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Pipeline Following by Visual Servoing for Autonomous Underwater Vehicles

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Pipeline Following by Visual Servoing for Autonomous Underwater Vehicles Pipeline following by visual servoing for Autonomous Underwater Vehicles Guillaume Alliberta,d, Minh-Duc Huaa, Szymon Krup´ınskib, Tarek Hamela,c aUniversity of Cˆoted’Azur, CNRS, I3S, France. Emails: allibert(thamel; hua)@i3s:unice: f r bCybernetix, Marseille, France. Email: szymon:krupinski@cybernetix: f r cInstitut Universitaire de France, France dCorresponding author Abstract A nonlinear image-based visual servo control approach for pipeline following of fully-actuated Autonomous Underwater Vehicles (AUV) is proposed. It makes use of the binormalized Plucker¨ coordinates of the pipeline borders detected in the image plane as feedback information while the system dynamics are exploited in a cascade manner in the control design. Unlike conventional solutions that consider only the system kinematics, the proposed control scheme accounts for the full system dynamics in order to obtain an enlarged provable stability domain. Control robustness with respect to model uncertainties and external disturbances is re- inforced using integral corrections. Robustness and efficiency of the proposed approach are illustrated via both realistic simulations and experimental results on a real AUV. Keywords: AUV, pipeline following, visual servoing, nonlinear control 1. Introduction control Repoulias and Papadopoulos (2007); Aguiar and Pas- coal (2007); Antonelli (2007) and Lyapunov model-based con- Underwater pipelines are widely used for transportation of trol Refsnes et al. (2008); Smallwood and Whitcomb (2004) oil, gas or other fluids from production sites to distribution sites. mostly concern the pre-programmed trajectory tracking prob- Laid down on the ocean floor, they are often subject to extreme lem with little regard to the local topography of the environ- conditions (temperature, pressure, humidity, sea current, vibra- ment. tion, salt, dust, etc.) that may lead to multiple problems such as corrosion, crack, joint failure, shock loading and leakage. Reg- In this paper, the problem of pipeline following for AUVs, ular inspection, monitoring and maintenance of transportation commonly addressed by using either a monocular camera or an pipelines are thus highly recommended for safe operation. Con- acoustic sensor such as side scan sonar (SSS) or multi-beam ventional pipeline monitoring and inspection methods generally echo-sounder, is revisited. Control objectives often consist in consist in using surface ships and remotely operated underwa- steering the vehicle above the pipeline and in regulating its for- ter vehicles, with the consequence of slow response and mo- ward speed to a reference value that can be specified in advance bilization time Christ and Wernli (2007). Moreover, methods or online by a human operator. Most existing works on this involving human divers in deep water are difficult to implement topic have been devoted to pipeline detection from camera im- due to the inhospitable environment with high health and safety ages or SSS-images and to the derivation of the relative head- risks. As underwater operations increase in scale and in com- ing and position (up to a scale factor) of the AUV with respect plexity, the need for employing Autonomous Underwater Ve- to (w.r.t.) the pipeline. Basic kinematic controllers have been hicles (AUV) increases Shukla and Karki (2016b,a). However, applied without considering the system dynamics Matsumoto unlike unmanned aerial vehicles that have seen an impressive and Yoshihiko (1995); Antich and Ortiz (2003); Inzartsev and growth within the last two decades, progress in AUV research Pavin (2009); Bagnitsky et al. (2011) with the consequence and development has been drastically hindered by the lack of that the stability is not systematically guaranteed. Other con- global positioning systems, particularly due to the attenuation trol approaches for pipeline following have been proposed in a of electromagnetic waves in water. more “abstract” manner in the sense that error tracking terms The dynamics of AUVs are very nonlinear, with highly are directly defined from image features Rives and Borrelly coupled translational and rotational dynamics Fossen (2002); (1997); Krup´ınski et al. (2012). These image-based visual ser- Leonard (1997). Strong perturbations due to sea currents voing (IBVS) approaches do not require much knowledge about are also a source of complexity. Robust control design for the 3D environment and demand less computations. For in- AUVs thus has been extensively investigated. However, exist- stance, Rives and Borrelly (1997) proposed an IBVS controller ing control approaches such as PID Allen et al. (1997), LQR for fully-actuated AUVs using polar representation of lines (i.e. Naeem