L.A.M. Polyline Reshaping: Solutions & Ideas

[szandara]

Hi everybody

I am working on SLAM, the localization problem in robotics. I have a trajectory generated from my odometry sensors that is composed of a set of points ( O ). ( S ) is the starting point end ( E ) is the ending point of the trajectory. These points can define a polyline

S$\mapsto$O$\mapsto$O$\longmapsto$E

the arrows represent the transactions which are known and are not identical. The drawing is a 1D case but I am working on 3D.

Say I correct the ending ( E ) and move it forward a certain amount $\delta$.

S$\mapsto$O$\mapsto$O$\longmapsto$$\stackrel{\delta}{\rightarrow}$E

I know that the correction of E affects the rest of the points but I don't know how. So I need to suppose an intelligent way to reshape the rest of the trajectory, in this case to stretch it. There's not a specific way to define "intelligent", I just would like to know if there's a known way to apply the correction to the whole trajectory in a way that make sense.

Maybe someone that works with computer graphics knows a simple idea?

some people suggested the use of springs but for a different case which you cannot easily apply to this case.

thanks and regards

S.

 

[jvicens]

Hello,

As a fellow scientist, I find your question very interesting. SLAM is definitely a fascinating topic in robotics and it's great to see that you are working on it.

In terms of correcting the ending point (E) and reshaping the rest of the trajectory, there are a few methods that come to mind. One approach could be to use a Kalman filter, which is commonly used in SLAM, to adjust the positions of the points in the trajectory based on the new corrected ending point. This would involve predicting the positions of the points using the odometry data and then updating them based on the corrected ending point.

Another approach could be to use an optimization algorithm, such as gradient descent, to minimize the error between the corrected ending point and the positions of the other points in the trajectory. This would involve defining an error function that takes into account the distance between the corrected ending point and the other points, as well as any other relevant parameters.

As for the idea of using springs, I can see how that could potentially work but it would require defining the stiffness and damping coefficients for each point in the trajectory, which could be challenging.

I would also suggest looking into research papers or discussions within the computer graphics community, as they often deal with similar problems and may have some insights or techniques that could be applicable to your case.

I hope this helps and good luck with your research!