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This paper proposes a kinematic model and an inertial localization system architecture for a riser inspecting robot. The robot scrolls outside the catenary riser, used for underwater petroleum exploration, and is designed to perform several nondestructive tests. It can also be used to reconstruct the riser profile. Here, a realistic simulation model of robot kinematics and its environment is proposed, using different sources of data: oil platform characteristics, riser static configuration, sea currents and waves, vortex-induced vibrations, and instrumentation model. A dynamic finite element model of the riser generates a nominal riser profile. When the robot kinematic model virtually scrolls the simulated riser profile, a robot kinematic pattern is calculated. This pattern feeds error models of a strapdown inertial measurement unit (IMU) and of a depth sensor. A Kalman filter fuses the simulated accelerometers data with simulated external measurements. Along the riser vertical part, the estimated localization error between the simulated nominal and Kalman filter reconstructed robot paths was about 2 m. When the robot model approaches the seabed it assumes a more horizontal trajectory and the localization error increases significantly.

One of the key elements of deep-water petroleum exploration is the production riser. Risers are the ducts that transport petroleum, water or gases from the exploitation well up to the production platform. Either rigid or flexible types of risers may be used in the oil field. Both types are submitted to a broad spectrum of failure causes [

A major technical problem in robotic underwater inspection is the navigation and/or localization of the robot in a highly dynamic sea environment. Navigation is especially critical for AUVs and somewhat critical for ROVs. Lee at al. [

Recently, our group designed and built a prototype of a robotic device specifically designed to perform nondestructive testing (NDT) in production risers [

Robot prototype.

Transversal view of the robot frame showing how it attaches the riser, by opening and closing its motorized arms. The polymeric free wheels that effectively touch the riser surface are also shown.

This paper proposes a kinematic model of the robot performing a riser profile cast mission, in a realistic simulated environment. Initially, a riser dynamic profile is estimated using a finite element model of the riser subjected to sea and ship motions. The nominal robot kinematic path (including position, velocity and acceleration), as it scrolls by the riser, is

The obtained profile can be used as an imposed displacement data for some structural analysis software based on finite elements techniques, that allows stress to be calculated. In addition, the localization algorithm can be used to associate each NDT measurement with its riser geometrical coordinate. These two aspects are intimately connected, and the localization algorithm can be used either to cast the profile, for fast robot runs, or localize the NDTs.

Reproducing the expected environmental conditions, to test the proposed approach, in a laboratory experiment is essentially impracticable. Field tests, by his turn, should require a expensive positioning system such as a 3D sonar, which does not operate at the required frequency resolution, due to the presence of vortex induced vibrations (VIVs). Therefore, a simulation of the riser application, together with simulated sensors, was used to assess the performance of the localization algorithm.

Actually, a particular environmental and riser configuration scenario is being addressed in this paper. However, the approach is likely to be applicable to similar situations. Other devices that move along subsea pipe systems, such as flowlines, jumpers, and umbilicals, could employ some of the main ideas presented in this paper. No additional localization devices, such as sonar beacons, are needed.

The localization problem formulation used a standard Kalman filter as a sensor fusion algorithm based on a simple kinematic model of a strapdown IMU fused with a depth sensor. More sophisticated sensor fusion algorithms or state-space models for the system (e.g., dynamical models) could also be tested in future implementations, but the problem formulation would be probably quite similar.

The particular sea and ship motion conditions selected for running the simulations corresponded to a

Parameters used in the simulations.

Parameter | Value |
---|---|

Robot length | 1133 mm |

Robot max. outside diameter | 800 mm |

Robot mass | 73 kg |

Riser outer diameter | 295.5 mm |

Riser inner diameter | 203.5 mm |

Riser length | 1530 m |

Riser internal pressure | 60 bar |

Outer riser drag coefficient (Cd) | 1.2 |

Water depth | 1180 m |

Seabed axial friction | 0.35 |

Seabed transversal friction | 0.9 |

Seabed vertical stiffness | 104.3 |

Wave height | 5 m |

Wave period | 10 seconds |

FPSO length | 330 m |

Identified parameters for the IMU sensor model^{1}.

