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Stabilization of a ROV in Three-dimensional Space Using an Underwater Acoustic Positioning System
7th IFAC Symposium on System Structure and Control 7th IFAC Symposium on System Structure and Control 7th IFAC Symposium on System and Control Sinaia, Romania, September 9-11,Structure 2019 7th Symposium on Structure and Sinaia, Romania, September 9-11, 2019 7th IFAC IFAC Symposium on System System Structure and Control Control Available online at www.sciencedirect.com Sinaia, Romania, September 9-11,Structure 2019 7th IFAC Symposium on System and Control Sinaia, Romania, September 9-11, 2019 Sinaia, Romania, September 9-11, 2019 Sinaia, Romania, September 9-11, 2019
ScienceDirect
IFAC PapersOnLine 52-17 (2019) 117–122
Stabilization of a ROV in Stabilization of a ROV in Stabilization of a ROV in an Three-dimensional Space Using Stabilization of a ROV in an Three-dimensional Space Using Three-dimensional Space Using an Three-dimensional Space Using an Underwater Acoustic Positioning System Three-dimensional Space Using an Underwater Acoustic Positioning System Underwater Acoustic Positioning System Underwater Acoustic Positioning System Underwater ∗,∗,Acoustic Positioning System∗∗ ∗ ∗ Simon Simon Simon Simon Simon Simon
Pedersen ∗, Jesper Liniger ∗ Fredrik F. Sørensen ∗ ∗, ∗ Pedersen F. Sørensen Jesper Liniger ∗∗∗ Fredrik ∗, ∗ ∗ Pedersen Fredrik F. Sørensen Jesper ∗, Schmidt ∗ ∗ Pedersen Jesper ∗∗∗∗Liniger Liniger Fredrik F. Kenneth Malte von Benzon ∗ Pedersen Fredrik F. Sørensen Sørensen Jesper Liniger Kenneth Schmidt Malte Benzon ∗, ∗von ∗ ∗ ∗ ∗ ∗ Pedersen Fredrik F. Sørensen Jesper Liniger Kenneth Schmidt Malte von Benzon ∗ Malte ∗ ∗ Kenneth Schmidt von Benzon Sigurd S. Klemmensen ∗ Kenneth Schmidt ∗ Malte von Benzon ∗ ∗ Sigurd S. Klemmensen ∗ Kenneth Schmidt Malte von Benzon Sigurd S. Klemmensen Sigurd Sigurd S. S. Klemmensen Klemmensen ∗ Sigurd S. Klemmensen ∗ ∗ ∗ Department of Energy Technology, Aalborg University, Niels Bohrs ∗ ∗ of Energy Technology, Aalborg University, Niels Bohrs ∗ Department Department Technology, Aalborg University, ∗ Department of of Energy Energy Technology, Aalborg University, Niels Bohrs Vej 8, 6700 Esbjerg, Denmark. Technology, Aalborg University, Niels Niels Bohrs Bohrs Vej 8, 6700 Esbjerg, Denmark. ∗ Department of Energy Department of Energy Technology, Aalborg University, Niels Bohrs Vej 8, 6700 Esbjerg, Denmark. Vej 8, 6700 Esbjerg, Denmark. Vej 8, 6700 Esbjerg, Denmark. Vej 8, 6700 Esbjerg, Denmark. Abstract: In subsea applications there are an increasing demand for Remotely Operated Abstract: In subsea applications there are an increasing demand for Remotely Operated Abstract: In subsea applications there are an increasing demand for Remotely Operated Abstract: In applications there are demand for Operated Vehicles (ROV’s). This study examines aa BlueROV2 inspection ROV prototype for autonomous Abstract: In subsea subsea applications there are an an increasing increasing demand for Remotely Remotely Operated Vehicles (ROV’s). This study examines BlueROV2 inspection ROV prototype for autonomous Abstract: In subsea applications there are an describes increasing demand for Remotely Operated Vehicles (ROV’s). This study examines a BlueROV2 inspection ROV prototype for autonomous Vehicles (ROV’s). This study examines a BlueROV2 inspection ROV prototype for autonomous operation in three-dimensional space. This study the ROV modelling, identification, Vehicles (ROV’s). This study examines a BlueROV2 inspection ROV prototype foridentification, autonomous operation in three-dimensional space. This study describes the ROV modelling, Vehicles (ROV’s). This study examines a BlueROV2 inspection ROV prototype for autonomous operation in three-dimensional space. This study describes the ROV modelling, identification, operation in three-dimensional three-dimensional space. This study studyand describes the ROV ROV modelling, identification, control development and closed-loop simulations experiments. The main transmitter applied operation in space. This describes the modelling, identification, control development and closed-loop simulations and experiments. The main transmitter applied operation in three-dimensional space. This study describes the ROV modelling, identification, control development and closed-loop simulations and experiments. The main transmitter applied control development and closed-loop simulations and The main applied for the navigation is an Underwater Acoustic Positioning System (UAPS) which acts as an control development and closed-loop simulations and experiments. experiments. The main transmitter transmitter applied for the navigation is an Underwater Acoustic Positioning System (UAPS) which acts as an control development and closed-loop simulations and experiments. The main transmitter applied for the navigation is an Underwater Acoustic Positioning System (UAPS) which acts as for the navigation is an Underwater Acoustic Positioning System (UAPS) which acts as an underwater GPS unit. The transmitter introduces a dominant output time delay which is for the navigation is anThe Underwater Acoustic Positioning Systemoutput (UAPS) which acts as an an underwater GPS unit. transmitter introduces a dominant time delay which is for the navigation ispredictor. anThe Underwater Acoustic Positioning System (UAPS) which acts as the an underwater GPS unit. transmitter introduces aaathe dominant output time delay which is underwater GPS unit. The transmitter introduces dominant output time delay which is handled by a smith The results show that smith predictor does not handle underwater GPS unit. The transmitter introduces dominant output time delay which is handled by a smith predictor. The results show that the smith predictor does not handle the underwater GPS unit. The transmitter introduces a dominant output time delay which is handled by a smith predictor. The results show that the smith predictor does not handle the handled by a predictor. The results show that the predictor does the time delay probably because the time delay time-variant. identification of the time handled bywell, a smith smith predictor. The results showis that the smith smithOnline predictor does not not handle handle the time delay well, probably because the time delay is time-variant. Online identification of the time handled bywell, a smith predictor. The results show that the smith predictor doesdelay not handle the time delay well, probably because the time delay is time-variant. Online identification of the time time delay probably because the time delay is time-variant. Online identification of the time delay is proposed as a potential solution for minimizing the impact of the time variations time delay well, probably becausesolution the timefor delay is time-variant. Online identification ofvariations the time delay is proposed as a potential minimizing the impact of the time delay time delay well, probably becausesolution the timefor delay is time-variant. Online identification ofvariations the time delay is delay is proposed as a potential minimizing the impact of the time delay over delaytime. is proposed proposed as as a a potential potential solution solution for for minimizing minimizing the the impact impact of of the the time time delay delay variations variations over time. delay is proposed as a potential solution for minimizing the impact of the time delay variations over time. over time. time. over over time.© 2019. Copyright The Authors. Published by modeling, Elsevier Ltd.subsea All rights reserved. Keywords: Time delay, mathematical control, ROV, offshore robotics Keywords: Time delay, mathematical modeling, subsea control, ROV, offshore robotics Keywords: Time delay, mathematical modeling, subsea control, ROV, offshore robotics Keywords: Time Time delay, delay, mathematical mathematical modeling, modeling, subsea subsea control, control, ROV, ROV, offshore offshore robotics robotics Keywords: Keywords: Time delay, mathematical modeling, subsea control, ROV, offshore robotics 1. INTRODUCTION the commonly applied transmitters for real-time feedback 1. INTRODUCTION INTRODUCTION the commonly applied transmitters for real-time feedback 1. the commonly applied transmitters for real-time feedback 1. INTRODUCTION INTRODUCTION the commonly applied transmitters for real-time feedback control of ROVs. First, a model of the ROV is described 1. the commonly applied transmitters for real-time feedback control of ROVs. First, a model of the ROV is described 1. INTRODUCTION the commonly applied transmitters for real-time feedback control of ROVs. First, a model of the ROV is described control of ROVs. First, a model of the ROV is described and identified, then a controller is developed using a LQRI Underwater robots are used in an increasing amount of control of ROVs. First, a model of the ROV is described and identified, then a controller is developed using a LQRI Underwater robots are used in an increasing amount of control of ROVs. First, a model of the ROV is described and identified, then a controller is developed using a LQRI Underwater robots are used in an increasing amount of and identified, then a controller is developed using a full-state feedback controller with a smith predictor on Underwater robots are used used in an an increasing increasing amount of of and tasks, such as asrobots mapping, surveillance, welding, inspections inspections identified, then controller a controllerwith is developed using a LQRI LQRI Underwater are in amount full-state feedback a smith predictor on tasks, such mapping, surveillance, welding, identified, then controller a controller is developed using a LQRI full-state feedback with a smith predictor on Underwater robots are used in an Wynn increasing amount of and tasks, such as mapping, surveillance, welding, inspections full-state feedback controller with a smith predictor on the linearized model. The controller is both evaluated in tasks, such as mapping, surveillance, welding, inspections and assembly (Mai et al. (2016); et al. (2014)). full-state feedback controller with a issmith predictor on tasks,assembly such as mapping, surveillance, welding, inspections and (Mai et al. (2016); Wynn et al. (2014)). the linearized model. The controller both evaluated in full-state feedback controller with a smith predictor on the linearized model. The controller is both evaluated in tasks, such as mapping, surveillance, welding, inspections and assembly (Mai et al. (2016); Wynn et al. (2014)). the linearized model. The controller is both evaluated in closed-loop simulations and experiments in a water basin and assembly (Mai et al. (2016); Wynn et al. (2014)). The offshore industry is the biggest user of Remotely the linearized model. The controller is both evaluated in and assembly (Mai et is al. the (2016); Wynn etofal.Remotely (2014)). closed-loop The offshore industry biggest user simulations and experiments in a water basin the linearized model. The controller is both evaluated in closed-loop simulations and experiments in a water basin and assembly (Mai et al. (2016); Wynn et al. (2014)). The offshore industry is the biggest user of Remotely closed-loop simulations and experiments in a water basin to demonstrate the closed-loop performance of the system. The offshore industry is the biggest user of Remotely Operated Vehicles (ROVs) and Autonomous Underwater closed-loop simulations and experiments in a water basin The