to find the state space representation of an underwater AUV

I want to know the method to create the state space representation of an underwater AUV dynamics for my SLAM project.

Answer 1

[Sam Chak]

Hi @BISWAJIT NAIK

You can try learning how to use the System Identification Toolbox to create the dynamical system model from measured input-output data of an autonomous underwater vehicle (AUV).

https://www.mathworks.com/products/sysid.html

If this is not what you are seeking for, please consult an Engineer or a Professor in Dynamical System on how to derive the state-space model from one of the following approaches:

1. Newton's 2nd Law,
2. Lagrangian mechanics,
3. Hamiltonian mechanics,
4. Kane's method,
5. Udwadia–Kalaba formulation.

[BISWAJIT NAIK]

Can you elaborate your answers's second part?

[Sam Chak]

They are suggested approaches that you can take. You are probably already familiar with Newton's 2nd law, . The motion of an AUV has 6 degrees of freedom and is constantly disturbed by the waves and ocean currents. So, you need to consider for the hydrodynamic forces, environmental forces, and control forces in the equation for each degree of freedom. That's why I suggest you to consult with your Professor or your Project Manager.

[BISWAJIT NAIK]

I have the Dynamic equations of motion AUV. Do you have any prior idea in how to create a linera state space model from the dynamic model?

[Sam Chak]

I see. In that case, you can try using the odeToVectorField() function.

https://www.mathworks.com/help/symbolic/odetovectorfield.html

[BISWAJIT NAIK]

Sir, Do you know How to calculate the vehicle pose using a camera or sonar sensor?

[BISWAJIT NAIK]

Hello Sir, can you tell me How to estimate the diagonal covariance matrix "R" for a measurement model ?

The measurement model is consists of sensor fusion of INS + DVL + pressure sensor.

[Sam Chak]

Hi @BISWAJIT NAIK

Perhaps you can use the Principle of Triangulation to determine the vehicle pose.

https://en.wikipedia.org/wiki/Triangulation_(surveying)

I think the covariance matrix can be computed using the cov() function:

https://www.mathworks.com/help/matlab/ref/cov.html

[BISWAJIT NAIK]

Sir, did you know How to properly define Extended kalman filter in matlab ? I am unable to define it . Majority times I am facing problem in defining the state transition function and Measurement function as the format it required to mentioned.