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Tracking of a Target Payload via a Combination of Input Shaping and Feedback Control
Proceedings of the 12th IFAC Workshop on Time Delay Systems Proceedings of the 12th IFACMI, Workshop on Time Delay Systems June 28-30, 2015. Ann Arbor, USA Proceedings of the the 12th IFACMI, Workshop on Time Time Delay Delay Systems Systems Proceedings of 12th IFAC Workshop on June 28-30, 2015. Ann Arbor, USA June June 28-30, 28-30, 2015. 2015. Ann Ann Arbor, Arbor, MI, MI, USA USAAvailable online at www.sciencedirect.com
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Tracking of a Target Payload via a Tracking of a Target Payload via a Tracking of a Target Payload via a Combination of Input Shaping and Combination of Input Shaping and Combination of Input Shaping and Feedback Feedback Control Control Feedback Control
Robert Schmidt ∗∗ Nicole Barry ∗∗ Joshua Vaughan ∗∗ Robert Schmidt ∗ Nicole Barry ∗ Joshua Vaughan ∗ Robert Robert Schmidt Schmidt ∗ Nicole Nicole Barry Barry ∗ Joshua Joshua Vaughan Vaughan ∗ ∗ ∗ Department of Mechanical Engineering, University of Louisiana at of Mechanical Engineering, University of Louisiana at ∗ Department Lafayette, Lafayette, LA 70504University USA, (e-mail: ∗ Department of Mechanical Mechanical Engineering, of Louisiana Louisiana at at Department of Engineering, of Lafayette, Lafayette, LA 70504University USA, (e-mail: [email protected]) Lafayette, Lafayette, LA 70504 Lafayette, Lafayette, LA 70504 USA, USA, (e-mail: (e-mail: [email protected]) [email protected]) [email protected]) Abstract: This paper investigates the use of the combination of a feedback controller and Abstract: This paper investigates the use of the combination of a feedback controller and input shaping to align crane hoist with desired, moving payload. The motivating application Abstract: This paper investigates the of combination of aa feedback controller and Abstract: This paperaa crane investigates the aause use of the themoving combination of The feedback controller and input shaping to align hoist with desired, payload. motivating application example is the to retrieval of an autonomous surface vessel (ASV) by a larger, host vessel following input shaping to align a crane hoist with a desired, moving payload. The motivating application input shaping align a crane hoist with a desired, moving payload. The motivating application example is the retrieval of an autonomous surface vessel (ASV) by a larger, host vessel following the completion of the ASV’s unmanned mission. Both the ASV by and the larger vessel arefollowing subject example is of autonomous surface vessel (ASV) larger, host vessel example is the the retrieval retrieval of an anunmanned autonomous surfaceBoth vessel (ASV) larger, host vessel the completion of the ASV’s mission. the ASV by andaa the larger vessel arefollowing subject to disturbances that make control of the crane-based operation difficult. This work focuses on the completion of the ASV’s unmanned mission. Both the ASV and the larger vessel are subject the completion ofthat the make ASV’scontrol unmanned mission. Both the ASV and the larger subject to disturbances of the crane-based operation difficult. Thisvessel work are focuses on the motion of the ASV and proper alignment of the host-vessel’s hoist with it leading to the to disturbances that make control of the crane-based operation difficult. This work focuses on to that make the crane-based operation difficult. This itwork focuses on thedisturbances motion of the ASV andcontrol properofalignment of the host-vessel’s hoist with leading to the initiation of of thethe lift.ASV Thisand alignment isalignment maintained via feedback mechanism as it well as a preview the motion properis alignment of via theaahost-vessel’s host-vessel’s hoist with with leading to the the the motion proper of the hoist leading to initiation of of thethe lift.ASV Thisand alignment maintained feedback mechanism as it well as a preview of incoming conditions. Input shaping greatly simplifies the design of this controller by reducing initiation of the alignment is via mechanism as preview initiation of conditions. the lift. lift. This ThisInput alignment is maintained maintained via aa feedback feedback mechanism as well well as as preview of incoming shaping greatly simplifies the design of this controller byaareducing commanded-motion-induced oscillation. of incoming conditions. Input shaping greatly simplifies the design of this controller by reducing of incoming conditions. Inputoscillation. shaping greatly simplifies the design of this controller by reducing commanded-motion-induced commanded-motion-induced oscillation. commanded-motion-induced oscillation. © 2015, IFAC (International Automatic Control) Hosting Hydrodynamics by Elsevier Ltd. All rights reserved. Keywords: Input Shaping,Federation