Low cut (Hz) | High cut (Hz) | |||||
---|---|---|---|---|---|---|

Roll° | 629 | 5 | 20 | 0.1635 | 0.0072 | |

Pitch° | 578 | 6 | 20 | 0.1553 | 0.0072 | |

Yaw° | 1403 | 5 | 12 | 0.2144 | 0.0095 | |

AccX g | 10 | 0.3 | 3 | 0.0041 | ||

AccY g | 10 | 0.25 | 3 | 0.0011 | 0.0037 | |

AccZ g | 10 | 0.3 | 3 | 0.0033 | ||

AngRateX°/s | 15 | — | — | 0.0076 | 0.0076 | |

AngRateY°/s | 20 | — | — | 0.0074 | 0.0074 | |

AngRateZ°/s | 10 | — | — | 0.0057 | 0.0057 |

Data from a flexible free-hanging riser installed in a PETROBRAS (Brazilian State oil company) Turret Floating Production Storage Offloading (FPSO) oil platform, which is currently in operation in the Campos Basin, was used as the inputs for the riser simulation software FLEXCOM. This is a finite elements software customized for nonlinear static and dynamic analysis of offshore systems, used worldwide by the petroleum industry from the last 20 years, and validated against experimental tests and other finite elements packages [

To estimate numerically the localization system performance and calculate the associated displacement errors, the arrangement shown in Figure

Overview of the system simulation analysis. A dynamic riser profile is generated through an FEM analysis. Using robot’s kinematical and instrumentation model, the expected sensor readings are used to reconstruct the riser profile by the localization algorithm, which is compared to the original profile from FEM output.

The proposed localization system, that will be simulated numerically here, is shown in Figure

Architecture of the proposed localization system architecture. The robot scrolling along the riser generates a set of kinematic variables that is measured by the IMU. The accelerations are transformed to the global reference system, using IMU attitude outputs, and considered as the inputs of the KF. To compensate the drift caused by integrated sensor noise, the KF fuses the IMU with depth sensor data, that is, an absolute measurement. Before entering in the KF, the external measurements are processed by the method described in Section

A simulated profile of inertial sensor physical excitation was obtained. First, the

Side and upper views of the FPSO and riser configuration. Global (

The local reference system (

In the sequence, a particular

Euler angles

A linear current profile

The robot can move freely along the riser in the

Velocity of the robot in

The effect of the longitudinal sheer between the robot and the riser due to the transversal current was not taken into account. This current component was expected essentially to increase the normal force that the robot applied to the outer surface of the riser. Because the riser was tightly fitted among the robot’s rigid free wells to avoid longitudinal and torsional slipping, the increase in the shear force of the wheels that could decelerate the robot was considered to be negligible.

Since all the elements of the FEM mesh have approximately the same length, the time steps are no longer uniformly distributed with such variable velocity profile. The resulting variable time array was calculated by:

This nonuniform time array was inconvenient for future calculations of velocity and acceleration profiles, and a new set of

The dynamic FEM analysis allows finding, along the time, the altered geometry of the riser, with respect to the nominal static profile. The finite elements model had 170 beam elements with flexion, axial, and torsional deformations. Each element had a nominal length of 10 m. Dynamic FEM analysis provided the

This vector was decomposed into its normal

Therefore, the new coordinates

The sea current passing through a circular cylinder produces vortex-shedding in the wake, which causes the structure to vibrate. This complex fluid-structure interaction is called Vortex Induced Vibration (VIV), and it occurs predominantly on the cross-flow direction [

To adapt the experimental data to the riser that was being analyzed, the displacement was scaled by the test riser diameter and multiplied by the actual riser diameter. The frequency of shedding (

Figure

RMS of riser motion in

To simulate IMU output, the expected physical acceleration at the sensor installation point must be found. This acceleration was used to feed the sensor model to find realistic sensor signals. The acceleration at point

The local acceleration

To solve (

A low-cost microstrain 3DMGX-1 IMU was the project choice. This is a compact and integrated device, suitable for a high-depth submarine application, where the electronic case must be as slender as possible, for mechanical structural reasons. It delivers 3D accelerations, angular velocities, and attitude/orientation matrix in a single-serial channel. The error characteristics of each output were modeled as a wide-band noise plus a first order moving bias Markov process [

The wide-band sensor noise was defined as

The moving bias was found by integrating the following finite difference equation with the Euler method:

