle C) in the horizontal plane through the source, and their sector planes each being inclined in opposing sense by about 45" to the horizontal. The pair of beams rotate as an inverted 'V' about a vertical axis through the source.

Figure 5 illustrates the geometry which applies to the leading beam of the pair as it sweeps across a fixed photocell P. LI represents the central ray of that fan beam which sweeps out a horizontal plane, and its length is equal to LB, where B is the intersection of the vertical through P with the horizontal reference plane. A vertical circle through B will cut the ray LP at A. 'cup' is the vertical angle of p from the source at L; y is the tilt angle of the fan (about 450 is optimum), and iy is the horizontal plane angle between the azimuth plane of P and that of the central ray of the fan at the instant that P is struck.

Applying Napier's Rule to the spherical triangle AIB: TAN? = TANy.SIN (1) But the horizontal circle scale at the source describes the rotation of the central ray LI in its sweep and there is no way that the system can sense when I is occupying the position of B; thus from a single beam the angle ç is indeterminate. If the source circle scale is read for the pair of beams, however, and assuming for now that the two beams have symmetrical geometry, then ç can be found.

If a is the magnitude of rotation of the horizontal angle circle between the two incidences of a laser beam on the cell P, then the 'internal' horizontal angles ç are equal, (Figure 6), and given by ç = (are)/2.

Therefore TANg = TANy.SIN(e-a) 2 2 and if the horizontal direction midway between the pair of beams is used as an azimuth pointer then, relative to the system zero direction, the azimuth for P is the circle reading for beam 2 less a/2.

From such a system both horizontal and vertical directions from a source point to a target point can be determined from a single sweep of the composite beam and by using only a single circular scale. Moreover the principle is unaltered if the fan tilt angles y are not identical and the beam separation angle e can take any value including zero, in which case the composite beams form an 'X' shape. Both e and y are system constants which must be determined by calibration.

Detection of such fan beams is similar to that earlier described and one arrangement for this is shown in Figure 7.

The square silicon cells PC are again connected in electrical opposition and the resulting "signature" SIG of the cell currents serves to identify the particular beam of the pair which is incident on the cell.

So far the system described provides spatial direction information for any photoelectric cell capable of intercepting the pair of laser beams. If two such cells were fixed to a vertical staff or rod then 3-dimensional position of the foot of the staff could be determined in a single beam sweep, which can be less than one second of time. In Figure 8 the single sweep of the beams provide both horizontal direction and VA's (gA and gB) to the two-staff-mounted cells A and B distance 'd' apart.

Since TAN wA = d+h ; TAN gB = h/R e (3) R so h = ( d . TAN 9R ) ; R = ( d ) (4) (TAN sA - TAN 9B) (TAN gA - TAN 9B) Thus 'h' the elevation of the lower photocell relative to the horizon plane through the source as well as the horizontal reduced range R from the vertical axis through the source -are determined uniquely from a single sweep of the pair of beams.

Further, there is no restriction on the number of spaced photocells used on the staff, and provided their positions relative to the staff foot are known, then any two of them which have a sight of the laser source can be used to generate a 3-D position fix for the staff foot.

A vertical attitude for the target staff is not necessary where a minimum of three photocells are struck. In this case the attitude of the staff, positions in space of each cell and full 3-D position of the staff foot can be uniquely determined from a single sweep data set. More cells and more sweeps would merely provide redundancy for increasing the measurement precision, and in the case of the former, would also provide some measure of immunity from obstruction of parts of the beams.

The essential features of this linear spatial resection analysis are given here with reference to Figure 9 (i) Internal plane angles and are computed from horizontal (H) and vertical (V) components of the directions OQ,OB and OC using the cosine rule of spherical trigonometry e.g., cosa = sin VA.sin VB + cos VA.cos VB.cos (HB-HA) (ii) From the two triangles OAB and OBC using the sine rule of plane trigonometry.

(OC.sinss)/b = (OA.sina)/a or OC = [(b.sina)/Ca.sin(3)1 OA = K . OA, where K is known from the cell positions on the staff A. B and C and also from (i).

(iii) Now using the cosine rule for plane triangles (a + b) 2 = OVA 2 + OCr2 - 2*0A*OC*cos(a+ss) = (1+K*K) OA-2 - 2*K*OA-2*cos(a+B) therefore OA = (a+b)/SQR [K*K - 2*K.cos(a+(3) + 1] (iv) Since the direction vector components of OA and OC are given by the measured horizontal and vertical directions viz.

