On controlling aircraft and underwater vehicles

In this paper we make the important observation that the attitude and angular velocity control systems for gas-jet aircraft and underwater vehicles are of a special form: they are affine control systems with constant control distributions and multi-affine drifts. For this general class of systems, we can construct (and check the existence of) bounded controls driving the system from initial to final regions of the state space. This can be used for tasks requiring repositioning or changing the velocity of the vehicle under constraints on both controls and state. We illustrate the procedure by solving the problem of changing the angular velocity of a parallelepiped aircraft under velocity and control constraints imposed by the task. The method should be seen as a "maneuver" procedure, allowing automatic generation of control laws for bringing the system in a desired region of its state space. If stabilization to a point is required, then locally stabilizing control laws can be used after the maneuver.