offshore industry is the biggest user of Remotely to demonstrate the closed-loop performance of the system. Operated Vehicles (ROVs) and Autonomous Underwater closed-loop simulations and experiments in a water basin to demonstrate the closed-loop performance of the system. The offshore industry is the biggest user of Remotely Operated Vehicles (ROVs) and Autonomous Underwater to demonstrate the closed-loop performance of the system. Operated(AUVs); Vehiclesprimarily (ROVs) and and Autonomous Underwater Vehicles (AUVs); primarily because of aa decrease decrease in operoper- to demonstrate the closed-loop performance of the system. Operated Vehicles (ROVs) Autonomous Underwater Vehicles because of in Operated Vehicles (ROVs) Autonomous Underwater Vehicles (AUVs); primarily because of decrease in Vehiclescost (AUVs); primarily because of aaaReid decrease in operoperational cost over the the last few fewand years, see Reid (2013); Brun to demonstrate the closed-loop performance of the system. Vehicles (AUVs); primarily because of decrease in operational over last years, see (2013); Brun Vehicles (AUVs); primarily because of a decrease in operational cost over the last few years, see Reid (2013); Brun ational cost cost overTechnology the last last few few years, (2017). see Reid ReidGlobally, (2013); Brun Brun (2014); Marine Technology Society (2017). Globally, most ational over the years, see (2013); (2014); Marine Society most 2. ational cost overTechnology the last few years, see Reid (2013); Brun (2014); Marine Society (2017). Globally, most 2. PLATFORM PLATFORM (2014); Marine Technology Society (2017). Globally, most industrial ROV operations are manually controlled, with (2014); Marine Technology Society (2017). Globally, most 2. PLATFORM industrial ROV operations are manually controlled, with 2. PLATFORM (2014); Marine Technology Society (2017). Globally, most 2. PLATFORM industrial ROV operations are manually controlled, with industrial ROV operations are manually controlled, with neither automatic automatic control functions functions nor other other autonomous industrial ROV operations are manually controlled, with 2. PLATFORM neither control nor autonomous industrial ROV operations are manually controlled, with neither automatic control functions nor other autonomous The ROV used in the project neither automatic control functions nor other autonomous capabilities Schjølberg and Utne (2015). However, automaneither automatic control functions nor other autonomous capabilities Schjølberg and Utne (2015). However, automaThe ROV ROV used used in in the the project project is is provided provided by by the the company company The is provided by the neither automatic control functions nor other autonomous capabilities Schjølberg and Utne (2015). However, automaThe ROV used in the project is provided by the company Blue Robotics Inc. and is a BlueROV2, see figure capabilities Schjølberg and Utne (2015). However, automation has proven to decrease both the time and cost of The ROV used in the project is provided by the company company capabilities Schjølberg and Utne (2015). However, automation has proven to decrease both the time and cost of Blue Robotics Inc. and is a BlueROV2, see figure 1. 1. The ROV used in theand project provided by see thecontrolled company Blue Robotics Inc. is aaaisbattery BlueROV2, figure capabilities Schjølberg and Utne (2015). However, automation has proven to decrease both the time and cost of Blue Robotics Inc. and is BlueROV2, see figure 1. The ROV is powered by a and is tion has proven to decrease both the time and cost of operation Tena (2011). One limitation of subsea operations Blue Robotics Inc. and is BlueROV2, see figure 1. 1. tion has proven to decrease both the time and cost of The ROV is powered by a battery and is controlled operation Tena (2011). One limitation of subsea operations Blue Robotics Inc. and is a BlueROV2, see figure 1. The ROV is powered by a battery and is controlled tion has proven to decrease both the time and cost of operation Tena (2011). One limitation of subsea operations The ROV is powered by a battery and is controlled from the surface by computer through a tether. The operation Tena (2011). One limitation of subsea operations is determining determining the positioning of the the ROV, ROV, as the the relative from The ROV is powered by a battery anda istether. controlled operation Tena the (2011). One limitation of subsea operations is positioning of as relative the surface by computer through The The ROV is powered by a battery and is controlled from the surface by computer through a tether. The operation Tena (2011). One limitation of subsea operations is determining the positioning of the ROV, as the relative from the computer through aa tether. The moves around six which are is determining determining the positioning positioning of the the ROV, ROV, available as the the relative relative position are restricted restricted by the the transmitters transmitters available (Fos- ROV from the surface surface byusing computer through tether. The is the of as position are by (FosROV moves aroundby using six thrusters thrusters which are paired. paired. from the surface byusing computer through a tether. The ROV moves around six thrusters which are paired. is determining the positioning of the ROV,are as either the relative position are restricted by the transmitters available (FosROV moves around using six thrusters which are paired. The embedded software do not allow for control of each position are restricted by the transmitters available (Fossen (2011)). Typically, these transmitters gyroROV moves around using six thrusters which are paired. position are restricted by the transmitters available (FosThe embedded software do not allow for control of each sen (2011)). Typically, these transmitters are either gyroROV moves around using six thrusters which are paired. The embedded software do not allow for control of each position are restricted by the transmitters available (Fossen (2011)). Typically, these transmitters are either gyroThe embedded software do not allow for control of each individually, but are preprogrammed to sen (2011)). (2011)). Typically, these these transmitters are or either gyro- thruster scopes or accelerometers accelerometers withtransmitters drifting, noisy noisy or deviating The embedded software not allow for control of each sen Typically, are either gyrothruster individually, butdo preprogrammed to actuate actuate scopes or with drifting, deviating The embedded software doare not allow for control of each individually, but to actuate sen (2011)). Typically, these transmitters are in either gyro- thruster scopes or with drifting, noisy or deviating thruster individually, but are preprogrammed to actuate the ROV in specific predetermined directions. Thus, the scopes or accelerometers accelerometers with drifting, noisy or deviating measurement properties, which often result result imprecise thruster individually, but are are preprogrammed preprogrammed to actuate scopes or accelerometers with drifting, noisy or deviating measurement properties, which often in imprecise the ROV in specific predetermined directions. Thus, the thruster individually, but are preprogrammed to actuate the ROV in specific predetermined directions. Thus, the scopes or accelerometers with drifting, noisy or deviating measurement properties, which often result in imprecise the ROV in specific predetermined directions. Thus, the ROV is directly able to sway, heave, surge, roll and yaw measurement properties, which often result in imprecise and unreliable measurement signals (Mai et al. (2017); the ROV in specific predetermined directions. Thus, the measurement properties, which often (Mai resultetinal.imprecise and unreliable measurement signals (2017); ROV is directly able to sway, heave, surge, roll and yaw the ROV in figure specific predetermined directions. Thus, the ROV is directly able to sway, heave, surge, roll and yaw measurement properties, which often result inal. imprecise and unreliable measurement signals (Mai et (2017); ROV is directly able to sway, heave, surge, roll and yaw as seen on 1 To monitor the ROV the onboard and unreliable measurement signals (Mai et al. (2017); Arnesen et al. (2017); Pedersen et al. (2018)). Besides, ROV is directly able to sway, heave, surge, roll and yaw and unreliable measurement signals (Mai et al. (2017); as seen on figure 1 To monitor the ROV the onboard Arnesen et al. (2017); Pedersen et al. (2018)). Besides, ROV is directly able to sway, heave, surge, roll and yaw as seen on figure 1 To monitor the ROV the onboard and unreliable measurement signals (Mai et al. (2017); Arnesen et al. (2017); Pedersen et al. (2018)). Besides, as seen on figure 1 To monitor the ROV the onboard sensors in the IMU are used as feedback. The IMU provides Arnesen et aaal. al. (2017); Pedersen et al. al. (2018)). (2018)). Besides, there exist lack of absolute absolute positioning transmitters due as seen inonthefigure 1 To monitor the ROV the provides onboard Arnesen et (2017); Pedersen et Besides, sensors IMU are are used as feedback. feedback. The IMU IMU there exist lack of positioning transmitters due as seen onthe figure 1 To monitor the ROV the provides onboard in IMU as The Arnesen et aathat al. (2017); Pedersen et al. (2018)). Besides, there lack of positioning transmitters due sensors in IMU are used as The IMU the ROVs depth orientation. To determine the there exist lack of absolute absolute positioning transmitters due sensors to theexist fact GPS signal does not operate subsea. sensors in the the IMU and are used used as feedback. feedback. The IMU provides provides there exist athat lack of absolute positioning transmitters due to the fact GPS signal does not operate subsea. the ROVs depth and orientation. To determine the 33sensors in the IMU are used as feedback. The IMU provides the ROVs depth and orientation. To determine the there exist a lack of absolute positioning transmitters due to the fact that GPS signal does not operate subsea. the ROVs depth and orientation. To determine the 3dimensional position in space an underwater positioning to the fact that GPS signal does not operate subsea. the ROVs depth and orientation. To determine the 33to the fact that GPS signal does not operate subsea. dimensional position in space an underwater positioning This paper will GPS examine BlueROV2, whichsubsea. is aa ROV ROV dimensional the ROVs depth and orientation. To determine the 3position in space an underwater positioning to thepaper fact that signalaa does not operate This will examine BlueROV2, which is dimensional position in space an underwater positioning system is installed on the ROV. An Underwater Acoustic dimensional position in space an underwater positioning system is installed on the ROV. An Underwater Acoustic This will aaa BlueROV2, which ROV This paper paperdeveloped will examine examine BlueROV2, which is is aaa tasks. ROV system prototype developed for minor minor offshore inspection inspection tasks. dimensional position in space anAn underwater positioning on the Acoustic This paper will examine BlueROV2, which is ROV prototype for offshore system is installed the ROV. An Underwater Acoustic System (UAPS) developed by is system is is installed installed on the ROV. ROV. An Underwater Underwater Acoustic This paperdeveloped willwork’s examine a BlueROV2, which the is a threeROV Positioning prototype for minor offshore