FeedbackofControl, Target Tracking, Keywords: Input Shaping, Feedback Control, Target Tracking, Hydrodynamics Keywords: Input Input Shaping, Shaping, Feedback Feedback Control, Control, Target Target Tracking, Tracking, Hydrodynamics Hydrodynamics Keywords: 1. INTRODUCTION 1. INTRODUCTION 1. INTRODUCTION INTRODUCTION 1. Crane use is ubiquitous in a multitude of industries. Crane use is ubiquitous in a multitude of industries. With the ever-increasing use ofmultitude ports for ofinternational Crane use ever-increasing is ubiquitous ubiquitous use in aaof multitude industries. Crane use is in industries. With the ports for of international commerce, cranes have found use on and around both With the ever-increasing use of ports for international With the ever-increasing use of ports for international commerce, cranes have found use on and around both large and small marine vessels. Consequently, this increase commerce, cranes have found use on and around both commerce, cranes havevessels. found Consequently, use on and around both large and small marine this increase in port use hasmarine caused portsConsequently, to become overcrowded. large anduse small vessels. this increase increase large and small vessels. this in port hasmarine caused portsConsequently, to become overcrowded. Normally, ships dock in port while their cargoovercrowded. is offloaded in port use use hasdock caused ports to their become in port has caused ports to become Normally, ships in port while cargoovercrowded. is offloaded and loaded. With overcrowding, some ports require ships Normally, ships dock in port while their cargo is offloaded Normally, ships dock in port while theirports cargorequire is offloaded and loaded. With overcrowding, some ships to wait until space becomes available. This has driven and loaded. With overcrowding, some ports require ships and loaded. overcrowding, some ports ships to wait untilWith space becomes available. Thisrequire has driven research to findspace a solution. There has beenThis recent research to wait until until becomes available. hasresearch driven to wait becomes available. has driven research to findspace a solution. There has beenThis recent on mobileto harbors to assistThere in port expansion [Hong and research find aa solution. solution. hasexpansion been recent recent research research find has been research on mobiletoharbors to assistThere in port [Hong and Ngo (2012); Ngo and Hong (2012)]. Besides port-use, on mobile harbors to assist in port expansion [Hong and on harbors to assist port expansion and Fig. 1. Oil Rig Crane Ngomobile (2012); Ngo and Hongin (2012)]. Besides[Hong port-use, marine cranes Ngo see significant use(2012)]. in the oilBesides and gas port-use, industry, Fig. Ngo (2012); and Hong Hong Oil Rig Crane Ngo (2012); and marine cranes Ngo see significant use(2012)]. in the oilBesides and gas port-use, industry, Fig. 1. 1. Oil Oil Rig Rig Crane Crane including loading supplies onto oil rigs, as shown in Fig. 1. Fig. 1. marine cranes see significant use in the oil and gas industry, marine cranes see significant useoil in the gas in industry, including loading supplies onto rigs,oil asand shown Fig. 1. including loading supplies supplies onto is oilthe rigs,deployment as shown shown in inand Fig.re1. including loading onto oil rigs, as Fig. 1. Another application of cranes Another application of cranes is the deployment and retrieval ofapplication surveying equipment, specifically, autonomous Another of cranes cranes is is specifically, the deployment deployment and rereAnother of the and trieval ofapplication surveying equipment, autonomous surface of vehicles (ASV). C&C Technologies, located in trieval of surveying equipment, specifically, autonomous trieval surveying equipment, specifically, autonomous surface vehicles (ASV). C&C Technologies, located in Lafayette, Louisiana, has several models of ASVs, like the surface vehicles (ASV). C&C Technologies, Technologies, located in surface vehicles (ASV). C&C located in Lafayette, Louisiana, has several models of ASVs, like the one shown in Fig. 2, that are used to survey geological Lafayette, Louisiana, has several models of ASVs, like the Lafayette, models of ASVs, like the one shownLouisiana, in Fig. 2, has thatseveral are used to survey geological formations or Fig. inspect pipelines. Duetotosurvey the varying sea one shown in in 2, that that are used used geological one shown 2, are geological formations or Fig. inspect pipelines. Dueto tosurvey the varying sea conditions, similar to those faced by some South Korean formations or inspect pipelines. Due to the varying sea formations or inspect pipelines. to the varying sea conditions, similar to those facedDue by some South Korean ports, retrieval of the ASV has proven arduous for C&C conditions, similar to those those faced by South Korean conditions, similar to facedproven by