Source Seeking for Two Nonholonomic Models of Fish Locomotion

Abstract

In this paper, we present a method of locomotion control for underwater vehicles that are propelled by a periodic deformation of the vehicle body, which is similar to the way a fish moves. We have developed control laws employing "extremum seeking" for two different "fish" models. The first model consists of three rigid body links and relies on a 2-degree-of-freedom (DOF) movement that propels the fish without relying on vortices. The second fish model uses a Joukowski airfoil that has only 1 DOF in its movement and, thus, relies on vortex shedding for propulsion. We achieve model-free and position-free "source seeking," and, if position is available, navigation along a predetermined path.

A framework for a class of hybrid extremum seeking controllers with dynamic inclusions

“…This result was later extended in Tan, Nesić, and Mareels (2006) to obtain a semi-global practical stability result, whose foundation exploits the ''two-time scale'' setting analyzed in Teel, Moreau, and Nesić (2003). In general, these methods of analysis have proven to be instrumental for the design of several different extremum seeking controllers during the last years, e.g., , Dürr, Stanković, Ebenbauer, and Johansson (2013), Ghods and Krstić (2012), Ghaffari, Krstić, and Nesić (2012), Haring, Wouw, and Nesić (2013), Mills and Krstić (2014), Moase and Manzie (2012), Nesić, Mohammadi, and Manzie (2013), Nesić, Tan, Moase, and Manzie (2010) and Poveda and Quijano (2015), with applications in ABS break control (Yu & Ozguner, 2002), formation flight optimization, (Binetti, Ariyur, Krstić, & Bernelli, 2003), learning in non-cooperative games (Frihauf, Krstić, & Başar, 2012;Kutadinata, Moase, & Manzie, 2015), dynamic resource allocation (Poveda & Quijano, 2012, robot source seeking (Cochran, Kanso, Kelly, Xiong, & Krstić, 2009), optimization of wind turbines (Ghaffari, Krstić, & Seshagiri, 2014), and human exercise machine control (Zhang, Dawson, Dixon, & Xian, 2006), for example. One of the main limitations of existing ESCs based on averaging and singular perturbation theory is that, in general, they cannot deal with the presence of hybrid dynamics during the seeking process, i.e., dynamics that exhibit characteristics typical of both continuous-time systems and discrete-time systems.…”

Nash equilibrium seeking with infinitely-many players

“…where we have applied the Cauchy-Schwarz inequality and substituted the bound (18). The remainder of the proof directly follows after noting u * (x) ≡ 0.…”

“…Many works have used the extremum seeking method, which performs non-model based gradient estimation, for a variety of applications, such as steering vehicles toward a source in GPS-denied environments [16], [17], [18], optimizing the control of HCCI engines [19] and nonisothermal continuously stirred tank reactors [20], reducing the impact velocity of an electromechanical valve actuator [21], and controlling Tokamak plasmas [22].…”

The contol of the motion through an ideal fluid of a rigid body by means of two moving masses

“…траектория в пространстве позиционных переменных g (в нашем случае в E(2)). В теории управления замкнутые кривые в пространстве β, которые обеспечивают наиболее «удачные» элементарные движения (например, разворот на месте или почти поступательное движение в каком-то направлении) в пространстве g, принято называть гейтами (см., например, [8,10,11,16]). Найдя для конкретной задачи ряд удач-ных гейтов, можно из них конструировать более сложные движения, решая тем самым те или иные задачи управления и оптимизации [8].…”