inspection tasks. Positioning Systemon (UAPS) developed by WaterLinked WaterLinked is prototype developed for minor offshore inspection tasks. The described objective is to stabilize system is installed on the ROV. An Underwater Acoustic System (UAPS) developed by WaterLinked is prototype developed for minor offshore inspection tasks. Positioning The described work’s objective is to stabilize the threePositioning System (UAPS) developed by WaterLinked is used. The UAPS transmits acoustic waves from the ROV Positioning System (UAPS) developed by WaterLinked is prototype developed for minor offshore inspection tasks. The described work’s objective is to stabilize the threeused. The UAPS transmits acoustic waves from the ROV The described described work’s of objective is to to stabilize the threethree- used. dimensional position of the ROV ROV using an underwater underwater Positioning System (UAPS) developed by WaterLinked is The UAPS transmits acoustic waves from the ROV The work’s objective is stabilize the dimensional position the using an used. The UAPS transmits acoustic waves from the ROV to several receivers on the water surface that calculate the used. The UAPS transmits acoustic waves from the ROV The described work’s objective is to stabilize the threedimensional position of the ROV using an underwater to several receivers on the water surface that calculate the dimensional positiontransmitter of the the ROV ROV using anexist underwater acoustic positioning transmitter where therean exist an domdom- to used. The UAPS transmits acoustic waves from the ROV several receivers on the water surface that calculate the dimensional position of using underwater acoustic positioning where there an to several several receivers onon thetrilateration water surface surface that calculate calculate the ROV’s position based distance calculations to receivers on the water that the ROV’s position based on trilateration distance calculations dimensional position of the ROV using underwater acoustic positioning transmitter where there an domacoustic positioning transmitter where thereanexist exist an dom- ROV’s inant time delay in the measured output. The acoustic to several receivers onon thetrilateration water surface that calculate the position based distance calculations acoustic positioning transmitter where there exist an dominant time delay ROV’s position based on trilateration distance calculations (Joaqun Aparicio and lvarez (2016)). In this configuration in the measured output. The acoustic ROV’s position based on trilateration distance calculations acoustic positioning transmitter where there exist an dominant time delay in the measured output. The acoustic (Joaqun Aparicio and lvarez (2016)). In this configuration inant time time delay delay in as thean measured output. acoustic (Joaqun transmitter operates as anmeasured underwater GPS. The The positionpositionROV’s position based on trilateration distance calculations Aparicio and lvarez (2016)). In this configuration inant in the output. acoustic transmitter operates underwater GPS. (Joaqun Aparicio and lvarez (2016)). In this configuration the UAPS uses Short Baseline (SBL) with four transducers (Joaqun Aparicio andBaseline lvarez (2016)). In this inant time delay in as thean measured output. acoustic transmitter operates underwater The the UAPS uses Short Short (SBL) with with fourconfiguration transducers transmitter operates as an underwater GPS. The positionpositioning transmitter will be investigated asGPS. an alternative alternative to the (Joaqun Aparicio andBaseline lvarez (2016)). In this configuration UAPS uses (SBL) four transducers transmitter operates as an underwater GPS. The positioning transmitter will be investigated as an to the UAPS uses Short Baseline (SBL) with four transducers which is lowered into the water, and send signals back the UAPS uses Short Baseline (SBL) with four transducers transmitter operates as an underwater GPS. The positioning transmitter will be investigated as an alternative to which is lowered into the water, and send signals back to to ingCorresponding transmitterauthor. will be be investigated as an an alternative alternative to to which UAPS uses Short Baseline (SBL) with four transducers is into the water, and send signals back ing transmitter will investigated as which is lowered lowered into theis water, and send signals back to to athe ground station, which above water level. E-mail: [email protected]. which is lowered into the water, and send signals back to a ground station, which is above water level. Corresponding author. E-mail: [email protected]. ing transmitter will be investigated as an alternative to which is lowered into the water, and send signals back to aaa ground station, which is above water level. Corresponding author. author. E-mail: E-mail: [email protected]. [email protected]. Corresponding ground station, which is above water level. ground station, which is above water level. Corresponding author. E-mail: [email protected]. Corresponding author. E-mail: [email protected]. a ground station, which is above water level. 2405-8963 Copyright © 2019. The Authors. Published by Elsevier Ltd. All rights reserved.
Copyright © 2019 IFAC 213 Copyright © 2019 213 Peer review responsibility of International Federation of Automatic Copyright © under 2019 IFAC IFAC 213 Control. Copyright © 213 Copyright © 2019 2019 IFAC IFAC 213 10.1016/j.ifacol.2019.11.037 Copyright © 2019 IFAC 213
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Fig. 1. The ROV placed in the two respective coordinate systems; the body and the world frame.
Fig. 2. The accelerometer and UAPS data in the xcoordinate. Notice that the figure only illustrates that time at which the transmitters detects the motion chance and that the units from the two transmitters are not comparable. In figure 2 the UAPS data is logged together with the acceleration data as a thruster step input is given to the surge motion (x-coordinate). The step input is given at 3 seconds. Although the accelerometer has the most noise, it is clear that it reacts immediately to the motion change. Hence, there is a time delay in the UAPS communication to the real-time operating computer. By doing several experiments the time delay, τ , is estimated to be τ = 2.05± 0.55s. 3. MODEL The model description is divided into three subsystems: The ROV frame, the thruster forces and the damping forces. 3.1 Dynamic model The dynamic behavior of the ROV is based on the Lagrangian relationship: L=T −V (1) 214
where V is a function of the generalized position vector that describes the potential energy of the ROV, and T is the kinetic energy of the moving ROV, not considering the fluid, but only rotation and translation, such that the vector form is 1 (2) T = vT M v 2 where M is the mass matrix and v is the generalized velocity vector. For the rotational motion v is replaced by the angular velocity and m is replaced by the mass moment of inertia. The potential energy of the system is given solely from the buoyancy force acting on the ROV, when the ROV is orientated of its stable point in either pitch or roll it creates a force and a moment moving the ROV back into its stable position. At its stable position the center of the buoyancy (COB) is located straight above the center of mass (COM) as shown in figure 4. Meaning that the angles θ and φ are zero. The buoyancy force which is acting on the ROV creates a torque with the distance from the COB to the resting position. This distance can be found since the distance between the COM and the COB is fixed. The distance in the D,w direction, between the COM and COB can be found by transforming the rotation matrix, Rf , and converting the LGB from body to world frame. As the LGB is described for body frame, the D component of the vector for the length between COM and COB is given by 0 0 0 0 · Rf (3) = LGB,D,w LGB,d,b As the ROV is assumed to be neutrally buoyant the total potential energy, V, is V = −LGB,D,ω Fb (4) where Fb is the force due to buoyancy of the ROV, Fb = ρgv, with ρ being the density of water and, g the gravitational acceleration and v the volume of the ROV. LGB,D,ω can be obtained from (5) −LGB,D,b = −LGB,d,b cos(θ)cos(φ) Now the Lagrangian can be obtained: 1 L = · vTw · Mrb · vw − lbθ · F b − lbφ · F b (6) 2 which can be included in the Euler-Lagrange equation, d δL δL = Tf · Fb (7) − dt δvw δpw The first term in equation 7 is d δL MRB 0 = · aw (8) 0 IO dt δvw
The second term is the restoring forces and are given as, δL 0 = . (9) G δpw Here, G represents the restoring forces (Fossen (1994)). Tf is a transformation matrix, which transforms the drag forces to torques by considering the distance from the thruster to the COM, this is Ls and Lr . It also transforms the body fixed translational forces to world frame by applying a rotation matrix Rf . Rf 0 Tf = (10) L s Lr
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119
Force - Fb (N)
50
0
Datapoints 9. order fit
-50 -1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Input (-)
Fig. 3. Shows force provided by 2 thruster with input from -100% to 100 %. A 9th order polynomial is applied to obtained an acceptable model accuracy.
3.2 Thruster model The thruster percentage to force must be modeled to find the correct actuator forces acting on the ROV. The thruster expression is obtained from Wang and Clark (2006): Fthrust = ρD4
α 2 · ua α1 + · η|η| nD
(11)
where α1,2 are the thruster coefficients describing the efficiency of the propeller, D is diameter, ua is the ambient water speed, Fthrust is the thrust of the propeller and η is the propeller rate. The coefficients in the thruster model are identified by connecting a newton meter to the ROV in water and gradually increasing the dedicated heave thrusters by 10 % in step size until reaching steady-state. The results are plotted in figure 3 where the modelled is fitted to a static 9th order polynomial. The obtained coefficients are used for all directions as it is assumed that the ROV has no geometry that will affect the flow from the thrusters unevenly. Motion around the axes, known as rotations, is possible through the thrusters applying torque to the ROV. The length from the thrusters to the center of gravity need to befound to determine the size of this torque, see figure 4 and 5.
Fig. 5. The ROV with the lengths between COM and centerlines of thrusters. Blue dotted line is the centerline of thrusters Hence, the pitch moment, Mθ,n , is a function of the surge thruster force: Mθ,n = Fn,b · Lθ , the moment caused by the roll thrusters can be described by Mφ = Fφ,b · Lφ , the roll moment for sway can be described by Mφ,e = Fe,b · Lθ where the length is the same as for the pitch. The yaw motion is effected by all four horizontal thrusters: Mψ = Fψ,b · Lψ,long + Fψ,b · Lψ,short . 3.3 Damping forces The damping forces derive from two sources, the drag and the added mass. The added mass is neglected in this project as it only is resisting movement during accelerations, and therefore, compared to the drag force it is thought to be insignificant at smaller accelerations. The general drag force for one direction is given by 1 (12) fdrag = · cd · ρ · A · v 2 2 where cd is the drag coefficient and A is the cross sectional area perpendicular to the flow. cd is a combination of skin friction drag and pressure drag, but can be assumed to be constant at Reynolds numbers between 103 − 105 (Cengel (2012)), which is assumed to be present in this study.