some some Southfor Korean ports, retrieval of the ASV has arduous C&C Technologies. Previous attempts have been made to reduce ports, retrievalPrevious of the the ASV ASV has have proven arduous forreduce C&C ports, retrieval of has proven arduous for C&C Technologies. attempts been made to the difficulty of this task including the implementation of Technologies. Previous attempts have been made to reduce Technologies. Previous attempts have been made to reduce the difficulty of this task including the implementation of feedback control and input shaping. Despite this, several the difficulty of this task including the implementation of the difficulty of this including implementation of feedback control andtask input shaping.the Despite this, several factors make the and mobile harbors’ cranes easier to control feedback control input shaping. Despite this, several feedback control input shaping. Despite this, several factors make the and mobile harbors’ cranes easier to control [Park and Kwon (2010); Kim et al.cranes (2013)]. Theto main diffactors make the (2010); mobile Kim harbors’ easier control factors make the mobile harbors’ easier control [Park and Kwon et al.cranes (2013)]. Theto main differenceand is the size(2010); of the vessels used during operation. The [Park and Kwon (2010); Kim et al. (2013)]. The main dif[Park Kwon Kim et al. (2013)]. The main difference is the size of the vessels used during operation. The Fig. 2. An Autonomous Surface Vehicle container ships and crane-equipped mobile harbors The are ference is the the sizeand of the the vessels operation. 2. An Autonomous Surface Vehicle ference is size of vessels used used during during operation. container ships crane-equipped mobile harbors The are Fig. Fig. 2. An Autonomous Surface Vehicle much larger than both the ASV and host vessel. Because container ships and crane-equipped mobile harbors are container ships crane-equipped mobile harbors are Fig. 2. An Autonomous Surface Vehicle much larger thanand both the ASV and host vessel. Because of this,larger somethan oceanboth effects can beand neglected in theBecause mobile in the mobile harbors’ case, a docking mechanism locks much the can ASVbe and host vessel. vessel. much the ASV host of this,larger somethan oceanboth effects neglected in theBecause mobile in the mobile harbors’ case, a docking mechanism locks harbor control problem, such as drift force in and current, the container ship to thecase, mobile harbor, mechanism eliminating some in the the mobile ship harbors’ docking locks of this, some ocean effects can be neglected in the mobile of this, some ocean effects can be neglected the mobile mobile harbors’ aa docking locks harbor control problem, such as drift force and current, in the container to thecase, mobile harbor, mechanism eliminating some that cannot for the retrieval of the ASV. In addition, translation effects [Hong and Ngo (2012)]. In the case of the container ship to the mobile harbor, eliminating some harbor control problem, such as drift force and current, harbor control problem, such as drift force and current, the container ship to the mobile harbor, eliminating some that cannot for the retrieval of the ASV. In addition, translation effects [Hong and Ngo (2012)]. In the case of when the loading and offloading tasks are being completed the ASV, no special docking mechanism exists. translation effects [Hong and Ngo (2012)]. In the case of that cannot for the retrieval of the ASV. In addition, that for the retrieval oftasks the are ASV. Incompleted addition, translation andmechanism Ngo (2012)]. In the case of when cannot the loading and offloading being the ASV, noeffects special[Hong docking exists. the ASV, no special docking mechanism exists. when the loading and offloading tasks are being completed when the loading and offloading tasks are being completed the ASV, no special docking mechanism exists.
Copyright © 2015, IFAC 2015 141 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright © IFAC 2015 141 Copyright © IFAC 2015 141 Peer review under responsibility of International Federation of Automatic Copyright © IFAC 2015 141Control. 10.1016/j.ifacol.2015.09.367
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x
under the assumption that the target is only translating. The linearized equations of motion of the planar crane model are: x + mp lθ¨ = f (1) (mp + mt )¨ 2¨ x + mp l θ + mp glθ = 0 (2) mp l¨
mt
f
where mp and mt are the mass of the payload and trolley, respectively. The cable, which is assumed to be massless and inextensible, has length l. The position of the trolley is described by x, and the angular position of the payload is represented as θ. The variable f represents the input force on the trolley. In terms of this model, the control objective is to choose this force such that the position of the payload tracks the position of the target, xd .
