eddy-morgan/diff_uv

A differentiable Underwater vehicles dynamic model with actuation in all DOFs and can control the position and attitude in 6 DOFs

Diff_UV (Differentiable Underwater Vehicle System)

A differentiable Underwater vehicles dynamic model with actuation in all DOFs and can control the position and attitude in 6 DOFs based on casadi operations.

The matrices 𝑀, 𝐶(𝜈) and 𝐷(𝜈), and vector 𝑔(𝜂) in the dynamics contain more than 300 unknown parameters in total. As a result, estimation of all parameters is infeasible. Yet, based on the features and operating speeds of the vehicle, several assumptions can be made to simplify the dynamic model and reduce the number of unknown parameters in the model.

The assumptions that have been made for the dynamics of a common ligtweight vehicle(the BlueROV2 Heavy) are listed in the following:

• BlueROV2 Heavy operates at relative low speeds (i.e. less than 2 m/s), lift forces can be neglected.
• BlueROV2 Heavy is assumed to have port-starboard symmetry and fore-aft symmetry; and the centre of gravity (CG) is assumed to be located in the symmetry planes.
• BlueROV2 Heavy is assumed to be hydrodynamically symmetrical about 6-DoF. Accordingly, the motions between DoFs of the vehicle in hydrodynamic can be decoupled.
• BlueROV2 Heavy is assumed to operate below the wave-affected zone. As a result, disturbances of waves on the vehicle are negligible.

Installation

The Diff_UV library has been implemented as a python3 pip package. To install and use this library in your own project, simply clone this repository to your workspace:

cd path/to/src
git clone https://github.com/Eddy-Morgan/Diff_UV.git
python3 -m build --sdist --wheel
pip install .

Getting Started

All hydrodynamic terms implemented in this project have been defined using Fossen's equations for hydrodynamics. The hydrodynamic terms implemented include:

• Mass: rigid body inertia and added mass
• Coriolis: centripetal, coriolis, and added coriolis
• Damping: linear and quadratic damping
• Restoring forces: buoyancy and gravitational forces

Each of the aforementioned terms provide their own distinct data class for independent use or can be managed altogether within the diffUV class.

from diffUV import dyn, kin
uv_dyn = dyn()

inertia_mat = uv_dyn.get_body_inertia_matrix()
coriolis_mat = uv_dyn.coriolis_body_centripetal_matrix()
restoring_vec = uv_dyn.gvect_body()
dampn_mat = uv_dyn.damping_body()
ned_accel = uv_dyn.forward_dynamics_ned()

Extending with CasADi Capabilities

All expressions obtained from the diffUV library methods (get_body_inertia_matrix(), coriolis_body_centripetal_matrix(), gvect_body, etc) are of CasADi type. This allows them to be integrated with CasADi's advanced functionalities for optimization, symbolic computations, and numerical integrations.

Symbolic Differentiation

Utilize CasADi's automatic differentiation to compute derivatives:

from casadi import jacobian
accel_jacobian = jacobian(ned_accel, uv_dyn.state_vector)

References

Fossen, T.I. (2011) Handbook of Marine Craft Hydrodynamics and Motion Control. John Wiley & Sons, Inc., Chichester, UK. https://doi.org/10.1002/9781119994138