- Input/output relation between tracking model and reference

- What is theta?

- Inner workings of model, is the source code uploaded somewhere for us to inspect?

- "Assume a constant longitudal velocity" - how would it a non-constant velocity impact the model?

- "Assume a constant longitudal velocity" - how would a non-constant velocity impact the model?

- In extension, how would one go about modelling it?

- Our model, while simplistic, captured this from open loop measurements

- The dynamic model is derived using Newtons laws?

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@@ -33,4 +32,50 @@ First off:

- Open loop reponse such as step, could this be useful?

## Answers / Notes

- Input/output relation between tracking model and reference

- What is theta?

Theta is a set of coefficients derived from the system (constants). These should make more sense when inspecting the project Cláudio gave us (source code for the paper).

- Inner workings of model, is the source code uploaded somewhere for us to inspect?

Yes. Cláudio has given us a snapshot of the source used for producing the results in the paper.

- "Assume a constant longitudal velocity" - how would a non-constant velocity impact the model?

In comparrison to ours, where our actuation model is used to determine the velocity, the models (should, could) be used together. However, this might yield issues.

The assumption stems from the idea that the system proposed in the paper "only" models to lateral dynamics of the system.

- The dynamic model is derived using Newtons laws?

Yes - the reference model is linked in the bibliography in the paper. (Kong et al 2015, Rajamani 2011) and based on previous model work done by Foldager.

- Sec. 4.1: The orientation and position integrating 8 and 9 twice? I dont quite follow

Integrated once to gain the position - twice is an error.

- Which parameters where they tuning to match reference path? Only tire cornering stiffness?

Yes, they tuned/calibrated a single parameter using a least mean squares approach to achieve convergence.

- Sec. 4.2. "No different than a model identification problem".

- Inspiration in regards to acquiring data to indentify the model?

- Open loop reponse such as step, could this be useful?

The phrase here should be held in conjunction with the single parameter tuned - this is not working on a basis of system identification between PT/DT. Allowing to tune singular parameters can yield better results - less error prone, easier to diagnose.

- About using a "datacentric" approach for calibrating the DT models.

By storing previous data (e.g, 2, 5 or more seconds), when divergence happens, the system can recalibrate by replaying previous data. However, key parameters to tune must be identified. In expansion here, our model is not really parameterized at the moment, and in order to allow for us to use this approach, we will need to rewrite/implement the actuation model of our system, such that the underlying parameters can be exposed.

- About Kalman filtering

Q from Jacob: While somewhat being familier with the overall concept of a kalman filter, I have not yet examined the inner workings of one.

A from Cláudio: Basicly there is two main components to the kalman filter, one is it's ability to predict the system state, another is the system has to be linearized for it to work. While the linearization might be a difficult task, the Kalman filter can be used to implicitly track model parameters which is not explicitly monitored by the DRobotti - e.g, we don't need to measure the tire stiffness coefficient, but if included in the dynamic model, the Kalman filter can implicitly solve for it (e.g when converging, it will assign the best fit values for it).

- About the "Incubator" project and determining cause for divergence

Q from Gill: How does one determine if divergence happens due to model inaccuracy or due to environment?

A from Cláudio: Here one could look at the divergence behaviour. Imagine having collected tremendous amount of data from steering the Robotti in circles. The model vs PT divergence behaviour might be somewhat "predictable", e.g in the sense that one would need new calibration every 2 seconds. Now imagine someone coming in and puncturing the tire on the Robotti. This will inevitably cause a rapid divergence between the model and PT system, and this rapid divergence can be distinguished from that of model inaccuracy.

Furthermore, to expand upon this, there is a "funny" phenonema of a incubator project where there is no divergence between model and actual system - maybe due to periodicity? System is tracking heat.

We would like to gain access to this, as it sounds quite interresting.

Lastly, if one where to train neural networks on the collected data for behaviours of the Robotti, a clear indicator of divergence not due to model innacuracy could be the NN prediction rate. E.g, training a NN to predict when recalibration is needed, and then running it in the system should allow for a high prediction rate. If someone then punctures a tire, the prediction rate will fall drasticly - e.g another measure for divergence.

## Resources provided by Cláudio

- recommended paper `kalman_filter_paper.pdf`

- paper repository `https://github.com/clegaard/pyfmu_paper` (we dont currently have access)