g
m
The target’s position, xd , is generated using [Fossen (1994)]:
xd
2 Vwind g Hs Awave = 2 g ωwave = 0.4 Hs
Hs = 0.21
ASV Fig. 3. Planar Crane Model with Target Vessel Input shaping, a well-researched, open-loop control method, has proven itself to be a robust and easy-to-implement way of reducing the residual vibration of a system [Smith (1957); Singer and Seering (1990); Singhose (2009)]. Input shaping is implemented using the knowledge of a system’s natural frequencies and damping ratios. There are several different types of input shapers that offer robustness to changes in the system’s parameters [Vaughan et al. (2008)]. Unfortunately, due to its open-loop nature, input shaping cannot counteract disturbances. Because of this, a feedback mechanism is necessary. Some research has been conducted using a combination of feedback control and input shaping [Huey and Singhose (2012); Majid et al. (2013); Huey (2006)]. Research has also been conducted on an operator’s performance using PD control and input shaping [Vaughan et al. (2011)]. This paper furthers this prior work by implementing a blend of input shaping and feedback control for target tracking with minimal vibration. This is accomplished by intelligently transitioning between moving to the target and tracking. In the next section, an explanation of the crane model used and the assumptions made will be presented. Section 3 will discuss the theory and implementation of the controllers used. This will include a discussion of the blend of input shaping, feedback control, and the transition from one to the other when tracking is initialized. Finally, conclusions will be made in Section 4. 2. MODEL The model used during the phase of this research is a simple, planar crane model, shown in Fig. 3. External forces from the wind and waves that affect the vessel containing the crane are neglected. These forces’ affects on the ASV include heave, sway, yaw, pitch, and rotation. In this work, focus is given to improving tracking of the target 142
(3) (4) (5)
These equations, from the Pierson-Moskowitz Spectrum, use the assumption that the wind has been blowing over such a great distance that the time it has been blowing is neglected. This is referred to as fully developed seas. Significant wave height, Hs , is obtained through an assumed wind velocity, Vwind . This height is then used to determine the frequency, ωwave , and amplitude, Awave , of the waves. The assumption is made that the target vessel follows the path of the waves exactly. If tracking the wave exactly is achieved with this controller, it can be assumed that the slower dynamics of the ASV can be tracked with the same controller. 3. CONTROLLERS This section presents the different types of controllers used to track the ASV. First, a traditional feedback control is applied to the system to achieve tracking without any conditional logic is presented. Following this, an algorithm for transitioning between gross motion and tracking is presented. Finally, input shaping is used to assist the developed tracking controller by greatly reducing the residual vibration of the payload caused by the initial move of the trolley. 3.1 Gross Motion and Tracking Algorithm To establish some basic tracking capabilities, LQR feedback was applied to the system. Using this achieves the goal of tracking the target ASV to an extent. As can be seen in Fig. 4, an initial move is made towards the moving target, and tracking immediately begins once the trolley is in range. This method does provide some tracking, but the residual vibration from the gross motion move adds to the error produced by the LQR controller during the tracking phase. To determine the performance of this controller, RMS error was calculated and can be seen for a range
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Fig. 4. Unshaped LQR Feedback with Wind Velocity of 20 knots without Transition Control Scheme 0.8
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Fig. 6. Flow Diagram of Logic for ASV Retrieval
0.4
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xd (t) 5
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Fig. 5. RMS Error of Tracking without Transition Control Scheme of wind speeds in Fig. 5. The error is always nonzero and increases with wind speed. This motivates the implementation of additional logic to decrease the error. By segmenting the two goals of the controller, moving to the target and tracking, and establishing when to transition between the two, error should be reduced. The primary mechanism for partitioning the control action is the natural partition between the two task objectives. For some part of each crane move, the crane must be moved to the nominal target location. Then, once near that location, a more-dedicated tracking algorithm can begin. Figure 6 shows a flow diagram depicting the decisions made during this natural partitioning of the task. Figure 7 further illustrates these decisions, where x ¯d (t) represents nominal location, xd represents the actual target location, and x(t) represents the current system state. The controller switches between the move-based controller, the top branch in Fig. 7, containing a command generation block, GCG , and the tracking controller, represented by the feedback block, GF B . Initially, the trolley and payload travel together towards the target. This move is shown in Fig. 8. Once both are within the buffer zone of the moving target, the trolley holds its position until the target is both near the payload and moving in the same direction. This time waiting falls between the “Move” section and the “Track” section of 143
x(t)
+ -
Fig. 7. Block Diagram of Control Scheme 14
Payload Trolley
12
Position (m)
Error (m)
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10 8
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Target
Track
6 4 2 0 0
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Fig. 8. Simulation Illustrating Transition to Tracking the figure, which is exaggerated to better separate the two phases. Once this occurs, tracking of the target may begin. The response of the system to the application of this logic is shown in Fig. 9. Once the conditions defined by the algorithm are met, tracking may begin. Some improvements, resulting from the implemented algorithm, in RMS error can be seen at lower wind speeds, as seen in Fig. 10. At higher wind speeds, the accuracy of tracking is more dependent on the quality of the tracking controller than
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Fig. 9. LQR Feedback Control with 20-knot Wind Velocity 0.8
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does not provide zero vibration at the model frequency. Instead, it is designed with a tolerable amount of vibration, Vtol , of 5% at the modeled frequency. As the system’s natural frequency moves away from the designed value, the percent residual vibration (PRV) decreases, providing extra robustness to the shaper.
