This invention relates to object detection and location systems and, more particularly, to a method for determining the configuration and location of an object with respect to an X, Y, X coordinate frame. In space applications in particular, there is a need to be able to passively determine the orientation of an object at a distance, for example, in the control of large, flexible space structures. At present, there is no available method or apparatus which will allow the operator to make such a determination. A similar problem and need exists in robotic application. It is the primary object of this invention to provide a system for remotely defining an object's configuration in a manner compatible with a computer's analytical capability

Schumacher, Larry L.

English

NASA Technical Reports Server

United States Patent t191 
Schumacher 
[54] REMOTEOBJECX 
C O N F I G U R A T I O N / O R O N  
DETERMINATION . 
[75] Inventor: Larry L. Schumacher, Newhall, Calif. 
[73] Assignee: The United States of America as 
represented by the Administrator of 
the National Aeronautics and Space 
Administration, Washington, D.C. 
[21] Appl. No.: 237,035 
[22] Filed: Aug. 29,1988 
[51] Int. (3.5 ....................... GOlB 11/26; GOlC 1/00; 
GOlC 3/08 
E521 U.S. Cl. ........................................ 356/152; 356/5; 
356/141 
[58] Field of Search ............................ 356/5, 141, 152 
[561 References Cited 
U.S. PATENT DOCUMENTS 
3,542,472 11/1970 Smith-Vaniz ........................... 356/4 
3,690,767 9/1972 Missio et al. ............................ 356/5 
3,698,816 10/1972 Lutchansky ........................ 356/152 
3,866,229 2/1975 Hammack ........................... 356/141 
3,961,851 6/1976 Gerharz .................................. 356/1 
4,047,816 9/1977 Pell et al. ............................ 356/152 
4,123,165 10/1978 Brown et al. ....................... 356/152 
4,134,681 1/1979 Elmer .................................. 356/152 
4,209,254 6/1980 Reymond et al. .................. 356/152 
4,261,107 4/1981 Coleman et al. .................. 33/174 L 
4,356,640 4/1982 Dreyfus et al. ..................... 356/376 
4,373,808 2/1983 Pell et al. ............................ 356/152 
1111 Patent Number: 4,964,722 
[45] Date of Patent: Oct. 23, 1990 
4,402,608 9/1983 DiMatteo et al. .................. 356/375 
4,529,316 7/1985 DiMatteo ............................ 356/376 
4,534,650 8/1985 Clerget et al. ...................... 356/376 
4,789,243 12/1988 Mathur ................................ 356/375 
PrimaTy Examiner-Stephen C. Buczinski 
Attorney, Agent, or Firm-Thomas H. Jones; John R. 
Manning 
A method for determining the configuration and loca- 
tion of an object with respect to an X, Y, X coordinate 
frame. The exterior surface of the sobject is equipped 
with a plurality of retroreflector surfaces capable of 
reflecting range measuring laser beams back to their 
sources. Three lasers, “A”, “ B ,  and “C”, are located 
orthogonally to one another to define the reference 
coordinate frame. The lasers are used to determine the 
range distance to each of the retroreflector surface 
within the coordinate frame. The space defined by the 
coordinate frame is divided into four quadrants and the 
location of the retroreflector within a particular quad- 
rant determines the value of variables qx and qy to be 
used in association therewith. Then, for each retrore- 
flector,, the measured ranges from the laser to the retro- 
reflector are designated as RA., from laser A, RB, from 
laser B and RC, from laser C. Finally the positional 
values of each retroreflector are calculated according 
to geometric relationships, whereby the configuration 
of the object within the coordinate frame is determined. 
3 Claims, 2 Drawing Sheets 
WI ABSTRACT 
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4,9 64,722 
1 
REMOTE omm 
C O N F I G U R A T I O N / O R O N  
DETERMINATION 
ORIGIN OF THE INVENTION. 
The invention described herein was made in the per- 
formance of work under a NASA contract, and is sub- 
ject to the provisions of Public Law 96-517 (35 USC 
202) in which the Contractor has elected not to retain 
title. 
