Abstract: The Lie group modeling method and gauss pseudo-spectral energy optimal control of the underwater vehicle are in research. Simplifying the underwater vehicle to be a free rigid body, in view of the possible large attitude angle maneuvering of the underwater vehicle, importing the concept of lie group and lie algebra, combining with the variation method and Lagrange method, the dynamics equation of the rigid body was derived, translating the tradition expression of the hydrodynamic force to obtain the dynamics equation of the underwater vehicle base on the lie group. With the Gauss pseudo-spectral method, the continue space optimal control problem of the underwater vehicle was translated into the nonlinear programming solved with MATLAB. According to the simulation of the energy optimal control of the underwater vehicle under the constraints of boundary values, path and control, the optimal control method can satisfy the constraint conditions, the method has a high accuracy, has a low dependency to the initial value, and the calculation method is feasible.

Key words: underwater vehicle, Lie group, variational method, energy optimum, pseudo-spectral method