Payload Error Trolley Error
0.5 0.4
In order to develop a command capable of decreasing the residual vibration of a system, knowledge of the system’s damping ratio, ζ, and natural frequency, ωn , is required. Due to the nature of cranes, the assumption can be made that the damping ratio is zero. This simplifies the calculations for the shaper command. The PRV produced by a shaper is [Singer and Seering (1990)]:
0.3 0.2 0.1 0.0 0
5
10
Fig. 11. Sensitivity Curves of ZV and EI Shapers
15
Wind Speed (knots)
20
25
Fig. 10. RMS Error of Unshaped Target Tracking
P RV = V (ζ, ω) = e−ζωtn
the transition between “Move” and “Track” segments. In an attempt to further improvements, the residual vibration caused by the initial move should be eliminated, allowing the tracking controller to begin without much error. This can be accomplished through the use of an input shaper. 3.2 Input Shaping
where C(ω, ζ) =
144
[C(ω, ζ)2 ] + [S(ω, ζ)2 ]
Ai eζωti cos(ωti
i=1
S(ω, ζ) =
Input shaping has proven a useful and easy-to-implement solution to vibration, including significant use on cranes [Yanyang et al. (2011); Vaughan et al. (2010)]. Although input shaping increases the rise time of a command, the percent overshoot and residual vibration can be drastically reduced. In this application, a slight increase in rise time is of no concern since the time it takes for the payload and trolley to reach the target is not the primary cost of the task. There exists multiple types of shapers. The differences become apparent when viewing the sensitivity curves of the shapers. Sensitivity curves are often used as a measurement of the performance shapers [Kozak et al. (2003)]. Figure 11 included the sensitivity curves for two shapers, the Zero-Vibration (ZV) shaper [Smith (1957)] and the Extra Insensitive (EI) shaper [Singhose (2009)]. As can be seen, each shaper behaves differently as one travels away from the model frequency, ωm , used to design the shaper. The ZV shaper provides zero vibration when the model is exact, but vibration rapidly increases as the modeled frequency deviates from the natural frequency. The EI shaper differs from the ZV shaper in that it
n
n i=1
Ai eζωti sin(ωti
(6)
1 − ζ 2)
(7)
1 − ζ 2 ).
(8)
This equation is used to form constraints on the residual vibration of the input shaper, along with additional constraints on impulse amplitudes is used in the formulation of the shaper. Applying this theory to the “Move” segment of the algorithm, a reduction in residual vibration can be achieved, allowing for more accurate tracking. Figure 12 shows the 5m move to tracking using a ZVshaper for the gross-motion portion of the move. Comparing this to Fig. 10, the residual vibration from that portion of the task is greatly reduced. In addition, the tracking portion of the command is able to begin almost immediately, as the payload has nearly settled upon arrival at the target location. The RMS error of tracking for 0 to 25 knot wind conditions following a ZV-shaped move is shown in Fig. 13. The error is much lower than the unshaped case at low wind speeds. At higher wind speeds, the performance of the tracking controller dominates the response, so less difference is seen between the unshaped and ZV-shaped cases.