An experiment was performed to collect the error characteristics by keeping the sensor stationary in laboratory while recording signals. Total acquisition time was 4 h 21 min, with a 75 Hz sampling frequency, after the internal temperature was stabilized. The first determined parameter was the time constant

Except for angular velocity (AngRate), the experiment time series was low-pass filtered before calculating

Comparative results for real and simulated IMU sensor error for Pitch angle. (a) Window of the time series (degrees). (b) Allan variance plot (degrees). (c) FFT of time series (

Comparative results for real and simulated IMU sensor error for

The water pressure-based depth sensor specified for this robot was the Digiquartz 8CB4000-I Depth Sensor (Paroscientific, Inc., Redmond, WA), provided a 0.01% accuracy and a resolution of

The localization problem consisted of estimating a set of states, which included robot position, by reading accelerations as inputs and considering the depth sensor signals as the external measurements. Since a strapdown navigation scheme is used, the localization algorithm assumes that the accelerations measured in the local frame are transformed into the global frame, by using the rotation matrices calculated from Euler angles measured by the IMU. It is also assumed that if a DC-acceleration sensible accelerometer is being used, the vertical acceleration was compensated for gravity. The problem state equations are formulated as [

The state vectors and matrices are given by the following:

An estimate

Prediction:

Update:

Here, we focus the analysis on the key aspect of this particular localization problem, which is determining the external measurements vector

We proposed the following method to estimate the complete

Position external measurements

Thus,

The same difference calculated in (

Since

Substituting

In the static case no riser motion is present. The

Problem neutral configuration, showing the FPSO, the riser profile and the robot attitude. The orthogonal arrows express the successive local reference frames position and orientation along the riser path. Only 1/8 of the 171 FEM mesh nodes used in the static analysis is shown to facilitate visualization.

Localization error (in global coordinates) for the static neutral case as a function of the distance from the seabed.

Total localization error (in global coordinates) as a function of distance from the seabed, for neutral, near and far configurations with the mesh of 1.680 points (1.44 Hz). The neutral configuration error for the mesh with 7.630 points (5 Hz) is also shown.

Figure

By including the wave and VIV effects in the riser nodal displacement profile, the robot trajectory becomes more complex (Figure

Robot attitude profile in the dynamic condition, including wave and VIV effects. Only 1/150 of the 7.630 grid points are shown to keep the figure clearer.

Localization error (in global coordinates) as a function of the distance from the seabed, for the dynamic condition.

Mean localization error (in global coordinates) as a function of distance from the seabed, for both static and dynamic conditions.

The simulations show that the robot trajectory using the localization algorithm, in the dynamic case, presented a wavy pattern. The pattern corresponds to the path that is traveled by the robot, and not the nominal riser profile, as expected. If an estimate of the riser catenary shape is desired, the obtained path could be used to fit a smooth profile curve.

In the more vertical part of the riser (above 15 m from seabed), the average estimated error (standard dev.) was 0.76 (0.47) m (Figure

The localization algorithm depends strongly on the external measurements, which are provided by the depth sensor and the IMU, using (

In our opinion, the simple and standard KF implementation that was presented in this study is sufficient to provide the localization accuracy required for the proposed application. In the case of rigid risers and other predominantly vertical offshore structures, the observed loss of accuracy is not expected to occur. The kinematic model used to formulate the sensor fusion problem was linear, and therefore the standard KF implementation is appropriate. Other models could be proposed, incorporating robot, riser or sea dynamic features. In such cases, using an extended Kalman filter or a particle filter should be necessary for handling the associated nonlinearities. In any case, the external measurements reliability seems to be key aspect for localization accuracy in this problem.

Using a higher grade low drift IMU instead of a low-cost one could eliminate the need for external measurements in a critical region but at the price of increasing payload, cost and volume. Acoustic positioning systems could be used to localize the robot in the most horizontal parts of the trajectory. However, these systems work at a very low sampling frequency (0.1 to 1 Hz) [

The authors are gratefully thankful to CAPES (Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior), FINEP (Financiadora de Estudos e Projetos), CNPq (Conselho Nacional de Desenvolvimento Cientifico e Tecnologico), and FAPERJ (Fundacao de Amparo a Pesquisa do Estado do Rio de Janeiro) for financial support.