Fig. 6. Illustration of the test setup for determination of drag forces. Fig. 4. The ROV with the lengths between COM and centerlines of thrusters. Blue dotted line is the centerline of thrusters 215
Figure 6 illustrates the test setup used to identify the Cd coefficients. To find the force-velocity relations, the ROV
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3.4 The complete model After the model was identified it was validation based on a variety of experiments. The error distribution with subject to thruster actuation showed that the model overall is sufficiently accurate for model-based control applications. The combined model description can be expressed by equation (14). MRB 0 0 Rf 0 Rf 0 = fb,b · · aw − − fd,b · G 0 IO 0 I3 Ls Lr (14) A table with all model parameters and dimensions is seen in the table 1. Table 1. Table of all parameters Description Volume Length from COM to COB Length from COM to pitch thruster Length from COM to roll thruster Short length from G to yaw thruster Long length from G to yaw thruster Height of ROV Length of side Length of front Drag coefficient for front and back Drag coefficient for top and bottom Mass of ROV MOI around x axis MOI around y axis MOI around z axis
Symbol υ LGB,b Lφ Lθ Lψ,short Lψ,long h Lside Lfront Cdfor Cdtop m Iφ Iθ Iψ
Value 0.011167 0.028 0.005 0.111 0.148 0.089 0.254 0.457 0.338 1.6 1.48 11.167 0.2 0.243 0.239
Unit m3 m m m m m m m m kg kg · m2 kg · m2 kg · m2
4.1 Linearization and open-loop analysis The model is linearized using Taylor expansion to obtain the state-space Jacobians. The linearized model is compared to the non-linear model, and the comparison shows that the linear model deviates somewhat from the nonlinear model. One of the experiments is shown in figure 7 where a unity input step is applied to the surge thrusters. As this motion also impacts the pitching, the pitch output is also plotted. The respective transient responses are almost identical, while a larger deviation exist at steadystate. This can be explained by the thruster operating far from the linearization point. 4
4
Linear - North position Non-linear - North position Linear - Pitch orientation Non-linear - Pitch orientation Linear - North velocity Non-linear - North velocity Linear - Pitch rotation Non-linear - Pitch rotation
3 2 1
3 2 1
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is dragged through the water with constant velocity by a motor and the force required to do so is measured with a Newton meter. This procedure is carried out for surge and sway, but as the distance for the vertical movement (heave) is limited by the test facility, a different test is performed where weight is added to the ROV and the downwards acting force is measured. For the rotational movements of the ROV, described as roll, pitch and yaw, a lesser accurate method is used, as these movements do not influence the ROV as much. For yaw and roll, the maximum angular velocity is found together with the angular velocity at 50 % thrust. This provides three points as the drag torque should always go through 0. The pitch is identified by applying equation (11) to determine Cd based on a known velocity. It is assumed that the drag for the front is equal the back, and drag for the top is equal the bottom. Then, the drag torque for pitch can be determined as an expression for linear drag on a rotational movement, such that Mdθ,b = Lside 2 1 2 · ρ · (ωθ,b · r1 ) · (r1 · Lf or ) · Cdtop dr1 + 2· 2 0 h2 1 2 · ρ · (ωθ,b · r2 ) · (r2 · Lf or ) · Cdf or dr2 2· 2 0 (13)
Posistion (m), Orientation (rad)
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Fig. 7. This figure shows the simulated linear and nonlinear models when a unit step is applied to the surging thrusters. The obtained linearized state-space model consists of all positions, orientations, velocities and angular velocities are added as states; which results in a total of 12 states. Although the velocities are not directly measured, they are simply derivatives of the 6 measured outputs, resulting in 12 outputs. The model is both fully controllable and observable as the observability and controllability matrices have full rank. The model is marginally stable as the poles related to the positions are located at the origin of the s-plane. 4.2 Linear quadratic regulator with integral action The LQR controller is a full-state feedback optimal control method which finds the minimimum solution to a defined cost function. LQR is unconstrained which means it is not possible to define saturation limits directly into the method. The cost function penalizes both the inputs and states of the system to find a controller gain, K, such that u = −Kx. The cost function, J, is defined as a time integration of the two respective weighted terms, such that ∞ T T J(t) = x(t) · Q · x(t) + u(t) · R · u(t) dt 0
(15) where J(u) is the cost function, x is the states, u is the inputs, Q is a 16x16 semi-positive definite matrix which weighs the states and R is a 5x5 is a positive definite matrix whitch weighs the inputs.
4. CONTROL DEVELOPMENT This section describes the control development which consists of a Linearquadratic regulator with integral action (LQRI) including a Smith predictor. 216
To eliminate steady-state error for any output an integral term is introduced, such that the updated system can be expressed as x˙ i 0 C xi 0 = · + · u − Br · ref (16) 0A x B x˙ s where u = −Ka x, Ka = [Ki K] and Br (16x4) is a matrix which scales the reference to be the same size as the other
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121
Position (m), Orientation (rad)
Closed loop response - Final tune of Q and R on non-linear plant 3
North East Down
2.5 2 1.5 1 0.5 0 0
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Fig. 8. Output response of a reference change of 3 m in nw and ew , 1 m in dw and a change in orientation of π4 in ψw , with the final LQRI controller simulated with the non-linear model.
components in the system. The new A and B matrices are used, such that Q (16x16) weights 16 states and R (5x5) still weights 5 inputs. Bryson’s rule is applied for the Q and R matrices similar to Mai et al. (2017). By normalizing the states’ and inputs’ maximum values this method ensures that all are weighted equally from the beginning. The Q and R matrices are then manually tuned further based on nonlinear model simulations, which leads to a decrease in the integral terms in order to minimize the overshooting. In this tuning process, the pitch penalty is also decreased to allow a more aggressive surge motion. Moreover, integral anti-windup is added to all integral terms to avoid the integral term to accumulate when the ROV is far from the reference point and the actuators are saturated. The final non-linear closed-loop simulation of the theoretically tuned output responses is seen on figure 8. The control objective was to reduce the overshooting to a minimum while keeping an acceptable settling time. Thus, based on the simulations the controller was found acceptable for fulfilling the objectives.
4.3 Smith predictor
The time delay from the UAPS sensor is addressed by included a smith predictor to the control scheme. A Smith predictor predicts the positions of the the ROV and corrects potential model deviations by subtracting time delayed model outputs from the corresponding measured values. Figure 9 shows a block diagram of the system with the final control scheme in the discretized form. For simplicity the anti-windup is not illustrated in the block diagram. The forward estimator simply takes the derivative of the positions to obtain the velocities. The output filter is a vector of first order low-pass filters with equal cut-off frequencies 100 times higher than the fastest of the system’s respective bandwidths. 217
Fig. 10. Result for steady position controller with the obtained controller, the red dot is the initial position
Fig. 9. The entire discretized closed-loop control structure with LQRI and Smith Predictor. 5. RESULTS The closed-loop results are based on experimental results in a water pool. The first experiment is focusing on keeping a two-dimensional position in the north and east directions; see figure 10 which plots the two-dimensional motion during a 10 second test. It is clear that the ROV drifts and that the controller does not operate as intended. The controller gains are now reduced to observe if it improves the stabilization; see figure 11 which plots the two-dimensional motion during a 10 second test. As it still drifts it is concluded that the Smith predictor does not work well for handling the time delay on the output, probably due to the time delay being time variant. Lastly, a test is carried out where only the yaw and heave is controlled as they are not effected by the UAPS’ time delay. If these motions are stable without further tuning it is clear that it is verificed that the Smith predictor caused the problems for the control scheme. This test is seen in figure 12. It is clear that, although there are more fluctuations present for both heave and yaw in the experiments than in simulations, both output drifts. By reducing the integral gains the fluctuations are expected to be reduced, however, by now it is clear that the developed
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REFERENCES
Fig. 11. Result for steady position controller with the final tune of the controller, the red dot is the initial position.
Fig. 12. Result comparison of the test and the simulation of the controller for yaw and heave LQRI controller operates better than the UAPS controller.
6. CONCLUSION This study examines the modeling, identification and control of a BlueROV2 using an UAPS underwater position transmitter. The model is shown to fit the obtained data acceptably but with some deviations from reality. The developed LQRI controller with a Smith predictor did not stabilize the ROV in a two-dimensional space, probably because the Smith predictor not properly eliminating the negative effect of the UAPS time delay. When controlling the ROV using alternative heave and yaw transmitters the control scheme operates better. In future work an online identification of the time delay will be used to catch the potential time-variant features. At this stage it is uncertain how fast the time delay changes with respect to time and, thus, the cause of the communication delay needs to be examined further. 218
Arnesen, B.O., Lekkas, A.M., and Schjoelberg, I. (2017). 3d path following and tracking for an inspection class rov. ASME 36th International Conference on Ocean, Offshore and Arctic Engineering, 7a(OMAE2017-61170), V07AT06A019. Brun, L. (2014). ROV/AUV Trends: Market and Technology. DOI: 10.13140/RG.2.1.4062.5686. Cengel, Y. (2012). Fundamentals of Thermal-Fluid sciences. McGraw-Hill. ISBN-13: 978-0071325110. Fossen, T.I. (1994). Guidance and Control of Ocean Vehicles. Wiley. ISBN-13: 978-0471941132. Fossen, T.I. (2011). Handbook of Marine Craft Hydrodynamics and Motion Control. Wiley. ISBN: 978-1-11999149-6. Joaqun Aparicio, A.J. and lvarez, F.J. (2016). Characterization of an underwater positioning system based on gps surface nodes and encoded acoustic signals. IEEE Transactions on Instrumentation and Measurement. URL https://ieeexplore.ieee.org/stamp/ stamp.jsp?tp=&arnumber=7469873. Mai, C., Pedersen, S., Hansen, L., Jepsen, K.L., and Yang, Z. (2016). Subsea infrastructure inspection: A review study. In 2016 IEEE International Conference on Underwater System Technology: Theory and Applications (USYS), 71–76. Mai, C., Pedersen, S., Hansen, L., Jepsen, K.L., and Yang, Z. (2017). Modeling and Control of Industrial ROV’s for Semi-Autonomous Subsea Maintenance Services. IFAC Congress. Marine Technology Society (2017). ROV Applications What ROVs can do. Online. URL http://www.rov. org/rov_applications.cfm. Pedersen, S., Enevoldsen, T.T., and Einarsson, E.M. (2018). Model comparison of a videoray pro 4 underwater rov. IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM). doi:10.1109/ AIM.2018.8452445. Reid, A. (2013). ROV Market Prospects. Subsea UK, Aberdeen. URL http : / / www . subseauk . com / documents / presentations / ssuk % 20 - %20rov % 20event%20-%20sep%202013%20%5Bweb%5D.pdf. Schjølberg, I. and Utne, I.B. (2015). Towards autonomy in rov operations. IFAC-PapersOnLine, 48(2), 183 – 188. Tena, I. (2011). Automating ROV Operations in aid of the Oil & Gas Offshore Industry. SeeByte Whitepaper. Wang, W. and Clark, C.M. (2006). Modeling and Simulation of the VideoRay Pro III Underwater Vehicle. IEEE OCEANS 2006. Wynn, R.B., Huvenne, V.A., Bas, T.P.L., Murton, B.J., Connelly, D.P., Bett, B.J., Ruhl, H.A., Morris, K.J., Peakall, J., Parsons, D.R., Sumner, E.J., Darby, S.E., Dorrell, R.M., and Hunt, J.E. (2014). Autonomous Underwater Vehicles (AUVs): Their past, present and future contributions to the advancement of marine geoscience. Marine Geology, 352, 451 – 468.