X(A) = cos HA.cos VA ; Y(A) sin HA.sin VA ; Z(A) = sin VA. and similarly for OC, so the position co-ordinates of the foot of the staff F may be found by direct extrapolation given the value of CF.

The technique of spatial resection may be further extended in the performance of the invention for the purpose of position calibration of computer-controlled robots. Here the robot 'hand' is provided with a hollow and rigid cubic shaped cage, on the corner faces of which are mounted photoelectric cells. The relative positions within the cage of the centres of the cells are known from previous measurements and the co-ordinates of the laser generating source of the present invention are then determined by spatial resection from any four of the cells whose directions are measured by the sweep of the beams. The process is equivalent to an origin translation and three independent rotations of the internal co-ordinate system of the control frame into a new coordinate system based on the optical centre of the laser source unit.

By moving the robot 'hand' to various pre-programmed positions within its spatial operation envelope and stopping momentarily the sweeping laser beams can provide full spatial displacement and orientation measurements in a very short time.

For fast rotations of the laser beams pseudo real-time measurements may be performed for continuous movements of the robot hand, and some kind of Kalman filtering may be used to smooth the trajectory between beam edge readings within a sweep.

The measurement principle described can be usefully generalised by considering that the great circle in the horizon plane (equatorial plane) can in some applications be reduced to a cone, i.e., be replaced by a smaller circle of elevated latitude. Figure 10 illustrates this concept, and the spherical triangle AIB of Figure 5 has now been raised in latitude on the sphere. The appropriate form of Napier's Rule is now: TAN ' = TANy.SIN +' (5) where ' is the difference in vertical angle between the reference cone surface (wO) and that of the cell (wc) : : 4,' is the horizontal angle at an elevation (po between the meridian circles passing through I and B.

From the cosine rule of spherical trigonometry: cos #' = sin#0 + cos#0.cos#0 (6) where to is the angle between the two meridians in the equatorial plane through the source, i.e. the measured angle on the horizontal circle. One advantage of this more concentrated sweep of the crossed beams is that the tangential velocity of the beams across the photocells is reduced so that the beam rotation rate about the vertical axis (in this example) may be increased without reducing the exposure of the cells.

Further, the main angle measurement circle scale within the source can be of lower precision than that necessary for the original system described. As an example of this consider a 'search' cone of 20 equivalent to an elevation angle above the horizon plane of 800. wO = 800 so cos#'= 0.97 + 0.03 . cos4,0 which for a 10 intermeridian angle in the horizon plane C4,) is equivalent to 0 .17 is, a dilution of the main scale precision required by a factor of 6. The smaller the cone of interest the greater is the amplification obtained from the intrinsic precision of the main scale.Finally, the central axis of the search cone need not be in the vertical plane but its orientation in space would have to be known if absolute position measurement is required.

Finally an embodiment in the form of an automatic theodolite is now described in which the measurement.fine.of spatial direction according to the invention provides an automatic reading or correction to a normal main scale circle reading.

In Figure 11 is shown an outline design of an automatic theodolite which comprises a motor-driven alidade or frame F, rotatable about a bearing B and housing a laser L, an optical unit 0 and a vertical circle scale V. The stationary base unit of the instrument contains a further circle scale H. The circle scales are preferably Moire encoder optical discs and the disposition of the reading head r for such a disc is shown for the horizontal circle of the instrument.

In operation a staff S ( Fig.12), comprising an array of fixed photocells PC, will generally face the theodolite and the measurement will be initiated by the operator at the staff; this will switch on a modulated infra-red or microwave beacon on the staff and broadly directed at the theodolite. The theodolite will rotate in a continuous sweep mode about its central vertical axis until it receives at its receiver R the staff beacon signal, whereupon it settles to within a few degrees of the horizontal direction of the staff beacon.

During this process, and in fact continuously, the optical unit 0 rotates about the horizontal trunnion axis of the theodolite and generates four alternately sloping beams, the central rays of which are separated by 90 in a vertical plane perpendicular to the trunnion axis fig.13). The angular position of each beam is measured continuously by the vertical circle scale V and its output is transmitted by a VHF transmitter T to the staff.

