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Let us assume there are $N$ sensors permanently fixated on a rigid body each measuring the orientation (call it $q_i$) at their corresponding location (call it $p_i$) with respect to a fixed/well-defined coordinate system.

Now, if the rigid body is moved/rotated, the orientation reported by each sensor would be different (call it $Q_i$). How can I related $p_i$, $q_i$ and $Q_i$ to the translation/rotation information. I currently have the orientations in quaternion form.

One way I assume that the problem can be tackled is to define four points ($p_i$, $p_{ix}$, $p_{iy}$ and $p_{iz}$) all of which are part of the rigid body. Then $q_i$ is defined by those four points (think of the points as $(0,0,0)$, $(\delta_x,0,0)$, $(0,\delta_y,0)$ and $(0,0,\delta_z)$ localized to the location of each $p_i$). $q_i$ can now be fully determined from each set of four points. Similarly $Q_i$'s can be defined after moving/rotating the $N \times 4$ points.

John Brown
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  • I am pretty sure one can use the property of a rigid body, that the positions on such a body are fixed relative to that body. If one knows the position of the rigid body, e.g. of its center of mass or of a reference point, it is easy to calculate the position of all points on the rigid body, because one knows the fixed relative distances. Such a feat might apply for your property as well. – mvw Feb 29 '16 at 06:13
  • Orientation/attitude is what is reported by the sensors, we can assume that the reference frame is defined as x-axis pointing to the north pole and z-axis pointing to the center of earth (i.e. direction of gravity). – John Brown Feb 29 '16 at 06:23
  • mvw, Thanks for the comments, I am having issues formulating the problem (due to my limited knowledge on this context). I understand how each position is related to the movement/rotation of the body, but that has not helped me much. See my updated comments above. – John Brown Feb 29 '16 at 06:36
  • I would try a simple example. e.g. if you have a suitcase and a sensor on three surfaces, each surface orthogonal to the others. It seems to be just a problem of understanding the geometrical definitions and then a bunch of coordinate transformations. – mvw Feb 29 '16 at 06:50

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