How to Measure the Relative Position of Two Objects

So you have a frame of reference which is moving (traslations and rotations) ? .
Seems like a tough one to me...
Del

Yes. But obviously, if you need to set an absolute frame of reference which doesn't move, you can.... but I need to measure the relative position between the two objects (not just the distance).

Thank you Nick Name, but I've already made your considerations about the solution with inertial sensors. I think it is the best solution too, but I want to be sure that there are not other interesting way to do it. To answer to your question, I need to know the coordinates of B (you can imagine it as a point) with respect to the reference frame on A, so it's not just the distance. I have just an observation for you, in the case we wanted to measure only the distance between A and B, we need also the gyroscopes. Because the accelerometers measure the accelerations in the local reference and not in the global one, so we need in any case to know how the local references are oriented with respect to the global one. I also think about using light rays or ultrasonic sensors, but their problem is to align the emitter to the receiver. About the magnetic field sensors, the problem is that there are several electric motors working on the object A.

NO : if you have inertial sensors on BOTH you have as result the position VARIATIONS of both "points" with respect to the initial positions which I suppose as known.

The distance is D= √Σ(Vbi-Vbi)² for i=1to3 for the 3 directions. You need angular informations ONLY if you are obliged to define the PROJECTIONS of D on the reference frame axis.

As mentioned in previous comment the number and type of sensor depends on what you want to obtain as result.

YES: because A and B can rotate on the space, consider the following example: On the plane XY. Initial positions: A(0,0) and B(1,0); The local reference frames of A,B and the absolute one are parallel. Case 1: A and B traslate along Y of 1 m. The final distance is 1 m. OK. Case 2: B rotates along Z of 90° clockwise, then both A and B traslate along their local Y axis of 1 m. Using only accelerometers you obtain the same final distance as above. You need a gyro on B to detect that its local Y axis become parallel to the absolute X axis and then calculate the correct distance.

I come back YES the angular position is needed since the sensors turn and their output is relative to own reference frame. Good point for you. I was too quick and neglected an aspect, it happens.

With respect to other possibilities. The signal coming from a body considered as emitter must have a distance depending information. It has to be either a sound wave or an electromagnetic wave. I would prefer as the following shows a lower frequency to avoid an unidirectional which makes the sensing more complex.

Let assume each body has 3 emitters distant from each other with a spherical emitting profile. Each one has its own frequency. The receiver gets 3 signals with intensities proportional to 1/ Li² where Li is the distance from receiver to one of emitters. The intensity of every received signal will be proportional to the distance to the emitter this way you dispose of 3 distances to 3 origins. It is enough to determine the distance between receiver and center of emitters. It is a triangulation the position being at the intersection of 3 spheres. I did not look at details but I have the feeling that the signals could be also used for the angular position. Or it would be needed to have 4 emitters ? the problem is always in this situation the ambiguity due to symmetries.

PS.: I wrote it before reading you last comment.

I continue the idea of spherical wave fields of medium frequencies. The first idea based on 3 emitters is ambiguous as result. I came to the idea that 4 emitters placed at the corners of an equilateral tetrahedron will bring the required information with respect to position since 3 will define a plane and the forth the position with respect to the plane.

I do not know yet how the angles can be determined. A couple of thoughts more, may be it is possible.

Hi Nick Name. I'm agree with you, we need at least 4 distances from 4 points not complanar to define the position of a point in the space. But maybe 3 distances are enough, in fact the problem is equivalent to find the intersection of 3 spheres and, if the centers are not aligned, the results are two points and in some case we can exclude one of this... for example if we track the position of B over the time, and we know the initial position we can choose the point nearest to the previous position. Anyway, I have some questions (I'm a mechanical eng. and so actually i'm not expert on electromagnetic topics). Are you talking about medium frequencies radio wave? Using the measurement of variation of intensity, is it possible to measure also short distances, about 10 cm? If we use 1 emitter on B and 4 receivers on A, is not a more simple solution? I'm not interesting about the orientation of B with respect to A, but only the coordinates of B in the local reference frame A.