TECHNICAL FIELD: 
The invention relates to object detection and location 
systems and, more particularly, to the method of deter- 
mining the configuration and location of an object with 
respect to an X, Y, X coordinate frame comprising the 
steps of, equipping the exterior surface of the object 
with a plurality of retroreflector surfaces capable of 2o 
reflecting range measuring laser beams back to their 
sources; locating three lasers, ‘‘A”, “B’, and “C”, or- 
thogonally to one another such that laser “ B  defines 
the origin of the reference coordinate frame, laser “A” 
defines an X axis, and laser “C” defines a Y axis with a 25 
Z axis normal to a plane defined by the three lasers 
whereby to define the reference Coordinate frame; em- 
ploying the lasers to determine the range distance to 
each of the retroreflector surface within the coordinate 
frame by reflecting laser beams from the retroreflector 3o 
surfaces; dividing the space defined by the coordinate 
frame into four quadrants; for each retroreflector, using 
the location of the retroreflector within a particular 
quadrant to determine the value of variables qx and qy 
to be used in association therewith according to the 35 
following relationship, 
5 
15 
Quadrant Xpolarity Ypolarity qxvalue qxvalue 
I positive positive 0 0 
I1 positive negative 1 0 4 . 0  
111 negative negative 1 1 
IV negative positive 0 1 
where the values of X, Y, and Z are defined as positive 
going towards lasers A and C from laser B and Z is 45 
taken as positive going upward from the X-Y plane; and 
for each retroreflector, designating the measured 
ranges from the laser to the retroreflector as RA,, from 
laser A, RB, from laser B and RC, from laser C; and, 
calculating the positional values according to the fol- 50 
lowing geometric relationships: 
the angle alx between the X axis and the measured 
range RJ3, being, 
the X axis coordinate xl of the retroreflector being, 
60 
xl =(RB,)[CoS(aLx)l[(- 1YX1 
the angle aly between the Y axis and the measured 
range RB, being, 
Cos-’[(RBn)’ + (bc)’ - (RCn)’] 
2be(RBn) 
aly = 
the Y axis coordinate yl of the retroreflector being, 
65 
~~ 
2 
~1 =(R&dW&91[(- 1P 
and, 
the Z axis coordinate Z1 of the retroreflector being, 
zl=[(RBn~’-(xl~*-cvl~’l-’ 
whereby the configuration of the object within the 
coordinate frame is determined. 
BACKGROUND ART 
In the field of object detection and location systems, 
it is well known how to locate objects and determine 
their position relative to the Earth’s surface. For exam- 
ple, as depicted in FIG. 1, an airplane 10 can calculate 
its position by employing a directional antenna to 
determine the direction from the airplane 10 to a pair of 
radio broadcasting transmitters 12 whose location is 
known. Likewise, as depicted in FIG. 2, a radar site 14 
can determine the direction and range of the airplane 
10 by transmitting radar pulses 16 and detecting the 
return signals 18 from the airplane 10. As is well known 
and as world events continually demonstrate, the radar 
system of FIG. 2, cannot determine object orientation. 
For example the airplane 10 shows up on a CRT radar 
display as a “blip” or dot of light. It is assumed that 
the airplane 10 is oriented in the direction of movement 
of the bilip. It could be flying upside down, however, 
and the radar operator would not be able to determine 
that fact. Likewise, a helicopter flying backwards or 
sidewards would be assumed to be flying in a forward 
direction from the few facts available to the radar 
operator. 
In space applications in particular, there is a need to 
be able to determine the orientation of an object at a 
distance. As depicted in FIG. 3, there are instances 
where an operator at a site 20 on Earth has need to be 
able to send some sort of beam 22 to an orbiting space 
station 24, or the like, and passively determine there- 
from the orientation of the station 24 relative to an 
Earth-oriented coordinate system. Such inputs would 
be desirable and necessary, for example, in the control 
of large, flexible space structures. At present, there is no 
available method or apparatus which will allow the 
operator to make such a determination. A similar prob- 
lem and need exists in robotic applications. While the 
need has been continuous and computers have been 
available to provide the computational capability re- 
quired, to date there has been no system capable of 
harnessing the computer’s capability to solve the prob- 
lem. 