et al. (2003), H1 Fryxell et al. (1996), optimal control pipeline borders) while exploiting the so-called task-function Spangelo and Egeland (1994), sliding mode control Josserand approach developed by Samson et al. (1991). However, only (2006); Lapierre et al. (2008), Lyapunov backstepping-based local stability is proved since both the image Jacobian and Hes- Preprint submitted to Control Engineering Practice October 22, 2018 B B sian matrices considered in the control design are evaluated at −!e b −!b 1 the desired pose in the image plane. The domain of convergence e 2 −!e b is thus impossible to be characterized. The present paper aims 3 rC C C Vehicle rG −! e c pipeline at extending the provable domain of stability by taking the ve- 1 −!e c hicle dynamics into account and by adapting the IBVS control G 2 Camera View −!e c approach proposed in Mahony and Hamel (2005) to the case 3 of AUVs. More precisely, image features used for control de- sign are the bi-normalized Plucker¨ coordinates Plucker¨ (1865) of the pipeline borders. The resulting dynamic IBVS controller pipeline ensures the semi-global asymptotic stability. This paper is organized as follows. Section 2 recalls notation and system modeling. In Section 3, the problem of pipeline fol- lowing by visual servoing is formulated. Section 4 presents the Figure 1: Notation proposed controller based on a cascade inner-outer loop control −! −! −! architecture, where the inner-loop controller stabilizes the vehi- •A = fO; e a; e a; e ag is an inertial frame. Let B = cle’s velocities about a desired velocity setpoint and the outer- −! −! −! 1 2 3 fB; e b; e b; e bg denote a frame attached to the AUV, with ori- loop controller derives the desired velocities and their deriva- 1 2 3 −! −! −! gin coinciding with the vehicle’s CoB. Let C = fC; e c; e c; e cg tive from image features. Convincing comparative simulation 1 2 3 be a frame attached to the camera, which is displaced from the results and experimental validations, with a video as supple- −−! origin of B by a vector BC and whose base vectors are parallel mentary material, are reported in Section 5 to illustrate the ro- −−! bustness and performance of the proposed control approach. Fi- to those of B. The vectors of coordinates expressed in B of BC −−! 3 3 nally, concluding remarks are provided in Section 6. and BG are denoted as rC 2 R and rG 2 R , respectively. Some basic materials of this paper such as notation and sys- • The orientation (i.e. attitude) of B w.r.t. A is represented tem modelling are borrowed from our other work Krup´ınski by the rotation matrix R 2 SO(3). Let p and pC denote the et al. (2017), which deals with a completely different IBVS position of the origins of B and C expressed in A, respectively. control problem (i.e. fixed-point stabilization exploiting the ho- One has p = pC − RrC. mography matrix). Finally, for the sake of completeness in • The angular velocity vector of B relative to A, expressed in Section 4.2 the inner-loop controller is recalled from Krup´ınski B, is denoted as Ω 2 R3. The translational (or linear) velocity et al. (2017). Note, however, that the main contribution of the vectors of the origins of B and C, expressed in B, are denoted 3 3 present paper concerns the outer-loop control design level. as V 2 R and VC 2 R respectively. One has V = VC −Ω×rC. A primary version of this work has been presented in • The vector of coordinates of the fluid (i.e. current) velocity Krup´ınski et al. (2012) and a part of experimental results has in A and B are denoted as v f and Vf , respectively. In this paper, been reported in Krup´ınski et al. (2015). A number of improve- it is assumed that vf is constant. Vh , V − Vf is the vector of ments w.r.t. Krup´ınski et al. (2012) are proposed in this paper. coordinates of the CoB’s velocity w.r.t. the fluid. 3 For instance, to mitigate the strong coupling between the ver- • fe1; e2; e3g denotes the canonical basis of R . I3 is the iden- 3×3 3 tical motion and the transverse and yaw motions of the AUV tity matrix of R . For all u 2 R , the notation u× denotes the w.r.t. the pipeline that may lead to a large overshoot in altitude skew-symmetric matrix associated with the cross product by u, 3 > with a risk of collision with the ocean floor (see our prior work i.e., u×v = u × v, 8v 2 R . πx = I3 − xx is the projection onto Krup´ınski et al. (2012)), a decoupling strategy has been intro- the tangent space of the sphere S 2 of a point x 2 S 2. duced. Moreover, unlike Krup´ınski et al. (2012); Mahony and Hamel (2005) the desired feature is directly expressed in the 2.2. Recall on system modelling > > > 6 body-fixed frame, avoiding the need of full attitude estimation Define Wh , [Vh; Ω ] 2 R . The total kinetic energy of to compute the visual error. Finally, the comparative simulation the body-fluid system ET is defined as the sum of the kinetic study w.r.t.
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