Potential feature suggestion for tf extrapolation about geometry2

[tfoote]

Yes allowing extrapolation is technically relatively trivial. The original design of tf explicitly included this as a use case. After testing it was determined that using the naive extrapolation was actually very detrimental to operation because it is very sensitive to the noise signals and could easily turn stable systems into unstable systems.

In theory allowing extrapolation can help avoid phase lag in close loop control. However if the extrapolated values amplify the noise and not the signal it is much worse than waiting for the measurement to come in.

To this end we have been walking back the availability of extrapolation in the different generations of the tf APIs to the point in tf2 where it is not offered. So please don't take the time to add it back.

The problem with building the extrapolation into the generic tf API is that it does not have a model of the system. With a model of the system a estimator can be designed to estimate the state of the system and can estimate the future behaviour of the system using the model for feed forward. As a very trivial example use case, modelling a bouncing ball if the last measurement is when the ball is half way up it's parabola, and you use extrapolation based on the most recent measurements, your naive estimate of the balls position in the future is always rising which is obviously not true. For very short times linear extrapolation can be a good approximation, however the definition of short is completely dependent on the characteristics of the system, a ping pong ball and a barge have very different time scales over which extrapolation will remain valid.

Besides writing specific model/estimators for application specific extrapolation estimation, I think that there is room for building an extension/addon to tf2 which allows you to define a model and let it build up an estimate of the state of the model based on the tf history. And then support querying for times in the future based on the model's estimates in the future. This could provide the same API as the buffer and the model could have extrapolation tolerances built in which would limit the valid extrapolation distance.