STATEMENT OF THE INVENTION 
Accordingly, it is an object of the invention to pro- 
vide a method and associated apparatus for determining 
the orientation of a remotely deployed object. 
It is another object of the invention to provide a 
method and associated apparatus for determining the 
spatial orientation of an object in space with relation to 
an Earthoriented coordinate system. 
It is yet another object of the invention to provide a 
system for remotely defining an object’s configuration 
in a manner compatible with a computer’s analytical 
capability. 
Other objects and benefits of the invention will be- 
come apparent from the description which follows 
hereinafter when taken in conjunction with the drawing 
figures which accompany it. 
4.964,722 ,- 
3 
BRIEF DESCRIPTION OF THE DRAWINGS 
FIG. 1 is a simplified drawing showing a prior art 
system for determining position on the Earth from the 
direction to a pair of remote broadcasting stations. 
FIG. 2 is a simplified drawing showing a prior art 
radar system for determining an objects range and di- 
rection.. 
FIG. 3 is a simplified drawing depicting the problem 
solved by the present invention. 
FIG. 4 is a simpWied drawing showing how a plural- 
ity of retroreflectors are attached to an object prior to 
deployment in order to employ the technique of the 
present invention. 
FIG. 5 is a drawing showing the vectors to one retro- 
reflector used in the calculations for determining the 
orientation of a remotely disposed object. 
DETAILED DESCRIPTION OF THE 
INVENTION 
The solution to the above-described problem is to 
employ a set of high resolution range measuring lasers 
physically arranged so as to define a reference coordi- 
nate frame and, additionally, equip the object whose 
configuration is to be defined with a plurality of sur- 
faces capable of reflecting the range measuring laser 
beams back to their sources (i.e. retroreflectors). The 
retroreflectors are placed at known locations on the 
surface of the object. Then, from the range data ob- 
tained and the coordinate locations of the sources, cal- 
culate the coordinates of each retroreflecting surface, 
and thus determine the configuration of the object. 
FIG. 4 is a simplified drawing depicting how a plural- 
ity of retroreflectors 26 are attached to the object 28. 
Such retroreflectors are well known to those skilled in 
the art and, therefore, will not be described in any detail 
5 
10 
15 
20 
25 
30 
35 
4 
determines the value of variables qx and qy used in the 
calculations as follows: 
Quadrant Xpolarity Ypolarity qxvalue qxvalue 
I positive positive 0 0 
I1 positive negative 1 0 
111 negative negative 1 1 
N neuative wsitive 0 1 
The values of X, Y, and Z are defined as positive going 
towards A and C from B and, Z is taken as positive 
going upward from the X-Y plane. 
The measured ranges from each range measuring 
laser 30 to the retroreflector 26 of FIG. 5 (designated as 
retroreflector #1) are indicated as RA1, from laser A; 
RB1 from laser B; and RCI from laser C. Similarly, 
ranges to other retroreflectors would bear their number 
designation, as for example; RA,would be the measured 
range to retroreflector “n” from laser A. The three 
measured ranges serve as the basis of coordinate deter- 
mination according to the following geometric calcula- 
tions, which are repeated for each retroreflector 26, in 
determining object configuration. 
As depicted in FIG. 5, the angle alx between the X 
axis 34 and the measured range RB1 is calculated by: 
The X axis coordinate of retroreflector 1, XI ,is eval- 
uated as follows: 
xl =(ml)[cos(ah)][(- 1y q 
Similarly, angle aly, the angle between the Y axis 36 
and measured range RB1, is calculated by: 
herein in the interest of simplicity and the avoidance of 
redundancy. There are a plurality of reflecting surfaces 
on the object 28 provided by the retroreflectors 26; 40 
cos-1[(RB1)2 + (kp - (Rap] 
ob = 2bCiRBU 
which may be small retroreflectors, such as comer 
reflectors. 