Each detector receives two pairs of inclined beams per sweep and the intra-beam angles are determined from the incoming VHF pulses from the source transmitter. This could involve some measure of inter-pulse interpolation by timing at the staff in order to improve the resolution of the angle measured. For such an arrangement the geometry described earlier has been rotated by 900 and what was a vertical angle in the theory earlier presented now constitutes the fine correction to the instrument main horizontal scale reading. Similarly what was originally the azimuth measure now provides the vertical direction component of the detector from the instrument reference point viz., the intersection of primary vertical axis and horizontal trunnion axis.

The use of two pairs of oppositely inclined beams offers considerable advantages in the measurement. Firstly the effects of change of eccentricity of the mounting of the circle scale V during operation are totally compensated since the circle readings are taken in the four quadrants of the circle and the mean value for corresponding beams of each pair (1800 apart) are used in the analysis. Further, any movement in the primary laser beam issuing from the laser beam expander will produce equal and opposite deviations in the two pairs of beams and consequently the mean readings of corresponding beams in each pair will be immune from laser tilt effects.

The optical unit 0 may be designed as shown in Figure 14 where the two cylindrical lenses C Produce the fanning of the beams which enter the unit from opposite directions. The prisms P are beam-splitting cubes and the central glass cube has a fully reflecting mirror surface M in its diagonal plane.

In addition to the automatic compensation of systematic errors due to disc eccentricity and laser beam tilts described earlier, this embodiment of the invention provides a number of further practical advantages. For example, the theodolite has almost complete coverage in the vertical plane, and this means that one can set-out points on-line and behind the instrument with a 1800 off-set yet without the need to rotate the alidade.

Since the laser beams are providing an automatic fine reading to the initial coarse pointing of the instrument the lateral angular extent of the beams can be small viz., 2 or 3 degrees, thus conserving the radiant power provided at the source.

Further, the measurements at the detectors take place on well shaped edges of the fan beams which are close to the centres and consequently do not rely on high degrees of linearity of the beam edges over large fan angles. Finally, and arising from the laser beam tilt compensation described above, it is practicable to exchange the laser source in the field without the need for any precise alignment or recalibration of the instrument.

Within the ambit of the invention and in some applications the photoelectric cells, described as mounted on a receiving staff, may be replaced by radiation reflecting glass prisms such as trihedral corner-cube reflectors. In these circumstances the beams when intercepted at the target end of the system would be reflected back to the source and detected there serially by a single photoelectric device. Any such return pulses of light will be synchronised with the angle circle output controlling the motion of the beam and a similar algorithm applied as before in order to determine the spatial direction of the reflector or 'effective' sensor.

Claims (12)

1. Optical apparatus for the measurement of spatial position comprising generating means for generating radiation in the form of a divergent beam having a sectional shape with a leading edge and a trailing edge that are straight and diverge from one another, means for rotating said beam of radiation about an axis, sensor means for sensing the presence of said beam, means for determining the angular position of said beam about said axis and means for computing the direction in space of said sensor means relative to a reference point at the source of the radiation.

2. Optical apparatus for the measurement of spatial position as claimed in claim 1 wherein the sensor means comprises at least one pair of opposed photodetectors.

3. Optical apparatus for the measurement of spatial position as claimed in claim 2 wherein the photodetectors are substantially square in form.

4. Optical apparatus for the measurement of spatial position as claimed in either claim 2 or claim 3 including at least three pairs of photodetectors.

5. Optical apparatus for the measurement of spatial position as claimed in claim 4 including at least four pairs ofphotodetectors.

6. Optical apparatus for the measurement of spatial position as claimed in claim 5 wherein said sensor means includes mounting means movable to predetermined reading positions.

7. Optical apparatus for the measurement of spatial position as claimed in claim 6 including filter means to smooth the trajectory between reading positions.

8. Optical apparatus for the measurement of spatial position as claimed in claim 7 wherein said filter means includes a Kalman filter.

9. Optical apparatus substantially as herein described with reference to and as shown in the accompanying drawings.

10. A theodolite incorporating optical apparatus as claimed in any one of the preceding claims.

11. A theodolite as claimed in claim 10 comprising frame means rotatable about an axis, a source of radiation, optical means for separating beams of radiation from said radiation source into fan-shaped beams and angular reference means for the derivation of an indication of the orientation of said frame means in a vertical plane, together with fixed base means including angular reference means for the derivation of an indication of the orientation of said frame means in a horizontal plane.

12. A theodolite as claimed in claim 11 wherein said angular reference means include Moire encoder discs.