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8 6 4 2 10
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Wind Speed (knots)
20
0.0 0
25
40
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60
Payload Error Trolley Error
0.3
0.1 10
30
Time (s)
0.4 0.2
5
20
0.5
0.2 0.0 0
10
Fig. 14. EI-Shaped Response with Wind Velocity of 20 knots
Error (m)
Error (m)
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Target
2
Fig. 12. ZV-Shaped Response with Wind Velocity of 20 knots 0.8
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Wind Speed (knots)
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Fig. 13. RMS Error of Tracking Target Following a ZVshaped Move
Fig. 15. RMS Error of Tracking Target Following a EIshaped Move
Table 1. Percent Difference of the RMS Error of Travel
Table 2. Percent Difference of the RMS Error of Tracking
Wind Speed (knots) Payload ZV (%) Trolley ZV (%) Payload EI (%) Trolley EI (%)
5
10
15
20
25
4.38 3.47 7.46 6.42
4.28 4.15 7.33 7.08
4.16 2.95 7.19 6.34
2.97 2.15 5.62 4.49
2.80 1.98 5.90 4.93
Wind Speed (knots) Payload ZV (%) Trolley ZV (%) Payload EI (%) Trolley EI (%)
A similar trial, with similar results, for an EI shaper is shown in Fig. 14. The robustness of the EI shaper slightly reduces the residual vibration resulting from the move portion of the command from that of the ZV shaper. The RMS error over a range of wind speeds, shown in Fig. 15 nearly matches that of the ZV-shaped case. A comparison of several trials using both shapers can be seen in Table 1 and Table 2. The most significant improvements can be seen in the “Travel” partition. This can be attributed to the application of the input shapers. For the “Tracking” partition, the majority of improvements are seen at lower wind speeds. Even so, improved accuracy is still achieved through the implementation of the shapers. To improve upon the accuracy of the simulation, a time delay representing the processing time of the feedback mechanism, likely a machine vision system, could be introduced. Figures 16 and 17 show the response of the 145
5
10
15
20
25
1.84 4.00 1.76 3.75
0.20 0.57 0.19 0.56
0.40 0.71 0.35 0.61
0.01 0.05 0.20 0.24
0.15 0.10 0.01 0.01
system with a 100ms time delay with a wind speed of 20 knots. This time delay forces the trolley to lag behind the target, degrading tracking performance. Although the accuracy was improved with the implementation of the transition logic and the shaper, the tracking controller still produces error at higher wind speeds. The addition of a more robust tracking controller is necessary to cope with the varying wind speeds the ASV will experience. 4. CONCLUSION This paper introduced a planar crane and wave motion model to represent the crane-based retrieval of an Autonomous Surface Vehicle by its host vessel. With feedback control alone, there was significant vibration during the tracking stage of the retrieval process. Input shaping was
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Fig. 17. EI-Shaped Response with 100ms Time Delay at 20 knots implemented to reduce vibration during the gross positioning phase of the ASV retrieval. Two input shapers, the Zero-Vibration (ZV) shaper and Extra Insensitive (EI) shaper, were used and example results shown. The combination of an input shaper for gross positioning and an intelligent transition to tracking achieve the goal of decreasing the error in tracking from that which would have occurred if only a traditional feedback controller were used. REFERENCES Fossen, T.I. (1994). Guidance and Control of Ocean Vehicles. John Wiley Sons Ltd. Hong, K.S. and Ngo, Q.H. (2012). Dynamics of the container crane on a mobile harbor. Ocean Engineering, 53, 16–24. Huey, J.R. (2006). The Intelligent Combination of Input Shaping and PID Feedback Control. Ph.D. thesis, Georgia Institute of Technology. Huey, J. and Singhose, W. (2012). Design of proportionalderivative feedback and input shaping for control of inertia plants. Control Theory Applications, IET, 6(3), 357–364. Kim, D., Park, Y., and sik Park, Y. (2013). Terminal tracking control of mobile harbor crane subject to actuator saturation. In Control, Automation and Systems 146
(ICCAS), 2013 13th International Conference on, 1431– 1435. Kozak, K., Huey, J., and Singhose, W. (2003). Performance measures for input shaping. In Control Applications, 2003. CCA 2003. Proceedings of 2003 IEEE Conference on, volume 2, 1227–1232 vol.2. Majid, M., Ibrahim, W., Mohamad, S., and Bakar, Z. (2013). A comparison of pid and pd controller with input shaping technique for 3d gantry crane. In Systems, Process Control (ICSPC), 2013 IEEE Conference on, 144–148. Ngo, Q.H. and Hong, K.S. (2012). Sliding-mode antisway control of an offshore container crane. Mechatronics, IEEE/ASME Transactions on, 17(2), 201–209. Park, K.R. and Kwon, D.S. (2010). Swing-free control of mobile harbor crane with accelerometer feedback. In Control Automation and Systems (ICCAS), 2010 International Conference on, 1322–1327. Peng, K., Singhose, W., and Bhaumik, P. (2012). Using machine vision and hand-motion control to improve crane operator performance. Systems, Man and Cybernetics, Part A: Systems and Humans, IEEE Transactions on, 42(6), 1496–1503. Singer, N. and Seering, W. (1990). Preshaping command inputs to reduce system vibration. Journal of Dynamic Systems, Measurement and Control, 112, 76 – 82. Singhose, W. (2009). Command shaping for flexible systems: A review of the first 50 years. International Journal of Precision Engineering and Manufacturing, 10(4), 153 – 168. Smith, O.J. (1957). Posicast control of damped oscillatory systems. Proceedings of the IRE, 45(9), 1249–1255. Vaughan, J., Karajgikar, A., and Singhose, W. (2011). A study of crane operator performance comparing pdcontrol and input shaping. In American Control Conference (ACC), 2011, 545–550. Vaughan, J., Maleki, E., and Singhose, W. (2010). Advantages of using command shaping over feedback for crane control. In American Control Conference (ACC), 2010, 2308–2313. Vaughan, J., Yano, A., and Singhose, W. (2008). Comparison of robust input shapers. Journal of Sound and Vibration, 315(4-5), 797 – 815. Yanyang, L., Wei, X., and Li, W. (2011). Anti-swing control of the crane system based on input shaping technique. In Control and Decision Conference (CCDC), 2011 Chinese, 2788–2791. Yoshida, Y. and Tsuzuki, K. (2006). Visual tracking and control of a moving overhead crane load. In Advanced Motion Control, 2006. 9th IEEE International Workshop on, 630–635.