The real problem in this phantasy approach is the spherical wave front. It is assumed that the emitter energy will be uniform on a sphere radius "r". The density will be De= K/r² since there are not any other sources with same frequency. The change rate of the density will be d(De)/dr= -0.5*K/r^3. This means that the changes will decrease when distance (r) increase. I am not an radio specialist so that even if I can imagine the approach I cannot tell you how feasible it is. You know when you think a way and the question looks an other way first it is necessary to change your mind so that I shall make a comparison and give an answer but I do not want to make fast again and neglect some aspects.

you can use pyramid shapes on each object, or just on one. Use a camera and trigonmetric software to analyze the geometry of the pyramid. (angles & scale) Position the pyramid so that the initial position has an corner basically pointing at the camera in a middle position, (assuming the basic motion is oscillatory) and then you should always have two faces visible to the camera. As the objects move relative to each other, the apparent angles and apparent size will vary, and you can calculate position and rotation. (assuming there is no interference with the vision system)

chris

Very good solution assuming that the object does not come out of camera vision angle. Since there is no limitation for the relative angular movement with only one camera it is risky. The number of cameras should be so that never the target body comes out of view. It is not necessary to use a pyramid it can be also a parallelepiped. But how do you solve the problem if the body is a disc or a sphere? or a potato ? the body must have a projection profile which is directly related to the vision angle so that his position can be recognised. A regular profile gives same image at different angles thus not being without ambiguity.

The problem is again the complexity of the data acquisition and processing since depending on position data from 2 cameras (or more) have to be processed at same time.

Inertial sensors and the gyroscopes lead to the simplest approach provided that their uncertainty is low enough.

Nice solution Chrisg288, but as Nick Name observed the problem is the visual cone of the camera... I can mount the camera on a two dof base on A so it can search or follow B on the space... but it is too much complex for my application.

How about two separate, extremely accurate, GPS's?

Very good solution only how do you intend to determine the angular relative positions if it is required ?

The GPS uncertainty is higher than the requested uncertainty so that even with a trick one could determine the angles (although i do not know how) the solution will not satisfy the definition.

And a last aspect what happens if the bodies are out of range for the GPS ? for instance on the moon ? or Mars ?

That could be interesting... not using traditional GPS, because I don't think it could have a precision of 0.5 cm. But, if we place 3 radio emitters on A and a receiver on B, and we can measure the distance between each emitter and the receiver we can determine the space position of B with respect to A... what do you think? Is it possible to measure short distances (10 cm to 2 m) using radio waves (maybe some GHz)?

In an other thread the GPS uncertainty is mentioned as 6' ≈ 180mm.

The traditional gyroscopes or the actual systems are "rate sensors". Because of tradition in many papers new mms are called gyros still. The use of rate sensors progresses but is not yet general.

Measure the two angles (altitude and azimuth) then the distance from OXYZ to A and from B to A? You would need to put sensors on A.

Use optic sensors conected to stepper motors to find the Angels. This would be similar to a Solar Tracker device. You would need a reflector or infared source on OXYZ and B.

The third mesurement, the distance between is a very common circuit.

The semiconductor industry has new MEMs devices that can do that. They can give the xyz, and RPY coordinates accurately and quickly. They do not use gyros, but can operate similar to a gyro. For one example visit:

http://cache.freescale.com/files/shared/doc/selector_guide/SG2016.pdf?fsrch=1

Paint or otherwise, add reference information to object A - "YOU ARE HERE." Put a sensor (visible-light camera for example) on object B, have it examine object A and inform you where it is based on what it sees. If B can rotate, you'll need multiple detectors on it.

A visible-light camera with a narrow aperature lens (low f-stop) would result in various parts of the scene (object A) being sharp and the rest out of focus. I'm not sure how practical or easy to use are the algorithms for detecting sharpness, but edge detection is well-established in image processing.

perhaps you can use the same approached used by the David Laser Scanner system. It is a 3d laser scanning system using a simple construction laser, a web cam, and a background reference template, and it can produce high resolution surface scans (as point cloud) which is importable into 3d softwares (ie Solidworks)

The use of a reference background might help out with whatever sensor system you look into. I've seen a first hand presentation of this system (david) and can assure you that it works well for scanning. All you would need is a realtime software system.. maybe they can help.

Chris