Arbitrary 6-DOF large-angle tracking control for autonomous underwater vehicles via stochastic contraction stability and rotation matrix-based attitude representation

This paper investigates a stochastic-contraction-stability-based convex optimization control (SCOC) scheme for the trajectory tracking problem of stochastic autonomous underwater vehicles, where the rotation matrix is employed to represent the attitude and achieve arbitrary 6-DOF rotation with a large angle maneuver. Firstly, in contrast to the complexity introduced by directly using a rotation matrix in controller design, a novel error dynamics is developed for AUVs with an alternative attitude error vector. It has the potential to avoid singularities and unwinding phenomena under the influence of stochastic disturbance. A linear sliding manifold, together with the convex optimization, is utilized to construct an optimal contraction performance metric, which has the capability to minimize the upper bound of mean squared tracking errors greedily. The innovation of the SCOC lies in the transformation of the non-convex upper-bound minimization problem into an equivalent convex optimization framework with Riccati inequality constraints. The stochastic contraction theory demonstrates that SCOC can guarantee all-time exponential boundedness of the error for any initial condition with \({{\mathcal {L}}_{2}}\) ${\mathcal{L}}_2$ -robustness properties. To implement the sampling-based SCOC, the discrete-time stochastic contraction stability and its explicit relationship with the continuous-time counterpart will be introduced. Eventually, the theoretical analysis and comprehensive simulations are carried out to validate the feasibility and effectiveness of the proposed control scheme.