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Tracking of a Target Payload via a Tracking of a Target Payload via a Tracking of a Target Payload via a Combination of Input Shaping and Combination of Input Shaping and Combination of Input Shaping and Feedback Feedback Control Control Feedback Control
Robert Schmidt ∗∗ Nicole Barry ∗∗ Joshua Vaughan ∗∗ Robert Schmidt ∗ Nicole Barry ∗ Joshua Vaughan ∗ Robert Robert Schmidt Schmidt ∗ Nicole Nicole Barry Barry ∗ Joshua Joshua Vaughan Vaughan ∗ ∗ ∗ Department of Mechanical Engineering, University of Louisiana at of Mechanical Engineering, University of Louisiana at ∗ Department Lafayette, Lafayette, LA 70504University USA, (e-mail: ∗ Department of Mechanical Mechanical Engineering, of Louisiana Louisiana at at Department of Engineering, of Lafayette, Lafayette, LA 70504University USA, (e-mail: [email protected]) Lafayette, Lafayette, LA 70504 Lafayette, Lafayette, LA 70504 USA, USA, (e-mail: (e-mail: [email protected]) [email protected]) [email protected]) Abstract: This paper investigates the use of the combination of a feedback controller and Abstract: This paper investigates the use of the combination of a feedback controller and input shaping to align crane hoist with desired, moving payload. The motivating application Abstract: This paper investigates the of combination of aa feedback controller and Abstract: This paperaa crane investigates the aause use of the themoving combination of The feedback controller and input shaping to align hoist with desired, payload. motivating application example is the to retrieval of an autonomous surface vessel (ASV) by a larger, host vessel following input shaping to align a crane hoist with a desired, moving payload. The motivating application input shaping align a crane hoist with a desired, moving payload. The motivating application example is the retrieval of an autonomous surface vessel (ASV) by a larger, host vessel following the completion of the ASV’s unmanned mission. Both the ASV by and the larger vessel arefollowing subject example is of autonomous surface vessel (ASV) larger, host vessel example is the the retrieval retrieval of an anunmanned autonomous surfaceBoth vessel (ASV) larger, host vessel the completion of the ASV’s mission. the ASV by andaa the larger vessel arefollowing subject to disturbances that make control of the crane-based operation difficult. This work focuses on the completion of the ASV’s unmanned mission. Both the ASV and the larger vessel are subject the completion ofthat the make ASV’scontrol unmanned mission. Both the ASV and the larger subject to disturbances of the crane-based operation difficult. Thisvessel work are focuses on the motion of the ASV and proper alignment of the host-vessel’s hoist with it leading to the to disturbances that make control of the crane-based operation difficult. This work focuses on to that make the crane-based operation difficult. This itwork focuses on thedisturbances motion of the ASV andcontrol properofalignment of the host-vessel’s hoist with leading to the initiation of of thethe lift.ASV Thisand alignment isalignment maintained via feedback mechanism as it well as a preview the motion properis alignment of via theaahost-vessel’s host-vessel’s hoist with with leading to the the the motion proper of the hoist leading to initiation of of thethe lift.ASV Thisand alignment maintained feedback mechanism as it well as a preview of incoming conditions. Input shaping greatly simplifies the design of this controller by reducing initiation of the alignment is via mechanism as preview initiation of conditions. the lift. lift. This ThisInput alignment is maintained maintained via aa feedback feedback mechanism as well well as as preview of incoming shaping greatly simplifies the design of this controller byaareducing commanded-motion-induced oscillation. of incoming conditions. Input shaping greatly simplifies the design of this controller by reducing of incoming conditions. Inputoscillation. shaping greatly simplifies the design of this controller by reducing commanded-motion-induced commanded-motion-induced oscillation. commanded-motion-induced oscillation. © 2015, IFAC (International Automatic Control) Hosting Hydrodynamics by Elsevier Ltd. All rights reserved. Keywords: Input Shaping,Federation FeedbackofControl, Target Tracking, Keywords: Input Shaping, Feedback Control, Target Tracking, Hydrodynamics Keywords: Input Input Shaping, Shaping, Feedback Feedback