FIG. 5 illustrates the method of determining the co- 
ordinates of each retroreflector 26 mounted on the ob- 
ject 28 whose configuration or orientation is to be deter- 45 
mined in terms of the coordinate frame, generally indi- 
cated as 32, defined by the three range measuring lasers 
30. Laser range finders as employed for the lasers 30 are 
a relatively recent development; but, are well known to 
those skilled in the art. Thus, like the retroreflectors 26, 50 
they Will not be described in detail herein in the 
interest of simplicity and the avoidance Of redundancy. 
For convenience, the three lasen 30 are labelled “A”, 
This is used to calculate the Y axis coordinate of 
retroreflector 1, yl , by: 
,,l=(~sl)[c~~(~ry)][(- lp] 
The Z axis coordinate of retroreflector 1, zl , is then 
calculated directly by: 
zi ,[(~s1)2-(~1)2,011)21-1 
Again, the foregoing calculations are repeated for 
each retroreflector 26. The resulting N1 set of coordi- 
nates thus define the configuration/orientation of the 
object 28 as well as its location in space according to the 
“ B ,  and “C”. Note that the lasers 30 are located or- 
thogonally Such that laser “ B  defines the origin of the 55 range measuring lasers 30. 
reference coordinate frame 32, “A” defines the X axis 
34, and ‘‘C” defines the Y tlxk 36. The z axis 38 is, Of 
C0-9 normal to the Plane defined by the three range 
measuring lasers 30 (i.e. “A”, “ B ,  and “C”). For clarity 
and simplicity, Ody one retroreflector 26 iS illustrated in 60 
coordinate frame 32 determined by the placement of the 
I 
1. The method of determining the orientation and 
location of an object with respect to an X, Y, Z coordi- 
(a) equipping the exterior surface of the object with a 
nate frame comprising the steps of: 
FIG. 5, it being understood that the calculations involv- 
ing all retroreflectors are carried out by the same 
plete set of coordinates of all  the reflecting Surfaces 
defines the configuration of the object. 
For purposes of calculation, the space defined by the 
coordinate frame is divided into four quadrants; loca- 
tion of the retroreflector within a particular quadrant 
plurality of retroreflector surfaces capable of re- 
flecting range measuring laser beams back to their 
sources; 
(b) locating t h e  lasers, “A”, “B, and “c”, orthogo- 
nally to one another such that laser “ B  defines an 
origin of the reference coordinate frame, laser “A” 
with respect to laser “B’ defines an X axis, and 
laser “C” with respect to laser “ B  defines a Y axis 
method. Once the calculations are completed, the com- 
65 
4,964,722 
5 6 
such that a Z axis is normal to a plane defined by 
(c) employing the lasers to determine the range dis- 
(d5) the Z axis coordinate z1 of the retroreflector 
the three lasers; being, 
tance and angle from each of the three lasers to z 1 = [(rBnY - (XIY -&lY]- 1. 
each retroreflector 
frame by 
reflected laser beams to develop range data; and, 
(d) employing the range distance and angle data from 
each of the three lasers obtained from step (c) to lo 
calculate the coordinates of each retroreflecting 
surface within the coordinate frame whereby the 
orientation and location of the object within the 
coordinate frame is determined. 