ScienceDirect
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Stabilization of a ROV in Stabilization of a ROV in Stabilization of a ROV in an Three-dimensional Space Using Stabilization of a ROV in an Three-dimensional Space Using Three-dimensional Space Using an Three-dimensional Space Using an Underwater Acoustic Positioning System Three-dimensional Space Using an Underwater Acoustic Positioning System Underwater Acoustic Positioning System Underwater Acoustic Positioning System Underwater ∗,∗,Acoustic Positioning System∗∗ ∗ ∗ Simon Simon Simon Simon Simon Simon
Pedersen ∗, Jesper Liniger ∗ Fredrik F. Sørensen ∗ ∗, ∗ Pedersen F. Sørensen Jesper Liniger ∗∗∗ Fredrik ∗, ∗ ∗ Pedersen Fredrik F. Sørensen Jesper ∗, Schmidt ∗ ∗ Pedersen Jesper ∗∗∗∗Liniger Liniger Fredrik F. Kenneth Malte von Benzon ∗ Pedersen Fredrik F. Sørensen Sørensen Jesper Liniger Kenneth Schmidt Malte Benzon ∗, ∗von ∗ ∗ ∗ ∗ ∗ Pedersen Fredrik F. Sørensen Jesper Liniger Kenneth Schmidt Malte von Benzon ∗ Malte ∗ ∗ Kenneth Schmidt von Benzon Sigurd S. Klemmensen ∗ Kenneth Schmidt ∗ Malte von Benzon ∗ ∗ Sigurd S. Klemmensen ∗ Kenneth Schmidt Malte von Benzon Sigurd S. Klemmensen Sigurd Sigurd S. S. Klemmensen Klemmensen ∗ Sigurd S. Klemmensen ∗ ∗ ∗ Department of Energy Technology, Aalborg University, Niels Bohrs ∗ ∗ of Energy Technology, Aalborg University, Niels Bohrs ∗ Department Department Technology, Aalborg University, ∗ Department of of Energy Energy Technology, Aalborg University, Niels Bohrs Vej 8, 6700 Esbjerg, Denmark. Technology, Aalborg University, Niels Niels Bohrs Bohrs Vej 8, 6700 Esbjerg, Denmark. ∗ Department of Energy Department of Energy Technology, Aalborg University, Niels Bohrs Vej 8, 6700 Esbjerg, Denmark. Vej 8, 6700 Esbjerg, Denmark. Vej 8, 6700 Esbjerg, Denmark. Vej 8, 6700 Esbjerg, Denmark. Abstract: In subsea applications there are an increasing demand for Remotely Operated Abstract: In subsea applications there are an increasing demand for Remotely Operated Abstract: In subsea applications there are an increasing demand for Remotely Operated Abstract: In applications there are demand for Operated Vehicles (ROV’s). This study examines aa BlueROV2 inspection ROV prototype for autonomous Abstract: In subsea subsea applications there are an an increasing increasing demand for Remotely Remotely Operated Vehicles (ROV’s). This study examines BlueROV2 inspection ROV prototype for autonomous Abstract: In subsea applications there are an describes increasing demand for Remotely Operated Vehicles (ROV’s). This study examines a BlueROV2 inspection ROV prototype for autonomous Vehicles (ROV’s). This study examines a BlueROV2 inspection ROV prototype for autonomous operation in three-dimensional space. This study the ROV modelling, identification, Vehicles (ROV’s). This study examines a BlueROV2 inspection ROV prototype foridentification, autonomous operation in three-dimensional space. This study describes the ROV modelling, Vehicles (ROV’s). This study examines a BlueROV2 inspection ROV prototype for autonomous operation in three-dimensional space. This study describes the ROV modelling, identification, operation in three-dimensional three-dimensional space. This study studyand describes the ROV ROV modelling, identification, control development and closed-loop simulations experiments. The main transmitter applied operation in space. This describes the modelling, identification, control development and closed-loop simulations and experiments. The main transmitter applied operation in three-dimensional space. This study describes the ROV modelling, identification, control development and closed-loop simulations and experiments. The main transmitter applied control development and closed-loop simulations and The main applied for the navigation is an Underwater Acoustic Positioning System (UAPS) which acts as an control development and closed-loop simulations and experiments. experiments. The main transmitter transmitter applied for the navigation is an Underwater Acoustic Positioning System (UAPS) which acts as an control development and closed-loop simulations and experiments. The main transmitter applied for the navigation is an Underwater Acoustic Positioning System (UAPS) which acts as for the navigation is an Underwater Acoustic Positioning System (UAPS) which acts as an underwater GPS unit. The transmitter introduces a dominant output time delay which is for the navigation is anThe Underwater Acoustic Positioning Systemoutput (UAPS) which acts as an an underwater GPS unit. transmitter introduces a dominant time delay which is for the navigation ispredictor. anThe Underwater Acoustic Positioning System (UAPS) which acts as the an underwater GPS unit. transmitter introduces aaathe dominant output time delay which is underwater GPS unit. The transmitter introduces dominant output time delay which is handled by a smith The results show that smith predictor does not handle underwater GPS unit. The transmitter introduces dominant output time delay which is handled by a smith predictor. The results show that the smith predictor does not handle the underwater GPS unit. The transmitter introduces a dominant output time delay which is handled by a smith predictor. The results show that the smith predictor does not handle the handled by a predictor. The results show that the predictor does the time delay probably because the time delay time-variant. identification of the time handled bywell, a smith smith predictor. The results showis that the smith smithOnline predictor does not not handle handle the time delay well, probably because the time delay is time-variant. Online identification of the time handled bywell, a smith predictor. The results show that the smith predictor doesdelay not handle the time delay well, probably because the time delay is time-variant. Online identification of the time time delay probably because the time delay is time-variant. Online identification of the time delay is proposed as a potential solution for minimizing the impact of the time variations time delay well, probably becausesolution the timefor delay is time-variant. Online identification ofvariations the time delay is proposed as a potential minimizing the impact of the time delay time delay well, probably becausesolution the timefor delay is time-variant. Online identification ofvariations the time delay is delay is proposed as a potential minimizing the impact of the time delay over delaytime. is proposed proposed as as a a potential potential solution solution for for minimizing minimizing the the impact impact of of the the time time delay delay variations variations over time. delay is proposed as a potential solution for minimizing the impact of the time delay variations over time. over time. time. over over time.© 2019. Copyright The Authors. Published by modeling, Elsevier Ltd.subsea All rights reserved. Keywords: Time delay, mathematical control, ROV, offshore robotics Keywords: Time delay, mathematical modeling, subsea control, ROV, offshore robotics Keywords: Time delay, mathematical modeling, subsea control, ROV, offshore robotics Keywords: Time Time delay, delay, mathematical mathematical modeling, modeling, subsea subsea control, control, ROV, ROV, offshore offshore robotics robotics Keywords: Keywords: Time delay, mathematical modeling, subsea control, ROV, offshore robotics 1. INTRODUCTION the commonly applied transmitters for real-time feedback 1. INTRODUCTION INTRODUCTION the commonly applied transmitters for real-time feedback 1. the commonly applied transmitters for real-time feedback 1. INTRODUCTION INTRODUCTION the commonly applied transmitters for real-time feedback control of ROVs. First, a model of the ROV is described 1. the commonly applied transmitters for real-time feedback control of ROVs. First, a model of the ROV is described 1. INTRODUCTION the commonly applied transmitters for real-time feedback control of ROVs. First, a model of the ROV is described control of ROVs. First, a model of the ROV is described and identified, then a controller is developed using a LQRI Underwater robots are used in an increasing amount of control of ROVs. First, a model of the ROV is described and identified, then a controller is developed using a LQRI Underwater robots are used in an increasing amount of control of ROVs. First, a model of the ROV is described and identified, then a controller is developed using a LQRI Underwater robots are used in an increasing amount of and identified, then a controller is developed using a full-state feedback controller with a smith predictor on Underwater robots are used used in an an increasing increasing amount of of and tasks, such as asrobots mapping, surveillance, welding, inspections inspections identified, then controller a controllerwith is developed using a LQRI LQRI Underwater are in amount full-state feedback a smith predictor on tasks, such mapping, surveillance, welding, identified, then controller a controller is developed using a LQRI full-state feedback with a smith predictor on Underwater robots are used in an Wynn increasing amount of and tasks, such as mapping, surveillance, welding, inspections full-state feedback controller with a smith predictor on the linearized model. The controller is both evaluated in tasks, such as mapping, surveillance, welding, inspections and assembly (Mai et al. (2016); et al. (2014)). full-state feedback controller with a issmith predictor on tasks,assembly such as mapping, surveillance, welding, inspections and (Mai et al. (2016); Wynn et al. (2014)). the linearized model. The controller both evaluated in full-state feedback controller with a smith predictor on the linearized model. The controller is both evaluated in tasks, such as mapping, surveillance, welding, inspections and assembly (Mai et al. (2016); Wynn et al. (2014)). the linearized model. The controller is both evaluated in closed-loop simulations and experiments in a water basin and assembly (Mai et al. (2016); Wynn et al. (2014)). The offshore industry is the biggest user of Remotely the linearized model. The controller is both evaluated in and assembly (Mai et is al. the (2016); Wynn etofal.Remotely (2014)). closed-loop The offshore industry biggest user simulations and experiments in a water basin the linearized model. The controller is both evaluated in closed-loop simulations and experiments in a water basin and assembly (Mai et al. (2016); Wynn et al. (2014)). The offshore industry is the biggest user of Remotely closed-loop simulations and experiments in a water basin to demonstrate the closed-loop performance of the system. The offshore industry is the biggest user of Remotely Operated Vehicles (ROVs) and Autonomous Underwater closed-loop simulations and experiments in a water basin The offshore industry is the biggest user of Remotely to demonstrate the closed-loop performance of the system. Operated Vehicles (ROVs) and Autonomous Underwater closed-loop simulations and experiments in a water basin to demonstrate the closed-loop performance of the system. The offshore industry is the biggest user of Remotely Operated Vehicles (ROVs) and Autonomous Underwater to demonstrate the closed-loop performance of the system. Operated(AUVs); Vehiclesprimarily (ROVs) and