Closed loop control of 3D underactuated vehicles via velocity field tracking

A novel strategy to design time invariant motion controllers for underactuated mobile systems is applied to the position and attitude control of an underactuated 3D vehicle. The idea consists in defining a velocity vector field such that an ideal, fully actuated system would exponentially achieve the control objective by simply following such field. Then a steering law for the given underactuated system is designed such that it is exponentially stabilized parallel to the above mentioned velocity vector field. For the particular problem here addressed, due to the use of polar like coordinates, this method yields a discontinuous control law. Both the design process and the resulting solution have a most clear physical interpretation. Important practical requirements as approaching the target on a null curvature path, avoiding cusps in the whole path and moving in only one given forward direction are easily satisfied within this framework.