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Yes that is correct. Easiest way is probably to work with the homogeneous 4x4 Tranform Matrix($T$) composed of $\begin{bmatrix}R & t\\0 & 1\end{bmatrix}$. Then your new pose is then just $T_i$ multiplied by $\Delta T_{i+1}^{i}$(relative transform). For every new relative transform just do this concatenation. So $T_{i+1}=T_i*\Delta T_{i+1}^{i}$ Note:...

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The most traditional method is to keep looking at the trajectory and see if your current location is close enough to the previously visited place. Once this happens run the ICP. If ICP converged normally, that is your loop closure. A bit more advanced method is doing a place recognition. Generate a keyframe every few meters and extract a feature descriptor ...

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Matching point clouds can be very tricky. It is kind of a needle-in-a-haystack type of problem when you don't have an initial guess at the correspondence. As you found, if the point clouds are very different there really isn't a great way to quantify the similarity. This holds even if the two scans are similar (or even the same!) but have very different ...

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I don't know if your confusion is with applying the transform to the points or applying it to the pose. So I'll just show you both. The easiest way is to store your points and transform in the homogenous form. For 2D the transform is a matrix(3x3) that looks like T=\begin{bmatrix} cos(\theta) & -sin(\theta) & t_x\\ sin(\theta) & cos(\theta) &...

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