and Autonomous Underwater Vehicles (AUVs); primarily because of aa decrease decrease in operoper- to demonstrate the closed-loop performance of the system. Operated Vehicles (ROVs) Autonomous Underwater Vehicles because of in Operated Vehicles (ROVs) Autonomous Underwater Vehicles (AUVs); primarily because of decrease in Vehiclescost (AUVs); primarily because of aaaReid decrease in operoperational cost over the the last few fewand years, see Reid (2013); Brun to demonstrate the closed-loop performance of the system. Vehicles (AUVs); primarily because of decrease in operational over last years, see (2013); Brun Vehicles (AUVs); primarily because of a decrease in operational cost over the last few years, see Reid (2013); Brun ational cost cost overTechnology the last last few few years, (2017). see Reid ReidGlobally, (2013); Brun Brun (2014); Marine Technology Society (2017). Globally, most ational over the years, see (2013); (2014); Marine Society most 2. ational cost overTechnology the last few years, see Reid (2013); Brun (2014); Marine Society (2017). Globally, most 2. PLATFORM PLATFORM (2014); Marine Technology Society (2017). Globally, most industrial ROV operations are manually controlled, with (2014); Marine Technology Society (2017). Globally, most 2. PLATFORM industrial ROV operations are manually controlled, with 2. PLATFORM (2014); Marine Technology Society (2017). Globally, most 2. PLATFORM industrial ROV operations are manually controlled, with industrial ROV operations are manually controlled, with neither automatic automatic control functions functions nor other other autonomous industrial ROV operations are manually controlled, with 2. PLATFORM neither control nor autonomous industrial ROV operations are manually controlled, with neither automatic control functions nor other autonomous The ROV used in the project neither automatic control functions nor other autonomous capabilities Schjølberg and Utne (2015). However, automaneither automatic control functions nor other autonomous capabilities Schjølberg and Utne (2015). However, automaThe ROV ROV used used in in the the project project is is provided provided by by the the company company The is provided by the neither automatic control functions nor other autonomous capabilities Schjølberg and Utne (2015). However, automaThe ROV used in the project is provided by the company Blue Robotics Inc. and is a BlueROV2, see figure capabilities Schjølberg and Utne (2015). However, automation has proven to decrease both the time and cost of The ROV used in the project is provided by the company company capabilities Schjølberg and Utne (2015). However, automation has proven to decrease both the time and cost of Blue Robotics Inc. and is a BlueROV2, see figure 1. 1. The ROV used in theand project provided by see thecontrolled company Blue Robotics Inc. is aaaisbattery BlueROV2, figure capabilities Schjølberg and Utne (2015). However, automation has proven to decrease both the time and cost of Blue Robotics Inc. and is BlueROV2, see figure 1. The ROV is powered by a and is tion has proven to decrease both the time and cost of operation Tena (2011). One limitation of subsea operations Blue Robotics Inc. and is BlueROV2, see figure 1. 1. tion has proven to decrease both the time and cost of The ROV is powered by a battery and is controlled operation Tena (2011). One limitation of subsea operations Blue Robotics Inc. and is a BlueROV2, see figure 1. The ROV is powered by a battery and is controlled tion has proven to decrease both the time and cost of operation Tena (2011). One limitation of subsea operations The ROV is powered by a battery and is controlled from the surface by computer through a tether. The operation Tena (2011). One limitation of subsea operations is determining determining the positioning of the the ROV, ROV, as the the relative from The ROV is powered by a battery anda istether. controlled operation Tena the (2011). One limitation of subsea operations is positioning of as relative the surface by computer through The The ROV is powered by a battery and is controlled from the surface by computer through a tether. The operation Tena (2011). One limitation of subsea operations is determining the positioning of the ROV, as the relative from the computer through aa tether. The moves around six which are is determining determining the positioning positioning of the the ROV, ROV, available as the the relative relative position are restricted restricted by the the transmitters transmitters available (Fos- ROV from the surface surface byusing computer through tether. The is the of as position are by (FosROV moves aroundby using six thrusters thrusters which are paired. paired. from the surface byusing computer through a tether. The ROV moves around six thrusters which are paired. is determining the positioning of the ROV,are as either the relative position are restricted by the transmitters available (FosROV moves around using six thrusters which are paired. The embedded software do not allow for control of each position are restricted by the transmitters available (Fossen (2011)). Typically, these transmitters gyroROV moves around using six thrusters which are paired. position are restricted by the transmitters available (FosThe embedded software do not allow for control of each sen (2011)). Typically, these transmitters are either gyroROV moves around using six thrusters which are paired. The embedded software do not allow for control of each position are restricted by the transmitters available (Fossen (2011)). Typically, these transmitters are either gyroThe embedded software do not allow for control of each individually, but are preprogrammed to sen (2011)). (2011)). Typically, these these transmitters are or either gyro- thruster scopes or accelerometers accelerometers withtransmitters drifting, noisy noisy or deviating The embedded software not allow for control of each sen Typically, are either gyrothruster individually, butdo preprogrammed to actuate actuate scopes or with drifting, deviating The embedded software doare not allow for control of each individually, but to actuate sen (2011)). Typically, these transmitters are in either gyro- thruster scopes or with drifting, noisy or deviating thruster individually, but are preprogrammed to actuate the ROV in specific predetermined directions. Thus, the scopes or accelerometers accelerometers with drifting, noisy or deviating measurement properties, which often result result imprecise thruster individually, but are are preprogrammed preprogrammed to actuate scopes or accelerometers with drifting, noisy or deviating measurement properties, which often in imprecise the ROV in specific predetermined directions. Thus, the thruster individually, but are preprogrammed to actuate the ROV in specific predetermined directions. Thus, the scopes or accelerometers with drifting, noisy or deviating measurement properties, which often result in imprecise the ROV in specific predetermined directions. Thus, the ROV is directly able to sway, heave, surge, roll and yaw measurement properties, which often result in imprecise and unreliable measurement signals (Mai et al. (2017); the ROV in specific predetermined directions. Thus, the measurement properties, which often (Mai resultetinal.imprecise and unreliable measurement signals (2017); ROV is directly able to sway, heave, surge, roll and yaw the ROV in figure specific predetermined directions. Thus, the ROV is directly able to sway, heave, surge, roll and yaw measurement properties, which often result inal. imprecise and unreliable measurement signals (Mai et (2017); ROV is directly able to sway, heave, surge, roll and yaw as seen on 1 To monitor the ROV the onboard and unreliable measurement signals (Mai et al. (2017); Arnesen et al. (2017); Pedersen et al. (2018)). Besides, ROV is directly able to sway, heave, surge, roll and yaw and unreliable measurement signals (Mai et al. (2017); as seen on figure 1 To monitor the ROV the onboard Arnesen et al. (2017); Pedersen et al. (2018)). Besides, ROV is directly able to sway, heave, surge, roll and yaw as seen on figure 1 To monitor the ROV the onboard and unreliable measurement signals (Mai et al. (2017); Arnesen et al. (2017); Pedersen et al. (2018)). Besides, as seen on figure 1 To monitor the ROV the onboard sensors in the IMU are used as feedback. The IMU provides Arnesen et aaal. al. (2017); Pedersen et al. al. (2018)). (2018)). Besides, there exist lack of absolute absolute positioning transmitters due as seen inonthefigure 1 To monitor the ROV the provides onboard Arnesen et (2017); Pedersen et Besides, sensors IMU are are used as feedback. feedback. The IMU IMU there exist lack of positioning transmitters due as seen onthe figure 1 To monitor the ROV the provides onboard in IMU as The Arnesen et aathat al. (2017); Pedersen et al. (2018)). Besides, there lack of positioning transmitters due sensors in IMU are used as The IMU the ROVs depth orientation. To determine the there exist lack of absolute absolute positioning transmitters due sensors to theexist fact GPS signal does not operate subsea. sensors in the the IMU and are used used as feedback. feedback. The IMU provides provides there exist athat lack of absolute positioning transmitters due to the fact GPS signal does not operate subsea. the ROVs depth and orientation. To determine the 33sensors in the IMU are used as feedback. The IMU provides the ROVs depth and orientation. To determine the there exist a lack of absolute positioning transmitters due to the fact that GPS signal does not operate subsea. the ROVs depth and orientation. To determine the 3dimensional position in space an underwater positioning to the fact that GPS signal does not operate subsea. the ROVs depth and orientation. To determine the 33to the fact that GPS signal does not operate subsea. dimensional position in space an underwater positioning This paper will GPS examine BlueROV2, whichsubsea. is aa ROV ROV dimensional the ROVs depth and orientation. To determine the 3position in space an underwater positioning to thepaper fact that signalaa does not operate This will examine BlueROV2, which is dimensional position in space an underwater positioning system is installed on the ROV. An Underwater Acoustic dimensional position in space an underwater positioning system is installed on the ROV. An Underwater Acoustic This will aaa BlueROV2, which ROV This paper paperdeveloped will examine examine BlueROV2, which is is aaa tasks. ROV system prototype developed for minor minor offshore inspection inspection tasks. dimensional position in space anAn underwater positioning on the Acoustic This paper will examine BlueROV2, which is ROV prototype for offshore system is installed the ROV. An Underwater Acoustic System (UAPS) developed by is system is is installed installed on the ROV. ROV. An Underwater Underwater Acoustic This paperdeveloped willwork’s examine a BlueROV2, which the is a threeROV Positioning prototype for minor offshore inspection tasks. Positioning Systemon (UAPS) developed by WaterLinked WaterLinked is prototype developed for minor offshore inspection tasks. The described objective is to stabilize system is installed on the ROV. An Underwater Acoustic System (UAPS) developed by WaterLinked is prototype developed for minor offshore inspection tasks. Positioning The described work’s objective is to stabilize the threePositioning System (UAPS) developed by WaterLinked is used. The UAPS transmits acoustic waves from the ROV Positioning System (UAPS) developed by WaterLinked is prototype developed for minor offshore inspection tasks. The described work’s objective is to stabilize the threeused. The UAPS transmits acoustic waves from the ROV The described described work’s of objective is to to stabilize the threethree- used. dimensional position of the ROV ROV using an underwater underwater Positioning System (UAPS) developed by WaterLinked is The UAPS transmits acoustic waves from the ROV The work’s objective is stabilize the dimensional position the using an used. The UAPS transmits acoustic waves from the ROV to several receivers on the water surface that calculate the used. The UAPS transmits acoustic waves from the ROV The described work’s objective is to stabilize the threedimensional position of the ROV using an underwater to several receivers on the water surface that calculate the dimensional positiontransmitter of the the ROV ROV using anexist underwater acoustic positioning transmitter where therean exist an domdom- to used. The UAPS transmits acoustic waves from the ROV several receivers on the water surface that calculate the dimensional position of using underwater acoustic positioning where there an to several several receivers onon thetrilateration water surface surface that calculate calculate the ROV’s position based distance calculations to receivers on the water that the ROV’s position based on trilateration distance calculations dimensional position of the ROV using underwater acoustic positioning transmitter where there an domacoustic positioning transmitter where thereanexist exist an dom- ROV’s inant time delay in the measured output. The acoustic to several receivers onon thetrilateration water surface that calculate the position based distance calculations acoustic positioning transmitter where there exist an dominant time delay ROV’s position based on trilateration distance calculations (Joaqun Aparicio and lvarez (2016)). In this configuration in the measured output. The acoustic ROV’s position based on trilateration distance calculations acoustic positioning transmitter where there exist an dominant time delay in the measured output. The acoustic (Joaqun Aparicio and lvarez (2016)). In this configuration inant time time delay delay in as thean measured output. acoustic (Joaqun transmitter operates as anmeasured underwater GPS. The The positionpositionROV’s position based on trilateration distance calculations Aparicio and lvarez (2016)). In this configuration inant in the output. acoustic transmitter operates underwater GPS. (Joaqun Aparicio and lvarez (2016)). In this configuration the UAPS uses Short Baseline (SBL) with four transducers (Joaqun Aparicio andBaseline lvarez (2016)). In this inant time delay in as thean measured output. acoustic transmitter operates underwater The the UAPS uses Short Short (SBL) with with fourconfiguration transducers transmitter operates as an underwater GPS. The positionpositioning transmitter will be investigated asGPS. an alternative alternative to the (Joaqun Aparicio andBaseline lvarez (2016)). In this configuration UAPS uses (SBL) four transducers transmitter operates as an underwater GPS. The positioning transmitter will be investigated as an to the UAPS uses Short Baseline (SBL) with four transducers which is lowered into the water, and send signals back the UAPS uses Short Baseline (SBL) with four transducers transmitter operates as an underwater GPS. The positioning transmitter will be investigated as an alternative to which is lowered into the water, and send signals back to to ingCorresponding transmitterauthor. will be be investigated as an an alternative alternative to to which UAPS uses Short Baseline (SBL) with four transducers is into the water, and send signals back ing transmitter will investigated as which is lowered lowered into theis water, and send signals back to to athe ground station, which above water level. E-mail: [email protected]. which is lowered into the water, and send signals back to a ground station, which is above water level. Corresponding author. E-mail: [email protected]. ing transmitter will be investigated as an alternative to which is lowered into the water, and send signals back to aaa ground station, which is above water level. Corresponding author. author. E-mail: E-mail: [email protected]. [email protected]. Corresponding ground station, which is above water level. ground station, which is above water level. Corresponding author. E-mail: [email protected]. Corresponding author. E-mail: [email protected]. a ground station, which is above water level. 2405-8963 Copyright © 2019. The Authors. Published by Elsevier Ltd. All rights reserved.
Copyright © 2019 IFAC 213 Copyright © 2019 213 Peer review responsibility of International Federation of Automatic Copyright © under 2019 IFAC IFAC 213 Control. Copyright © 213 Copyright © 2019 2019 IFAC IFAC 213 10.1016/j.ifacol.2019.11.037 Copyright © 2019 IFAC 213
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Fig. 1. The ROV placed in the two respective coordinate systems; the body and the world frame.
Fig. 2. The accelerometer and UAPS data in the xcoordinate. Notice that the figure only illustrates that time at which the transmitters detects the motion chance and that the units from the two transmitters are not comparable. In figure 2 the UAPS data is logged together with the acceleration data as a thruster step input is given to the surge motion (x-coordinate). The step input is given at 3 seconds. Although the accelerometer has the most noise, it is clear that it reacts immediately to the motion change. Hence, there is a time delay in the UAPS communication to the real-time operating computer. By doing several experiments the time delay, τ , is estimated to be τ = 2.05± 0.55s. 3. MODEL The model description is divided into three subsystems: The ROV frame, the thruster forces and the damping forces. 3.1 Dynamic model The dynamic behavior of the ROV is based on the Lagrangian relationship: L=T −V (1) 214
where V is a function of the generalized position vector that describes the potential energy of the ROV, and T is the kinetic energy of the moving ROV, not considering the fluid, but only rotation and translation, such that the vector form is 1 (2) T = vT M v 2 where M is the mass matrix and v is the generalized velocity vector. For the rotational motion v is replaced by the angular velocity and m is replaced by the mass moment of inertia. The potential energy of the system is given solely from the buoyancy force acting on the ROV, when the ROV is orientated of its stable point in either pitch or roll it creates a force and a moment moving the ROV back into its stable position. At its stable position the center of the buoyancy (COB) is located straight above the center of mass (COM) as shown in figure 4. Meaning that the angles θ and φ are zero. The buoyancy force which is acting on the ROV creates a torque with the distance from the COB to the resting position. This distance can be found since the distance between the COM and the COB is fixed. The distance in the D,w direction, between the COM and COB can be found by transforming the rotation matrix, Rf , and converting the LGB from body to world frame. As the LGB is described for body frame, the D component of the vector for the length between COM and COB is given by 0 0 0 0 · Rf (3) = LGB,D,w LGB,d,b As the ROV is assumed to be neutrally buoyant the total potential energy, V, is V = −LGB,D,ω Fb (4) where Fb is the force due to buoyancy of the ROV, Fb = ρgv, with ρ being the density of water and, g the gravitational acceleration and v the volume of the ROV. LGB,D,ω can be obtained from (5) −LGB,D,b = −LGB,d,b cos(θ)cos(φ) Now the Lagrangian can be obtained: 1 L = · vTw · Mrb · vw − lbθ · F b − lbφ · F b (6) 2 which can be included in the Euler-Lagrange equation, d δL δL = Tf · Fb (7) − dt δvw δpw The first term in equation 7 is d δL MRB 0 = · aw (8) 0 IO dt δvw
The second term is the restoring forces and are given as, δL 0 = . (9) G δpw Here, G represents the restoring forces (Fossen (1994)). Tf is a transformation matrix, which transforms the drag forces to torques by considering the distance from the thruster to the COM, this is Ls and Lr . It also transforms the body fixed translational forces to world frame by applying a rotation matrix Rf . Rf 0 Tf = (10) L s Lr
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Force - Fb (N)
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-50 -1
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Fig. 3. Shows force provided by 2 thruster with input from -100% to 100 %. A 9th order polynomial is applied to obtained an acceptable model accuracy.
3.2 Thruster model The thruster percentage to force must be modeled to find the correct actuator forces acting on the ROV. The thruster expression is obtained from Wang and Clark (2006): Fthrust = ρD4
α 2 · ua α1 + · η|η| nD
(11)
where α1,2 are the thruster coefficients describing the efficiency of the propeller, D is diameter, ua is the ambient water speed, Fthrust is the thrust of the propeller and η is the propeller rate. The coefficients in the thruster model are identified by connecting a newton meter to the ROV in water and gradually increasing the dedicated heave thrusters by 10 % in step size until reaching steady-state. The results are plotted in figure 3 where the modelled is fitted to a static 9th order polynomial. The obtained coefficients are used for all directions as it is assumed that the ROV has no geometry that will affect the flow from the thrusters unevenly. Motion around the axes, known as rotations, is possible through the thrusters applying torque to the ROV. The length from the thrusters to the center of gravity need to befound to determine the size of this torque, see figure 4 and 5.
Fig. 5. The ROV with the lengths between COM and centerlines of thrusters. Blue dotted line is the centerline of thrusters Hence, the pitch moment, Mθ,n , is a function of the surge thruster force: Mθ,n = Fn,b · Lθ , the moment caused by the roll thrusters can be described by Mφ = Fφ,b · Lφ , the roll moment for sway can be described by Mφ,e = Fe,b · Lθ where the length is the same as for the pitch. The yaw motion is effected by all four horizontal thrusters: Mψ = Fψ,b · Lψ,long + Fψ,b · Lψ,short . 3.3 Damping forces The damping forces derive from two sources, the drag and the added mass. The added mass is neglected in this project as it only is resisting movement during accelerations, and therefore, compared to the drag force it is thought to be insignificant at smaller accelerations. The general drag force for one direction is given by 1 (12) fdrag = · cd · ρ · A · v 2 2 where cd is the drag coefficient and A is the cross sectional area perpendicular to the flow. cd is a combination of skin friction drag and pressure drag, but can be assumed to be constant at Reynolds numbers between 103 − 105 (Cengel (2012)), which is assumed to be present in this study.
