GUIDANCE OF 3D UNDERWATER NON-HOLONOMIC VEHICLE VIA PROJECTION ON HOLONOMIC SOLUTIONS

The feedback control of a nonholonomic 3D ∞oating vehicle is considered: namely the control objective is to drive a vehicle moving in 3D space to a given point and heading along a given line having as control inputs a 1D linear velocity (surge velocity) and a 2D angular one allowing the vehicle to rotate around any axis normal to the surge one. This kind of kinematic describes a large class of ∞oating systems including underwater or space vehicles. In this paper it is shown that a suitable choice of state variables, i.e. a polar-like set of coordinates, allows to easily determine a nonlinear time-invariant closed loop law that drives the conflguration error to zero as long as the vehicles is not initially positioned in the target point. The conflguration error is shown to tend asymptotically towards zero via a Lypaunov analysis. The proposed solution builds on previous work regarding the planar unicycle kinematic model and its efiectiveness is conflrmed by a simulation analysis.