| x | Coordinate position in x direction |
| y | Coordinate position in y direction |
| ψ | Direction angle of the AUV |
| u | Velocity in x direction |
| v | Velocity in y direction |
| r | Angular velocity of the AUV |
| m | Mass of the AUV |
| Iz | Moment of inertia |
| X(·) | Hydrodynamic coefficient |
| Y(·) | Hydrodynamic coefficient |
| N(·) | Hydrodynamic coefficient |
| Tu | Thrust generated by the propeller |
| Tv | Thrust generated by the propeller |
| Tr | Thrust torque generated by the propeller |
| tf | Terminal time of navigation |
| hi | Obstacle function |
| a | Radius of the obstacle |
| b | Radius of the obstacle |
| J | Objective function |
| ω1 | Weight coefficient |
| ω2 | Weight coefficient |
| τ | Time variable |
| Li(τ) | Interpolation basis function |
| D | Differential approximation matrix |
| x(τ) | State variable function |
| u(τ) | Control variable function |
| Xf | Terminal state |
| τk | LG points |
| ωk | Gauss weight |
| Ce | Equality constraints |
| Ci | Inequality constraints |
| ai | Spline coefficient |
| bi | Spline coefficient |
| ci | Spline coefficient |
| di | Spline coefficient |
| Si(x) | Cubic spline function |
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