Underwater Acoustic Source Seeking Using Time-Difference-of-Arrival Measurements

Abstract

The research presented in this paper is aimed at developing a control algorithm for an autonomous surface system carrying a two-sensor array consisting of two acoustic receivers, capable of measuring the time-difference-of-arrival (TDOA) of a quasiperiodic underwater acoustic signal and utilizing this value to steer the system toward the acoustic source in the horizontal plane. Stability properties of the proposed algorithm are analyzed using the Lie bracket approximation technique. Furthermore, simulation results are presented, where particular attention is given to the relationship between the time difference of arrival measurement noise and the sensor baseline-the distance between the two acoustic receivers. Also, the influence of a constant disturbance caused by sea currents is considered. Finally, experimental results in which the algorithm was deployed on two autonomous surface vehicles, each equipped with a single acoustic receiver, are presented. The algorithm successfully steers the vehicle formation toward the acoustic source, despite the measurement noise and intermittent measurements, thus showing the feasibility of the proposed algorithm in real-life conditions.

Extremum seeking control of nonlinear dynamic systems using Lie bracket approximations

“…The main idea therein is that trajectories of the extremum seeking system approximate trajectories of a so-called Lie bracket system which corresponds to a gradient-like dynamics which optimizes the cost function. Based on the Lie bracket system and its corresponding extremum seeking system, a whole analysis and design framework has been established, see, for example, References 16,17,[21][22][23][24][25][26][27][28][29][30][31][32] In particular, extremum seeking for dynamic nonlinear systems using Lie bracket approximations has been addressed in Reference 25. In that article, a combination of Lie bracket approximations and singular perturbations techniques (time-scale separation) has been proposed. In general, for dynamic extremum seeking systems, a singular perturbation approach is quite common, see, for example, the articles.…”

Extremum Seeking with Intermittent Measurements: A Lie-brackets Approach

“…Furthermore, we know from Step 1.2. (see (19)) that, for all ω ∈ (ω * 3 , ∞), k ∈ Z, t 0 ∈ [kT s + ǫ, (k + 1)T s ), and x(t 0 ) ∈ R n , it holds ||x(t) − x(t 0 )|| ≤ M S ω −0.5 , for all t ∈ [t 0 , (k + 1)T s ]. We may thus conclude that, for all ω ∈ (ω * 3 , ∞), t 0 ∈ R, and x 0 ∈ U x * R n (δ V ), the trajectory of system (7), through x(t 0 ) = x 0 , satisfies…”

“…[17] or [18]), or the source seeking, when the source emits a scalar signal achieving an optimum at its position (see e.g. [19] or [20]).…”

Marine Robots Mapping the Present and the Past: Unraveling the Secrets of the Deep

“…The long-term research goal of the authors is to develop the current unmanned survey/inspection missions by marine vehicles into missions that are performed by the marine vehicles in a fully autonomous manner controlled by artificial intelligence. This of course means that online sensor data processing must be developed to enable the vehicle to perceive its environment (as published in [19][20][21]), as well as mission and path planning algorithms, so that the behaviour of the vehicle is responsive to the new information about its environment, as published in [15,[22][23][24][25]. For successful, fully autonomous reconnaissance missions, it is of utmost importance that the marine vessels estimate their position accurately, as published by the authors in [12,26,27].…”