The goal of this paper is to show how geometric control theory can be used to design efficient trajectories for an autonomous underwater vehicle descending into a basin, as well as performing its recovery after experiencing an actuator failure. The underwater vehicle is modeled as a forced affine connection control system, and the control strategies are developed through the use of integral curves of rank one and kinematic reductions. Such a method is particularly efficient in case of actuator failure and it provides a constructive way to design trajectories for the new under-actuated system. A typical scenario of basin descent is presented, control signals are computed to realize the desired trajectories and some simulations are provided
A one degree-of-freedom precision position control system using an electrostatically actuated and capacitively sensed beam is reported. The beam is allowed to rock on a 10 µm high fulcrum which is fabricated from SU-8 deposited onto a glass substrate. The fulcrum establishes the nominal working gap between the beam and two electrodes located on the substrate. The differential capacitance formed by the beam and electrodes is sensed, however, the electrodes are also simultaneously used for applying controlled electrostatic forces to the beam. The system is unstable so feedback control is necessary to establish a desired stable gap but only after an appropriate feedforward filter that compensates for the forcer-to-pick-off coupling is implemented. The RMS displacement noise from DC to 100 Hz is 7 nm, and the gap can be regulated from DC to 600 Hz.
Autonomous underwater vehicles are commonly used for ocean exploration and this research illustrates one of their typical applications. Here, a practical mapping and sampling mission for the summit of the Loihi submarine volcano, a seismically active seamount southeast of the Island of Hawaii, is designed and simulated. Mapping the underwater volcano is safety-critical for monitoring earthquakes and tsunami warnings caused by the active volcano. Moreover, the deep-sea hydrother mal vents located at the summit also increase the Interest in exploration and experimentation. These kinds of underwater scenarios are highly dangerous. For instance, the rapidly chang ing landscape of Loihi witnesses continuously falling rocks. Therefore, the mathematical framework of geometric control theory is used to take into account the possibility of loosing some degrees of freedom due to actuator failures. Moreover, the proposed control strategy can be augmented with a state feedback control in case of full actuation. Graphic simulations show the effectiveness of this approach in handling initial perturbations.
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