Trajectory generation and tracking on SE(3) for an underactuated AUV with disturbances

This paper describes the trajectory tracking of an underactuated autonomous underwater vehicle (AUV) with three control inputs (surge, yaw and pitch moment) that operates in the presence of time-varying disturbances. The AUV kinematics are described in global coordinates as a Hamiltonian system on the Lie group SE(3) and the boundary-value problem arising from the geometric framing of Pontryagin's Maximum Principle is applied to the vehicle kinematics. This 6-dimensional boundary value problem is solved using a numerical shooting method and a novel semi-analytical Lie group integrator. The integrator uses Rodrigue's formula to express the exact solution of the solution curves, is symplectic and preserves energy and momentum. Inverse dynamics is applied to construct an inner-loop controller, which accounts for constraints on maximum torque and force via time reparametrization. This inner-loop control, which would drive the AUV along the reference trajectory in perfect conditions, is combined with a disturbance observer to construct an outer-loop controller, which ensures stability in the presence of bounded disturbances. Simulation results complete the work.