On a closed loop time invariant position control solution for an underactuated 3D underwater vehicle: implementation, stability and robustness considerations

Two discontinuous solutions for the kinematic position and attitude closed loop control problem of an underactuated floating body are considered. The first is derived on the basis of Lyapunov's stability theory while the second is designed exploiting a novel idea: first a vector field is defined such that an ideal point free to move in any direction would exponentially converge to the desired configuration and then a steering law for the underactuated vehicle is derived such that it is exponentially parallel to the above mentioned field. Both solutions yield cusp-free and asymptotically null curvature paths which is a major practical constraint in real world applications.