2. The method of claim 1 wherein said step (d) 
thereof of employing the range data obtained from step 
(c) thereof to calculate the coordinates of each retrore- 
flecting surface within the coordinate frame comprises 
the steps of: 
(a) dividing the space defined by the coordinate 
frame into four quadrants as defined in step (b) 
hereafter; 
(b) for each retroreflector, using the location of the 
retroreflector within a particular quadrant to deter- 25 
mine the value of variables qx and qy to be used in 
association therewith according to the following 
relationship, the coordinate frame; 
within the coordinate 5 3. The method of determining the orientation and 
location of an object with respect to an x ,  Y, z coordi- 
(a) equipping the exterior surface of the object with a 
plurality of retroreflector surfaces capable of re- 
flecting range measuring laser beams back to their 
sources; 
(b) locating three lasers, “A”, “B”, and “C”, orthogo- 
nally to one another such that laser “ B  defines an 
origin of the reference coordinate frame, laser “A” 
with respect to laser “B’ defines an X axis, and 
laser “C” with respect to laser “ B  defines a Y axis 
such that a Z axis is normal to a plane defined by 
the three lasers whereby to define the reference 
coordinate frame; 
(c) employing the lasers to determine the range dis- 
tance and angle from each of the three lasers to 
each retroreflector surface within the coordinate 
frame by reflecting laser beams from the retrore- 
flector surfaces and then receiving and processing 
reflected laser beams to develop range data which 
is the range distance and angle from each of the 
three lasers to each retroreflector surface within 
(d) dividing the space defined by the coordinate 
frame into four quadrants as defined in step (e); Quadrant Xpolarity Ypolarity qxvalue qxvalue (e) for each retroreflector, using the location of the 
I positive positive 0 0 retroreflector within a particular quadrant as deter- 
mined from the range data from step (c) to deter- n positive negative 1 0 111 negative negative 1 1 
IV negative positive 0 1 mine the value of variables qx and qy to be used in 
association therewith according to the following 
relationship, 
where the values of X, Y, and Z are defined as 
positive going towards lasers A and C from laser B 
and Z is taken as positive going upward from the Quadrant X polarity Y polarity qx value qx value 
laser beams from the retrore- 
flector s u r f a c ~  and then receiving and processing nate frame the Of: 
15 
20 
30 
35 
X-Y plane; and for each retroreflector,, 4 0 1  positive positive 0 0 
0 (c) designating the measured ranges from the laser to 11 positive negative 1 
the retroreflector as RA,, from laser A, RB, from 
laser B and RCK from laser C; and, 
(d) calculating the positional values according to the 
following geometric relationships, 
(di) the angle alx between the X axis and the mea- 
111 negative negative 1 1 
IV negative positive 0 1 
45 where the values of X, Y, and Z are defined as 
positive going towards lasers A and C from laser B 
and Z is taken as positive going upward from the 
X-Y plane; and for each retroreflectorn, 
(0 designating the measured ranges from the laser to 
the retroreflector as RAK, from laser A, RB, from 
laser B and RC, from laser C; and, 
(g) calculating the positional values according to the 
following geometric relationships, 
(g) calculating the positional values according to 
(gl) the angle alx between the X axis and the mea- 
sured range RB, being, 
coS-’[(mnY + (UbY - ( u n ) * l  
Wmn) 50 ULX = 
(d2) the X axis coordinate Xi of the retroreflector 
being, 
the following geometric relationships, 
sured range RB, being, 
X I  = W n )  [C~S(ar*l1K- 1)4”1 
(D3) the angle aly between the Y axis and the mea- 
55 
sured range RB, being, 
C O S - ~ [ ( R B , ) ~  + (ab)2 - ( R 4 3 2 ]  
2aMRBd 60 alx = 
C O S - ’ [ ( R B , ) ~  + (bc)’ - (RC,Jz1 
2WRBn) (g2) the X axis coordinate xl of the retroreflector aly = 
being, 
(d4) the Y axis coordinate Y1 of the retroreflector 
being, 65 1 =(RBn)]Cos@k)fl(- 1)qq 
(g3) the angle aly between the Y axis and the mea- 
sured range RB, being, 
7 
4,964,722 
8 
(g4) the Y axis coordinate yl) of the retroreflector 
being, 
u~=[(RB~)~-(x~~-CV~)~I-', 
5 
whereby the orientation and location of the ob- 
ject within the coordinate frame is determined. * * * * *  
10 
15 
20 
25 
30 
35 
45 
50 
55 
65 


Remote object configuration/orientation determination

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