Fig. 6. Illustration of the test setup for determination of drag forces. Fig. 4. The ROV with the lengths between COM and centerlines of thrusters. Blue dotted line is the centerline of thrusters 215
Figure 6 illustrates the test setup used to identify the Cd coefficients. To find the force-velocity relations, the ROV
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3.4 The complete model After the model was identified it was validation based on a variety of experiments. The error distribution with subject to thruster actuation showed that the model overall is sufficiently accurate for model-based control applications. The combined model description can be expressed by equation (14). MRB 0 0 Rf 0 Rf 0 = fb,b · · aw − − fd,b · G 0 IO 0 I3 Ls Lr (14) A table with all model parameters and dimensions is seen in the table 1. Table 1. Table of all parameters Description Volume Length from COM to COB Length from COM to pitch thruster Length from COM to roll thruster Short length from G to yaw thruster Long length from G to yaw thruster Height of ROV Length of side Length of front Drag coefficient for front and back Drag coefficient for top and bottom Mass of ROV MOI around x axis MOI around y axis MOI around z axis
Symbol υ LGB,b Lφ Lθ Lψ,short Lψ,long h Lside Lfront Cdfor Cdtop m Iφ Iθ Iψ
Value 0.011167 0.028 0.005 0.111 0.148 0.089 0.254 0.457 0.338 1.6 1.48 11.167 0.2 0.243 0.239
Unit m3 m m m m m m m m kg kg · m2 kg · m2 kg · m2
4.1 Linearization and open-loop analysis The model is linearized using Taylor expansion to obtain the state-space Jacobians. The linearized model is compared to the non-linear model, and the comparison shows that the linear model deviates somewhat from the nonlinear model. One of the experiments is shown in figure 7 where a unity input step is applied to the surge thrusters. As this motion also impacts the pitching, the pitch output is also plotted. The respective transient responses are almost identical, while a larger deviation exist at steadystate. This can be explained by the thruster operating far from the linearization point. 4
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is dragged through the water with constant velocity by a motor and the force required to do so is measured with a Newton meter. This procedure is carried out for surge and sway, but as the distance for the vertical movement (heave) is limited by the test facility, a different test is performed where weight is added to the ROV and the downwards acting force is measured. For the rotational movements of the ROV, described as roll, pitch and yaw, a lesser accurate method is used, as these movements do not influence the ROV as much. For yaw and roll, the maximum angular velocity is found together with the angular velocity at 50 % thrust. This provides three points as the drag torque should always go through 0. The pitch is identified by applying equation (11) to determine Cd based on a known velocity. It is assumed that the drag for the front is equal the back, and drag for the top is equal the bottom. Then, the drag torque for pitch can be determined as an expression for linear drag on a rotational movement, such that Mdθ,b = Lside 2 1 2 · ρ · (ωθ,b · r1 ) · (r1 · Lf or ) · Cdtop dr1 + 2· 2 0 h2 1 2 · ρ · (ωθ,b · r2 ) · (r2 · Lf or ) · Cdf or dr2 2· 2 0 (13)
Posistion (m), Orientation (rad)
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Fig. 7. This figure shows the simulated linear and nonlinear models when a unit step is applied to the surging thrusters. The obtained linearized state-space model consists of all positions, orientations, velocities and angular velocities are added as states; which results in a total of 12 states. Although the velocities are not directly measured, they are simply derivatives of the 6 measured outputs, resulting in 12 outputs. The model is both fully controllable and observable as the observability and controllability matrices have full rank. The model is marginally stable as the poles related to the positions are located at the origin of the s-plane. 4.2 Linear quadratic regulator with integral action The LQR controller is a full-state feedback optimal control method which finds the minimimum solution to a defined cost function. LQR is unconstrained which means it is not possible to define saturation limits directly into the method. The cost function penalizes both the inputs and states of the system to find a controller gain, K, such that u = −Kx. The cost function, J, is defined as a time integration of the two respective weighted terms, such that ∞ T T J(t) = x(t) · Q · x(t) + u(t) · R · u(t) dt 0
(15) where J(u) is the cost function, x is the states, u is the inputs, Q is a 16x16 semi-positive definite matrix which weighs the states and R is a 5x5 is a positive definite matrix whitch weighs the inputs.
4. CONTROL DEVELOPMENT This section describes the control development which consists of a Linearquadratic regulator with integral action (LQRI) including a Smith predictor. 216
To eliminate steady-state error for any output an integral term is introduced, such that the updated system can be expressed as x˙ i 0 C xi 0 = · + · u − Br · ref (16) 0A x B x˙ s where u = −Ka x, Ka = [Ki K] and Br (16x4) is a matrix which scales the reference to be the same size as the other
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Fig. 8. Output response of a reference change of 3 m in nw and ew , 1 m in dw and a change in orientation of π4 in ψw , with the final LQRI controller simulated with the non-linear model.
components in the system. The new A and B matrices are used, such that Q (16x16) weights 16 states and R (5x5) still weights 5 inputs. Bryson’s rule is applied for the Q and R matrices similar to Mai et al. (2017). By normalizing the states’ and inputs’ maximum values this method ensures that all are weighted equally from the beginning. The Q and R matrices are then manually tuned further based on nonlinear model simulations, which leads to a decrease in the integral terms in order to minimize the overshooting. In this tuning process, the pitch penalty is also decreased to allow a more aggressive surge motion. Moreover, integral anti-windup is added to all integral terms to avoid the integral term to accumulate when the ROV is far from the reference point and the actuators are saturated. The final non-linear closed-loop simulation of the theoretically tuned output responses is seen on figure 8. The control objective was to reduce the overshooting to a minimum while keeping an acceptable settling time. Thus, based on the simulations the controller was found acceptable for fulfilling the objectives.
4.3 Smith predictor
The time delay from the UAPS sensor is addressed by included a smith predictor to the control scheme. A Smith predictor predicts the positions of the the ROV and corrects potential model deviations by subtracting time delayed model outputs from the corresponding measured values. Figure 9 shows a block diagram of the system with the final control scheme in the discretized form. For simplicity the anti-windup is not illustrated in the block diagram. The forward estimator simply takes the derivative of the positions to obtain the velocities. The output filter is a vector of first order low-pass filters with equal cut-off frequencies 100 times higher than the fastest of the system’s respective bandwidths. 217
Fig. 10. Result for steady position controller with the obtained controller, the red dot is the initial position
Fig. 9. The entire discretized closed-loop control structure with LQRI and Smith Predictor. 5. RESULTS The closed-loop results are based on experimental results in a water pool. The first experiment is focusing on keeping a two-dimensional position in the north and east directions; see figure 10 which plots the two-dimensional motion during a 10 second test. It is clear that the ROV drifts and that the controller does not operate as intended. The controller gains are now reduced to observe if it improves the stabilization; see figure 11 which plots the two-dimensional motion during a 10 second test. As it still drifts it is concluded that the Smith predictor does not work well for handling the time delay on the output, probably due to the time delay being time variant. Lastly, a test is carried out where only the yaw and heave is controlled as they are not effected by the UAPS’ time delay. If these motions are stable without further tuning it is clear that it is verificed that the Smith predictor caused the problems for the control scheme. This test is seen in figure 12. It is clear that, although there are more fluctuations present for both heave and yaw in the experiments than in simulations, both output drifts. By reducing the integral gains the fluctuations are expected to be reduced, however, by now it is clear that the developed
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REFERENCES
Fig. 11. Result for steady position controller with the final tune of the controller, the red dot is the initial position.
Fig. 12. Result comparison of the test and the simulation of the controller for yaw and heave LQRI controller operates better than the UAPS controller.
6. CONCLUSION This study examines the modeling, identification and control of a BlueROV2 using an UAPS underwater position transmitter. The model is shown to fit the obtained data acceptably but with some deviations from reality. The developed LQRI controller with a Smith predictor did not stabilize the ROV in a two-dimensional space, probably because the Smith predictor not properly eliminating the negative effect of the UAPS time delay. When controlling the ROV using alternative heave and yaw transmitters the control scheme operates better. In future work an online identification of the time delay will be used to catch the potential time-variant features. At this stage it is uncertain how fast the time delay changes with respect to time and, thus, the cause of the communication delay needs to be examined further. 218
Arnesen, B.O., Lekkas, A.M., and Schjoelberg, I. (2017). 3d path following and tracking for an inspection class rov. ASME 36th International Conference on Ocean, Offshore and Arctic Engineering, 7a(OMAE2017-61170), V07AT06A019. Brun, L. (2014). ROV/AUV Trends: Market and Technology. DOI: 10.13140/RG.2.1.4062.5686. Cengel, Y. (2012). Fundamentals of Thermal-Fluid sciences. McGraw-Hill. ISBN-13: 978-0071325110. Fossen, T.I. (1994). Guidance and Control of Ocean Vehicles. Wiley. ISBN-13: 978-0471941132. Fossen, T.I. (2011). Handbook of Marine Craft Hydrodynamics and Motion Control. Wiley. ISBN: 978-1-11999149-6. Joaqun Aparicio, A.J. and lvarez, F.J. (2016). Characterization of an underwater positioning system based on gps surface nodes and encoded acoustic signals. IEEE Transactions on Instrumentation and Measurement. URL https://ieeexplore.ieee.org/stamp/ stamp.jsp?tp=&arnumber=7469873. Mai, C., Pedersen, S., Hansen, L., Jepsen, K.L., and Yang, Z. (2016). Subsea infrastructure inspection: A review study. In 2016 IEEE International Conference on Underwater System Technology: Theory and Applications (USYS), 71–76. Mai, C., Pedersen, S., Hansen, L., Jepsen, K.L., and Yang, Z. (2017). Modeling and Control of Industrial ROV’s for Semi-Autonomous Subsea Maintenance Services. IFAC Congress. Marine Technology Society (2017). ROV Applications What ROVs can do. Online. URL http://www.rov. org/rov_applications.cfm. Pedersen, S., Enevoldsen, T.T., and Einarsson, E.M. (2018). Model comparison of a videoray pro 4 underwater rov. IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM). doi:10.1109/ AIM.2018.8452445. Reid, A. (2013). ROV Market Prospects. Subsea UK, Aberdeen. URL http : / / www . subseauk . com / documents / presentations / ssuk % 20 - %20rov % 20event%20-%20sep%202013%20%5Bweb%5D.pdf. Schjølberg, I. and Utne, I.B. (2015). Towards autonomy in rov operations. IFAC-PapersOnLine, 48(2), 183 – 188. Tena, I. (2011). Automating ROV Operations in aid of the Oil & Gas Offshore Industry. SeeByte Whitepaper. Wang, W. and Clark, C.M. (2006). Modeling and Simulation of the VideoRay Pro III Underwater Vehicle. IEEE OCEANS 2006. Wynn, R.B., Huvenne, V.A., Bas, T.P.L., Murton, B.J., Connelly, D.P., Bett, B.J., Ruhl, H.A., Morris, K.J., Peakall, J., Parsons, D.R., Sumner, E.J., Darby, S.E., Dorrell, R.M., and Hunt, J.E. (2014). Autonomous Underwater Vehicles (AUVs): Their past, present and future contributions to the advancement of marine geoscience. Marine Geology, 352, 451 – 468.