Obtaining MIMO kinematic model (+ controller) using data-driven approaches

Hello, as part of a project that I am developing. I would like to ask some questions about a rather "complex" problem.

1- Problem:

• Let's assume I have the kinematic inputs and outputs of a vehicle w.r.t time. The vehicle operates in one of two modes 1) Manual mode without controller. 2) Path following mode. Unfortunately the kinematics of the model is unaccessible, but from the behaviour and preimplemented software, I can deduct that it either behaves like a differential drive or ackermann or a combination of both systems. The dimensions of the model are given as well.

2- So my questions would be:

• Which method would be optimal for obtaining the open loop model from the data (during manual mode)? i.e which path/technique should I follow, machine learning or system identification or sth. else?
• Can I get a function that represents the model + the controller from the data of the path following mode?

3- End Goal:

• To clarify my intentions, I am just interested in the overall behavior of the vehicle not necassary how the actuators are being controlled, so that I can change the general inputs (position, velocity, acceleration) and check how the vehicle would behave w.r.t the new inputs in a simulation.

Answer 1

[Sam Chak]

Hi @mgf_04

This sounds like a system identification problem. If you have the System Identification Toolbox™ installed, then try using it.

Else, since the vehicle behaves like either the Differential drive or the Ackermann steering, you can try identifying the values of the parameters in one of these models using the least-squares method.

Check out these two examples:

https://www.mathworks.com/help/optim/ug/fit-ode-problem-based-least-squares.html

https://www.mathworks.com/help/optim/ug/fit-differential-equation-ode.html

[mgf_04]

Hi @Sam Chak! thank you for your answer. I just realized today that it can behave like both at the same, because it has 6 wheels and each one is controlled independently, to be more clear it can rotate about its center but it can also move linearly while steering. So I am a bit confused to how to proceed.

Also I checked this library before but from my little understanding I believe it is only used for SISO unknown models, but please correct me if I am wrong.