Control, Control, Target Target Tracking, Tracking, Hydrodynamics Hydrodynamics Keywords: 1. INTRODUCTION 1. INTRODUCTION 1. INTRODUCTION INTRODUCTION 1. Crane use is ubiquitous in a multitude of industries. Crane use is ubiquitous in a multitude of industries. With the ever-increasing use ofmultitude ports for ofinternational Crane use ever-increasing is ubiquitous ubiquitous use in aaof multitude industries. Crane use is in industries. With the ports for of international commerce, cranes have found use on and around both With the ever-increasing use of ports for international With the ever-increasing use of ports for international commerce, cranes have found use on and around both large and small marine vessels. Consequently, this increase commerce, cranes have found use on and around both commerce, cranes havevessels. found Consequently, use on and around both large and small marine this increase in port use hasmarine caused portsConsequently, to become overcrowded. large anduse small vessels. this increase increase large and small vessels. this in port hasmarine caused portsConsequently, to become overcrowded. Normally, ships dock in port while their cargoovercrowded. is offloaded in port use use hasdock caused ports to their become in port has caused ports to become Normally, ships in port while cargoovercrowded. is offloaded and loaded. With overcrowding, some ports require ships Normally, ships dock in port while their cargo is offloaded Normally, ships dock in port while theirports cargorequire is offloaded and loaded. With overcrowding, some ships to wait until space becomes available. This has driven and loaded. With overcrowding, some ports require ships and loaded. overcrowding, some ports ships to wait untilWith space becomes available. Thisrequire has driven research to findspace a solution. There has beenThis recent research to wait until until becomes available. hasresearch driven to wait becomes available. has driven research to findspace a solution. There has beenThis recent on mobileto harbors to assistThere in port expansion [Hong and research find aa solution. solution. hasexpansion been recent recent research research find has been research on mobiletoharbors to assistThere in port [Hong and Ngo (2012); Ngo and Hong (2012)]. Besides port-use, on mobile harbors to assist in port expansion [Hong and on harbors to assist port expansion and Fig. 1. Oil Rig Crane Ngomobile (2012); Ngo and Hongin (2012)]. Besides[Hong port-use, marine cranes Ngo see significant use(2012)]. in the oilBesides and gas port-use, industry, Fig. Ngo (2012); and Hong Hong Oil Rig Crane Ngo (2012); and marine cranes Ngo see significant use(2012)]. in the oilBesides and gas port-use, industry, Fig. 1. 1. Oil Oil Rig Rig Crane Crane including loading supplies onto oil rigs, as shown in Fig. 1. Fig. 1. marine cranes see significant use in the oil and gas industry, marine cranes see significant useoil in the gas in industry, including loading supplies onto rigs,oil asand shown Fig. 1. including loading supplies supplies onto is oilthe rigs,deployment as shown shown in inand Fig.re1. including loading onto oil rigs, as Fig. 1. Another application of cranes Another application of cranes is the deployment and retrieval ofapplication surveying equipment, specifically, autonomous Another of cranes cranes is is specifically, the deployment deployment and rereAnother of the and trieval ofapplication surveying equipment, autonomous surface of vehicles (ASV). C&C Technologies, located in trieval of surveying equipment, specifically, autonomous trieval surveying equipment, specifically, autonomous surface vehicles (ASV). C&C Technologies, located in Lafayette, Louisiana, has several models of ASVs, like the surface vehicles (ASV). C&C Technologies, Technologies, located in surface vehicles (ASV). C&C located in Lafayette, Louisiana, has several models of ASVs, like the one shown in Fig. 2, that are used to survey geological Lafayette, Louisiana, has several models of ASVs, like the Lafayette, models of ASVs, like the one shownLouisiana, in Fig. 2, has thatseveral are used to survey geological formations or Fig. inspect pipelines. Duetotosurvey the varying sea one shown in in 2, that that are used used geological one shown 2, are geological formations or Fig. inspect pipelines. Dueto tosurvey the varying sea conditions, similar to those faced by some South Korean formations or inspect pipelines. Due to the varying sea formations or inspect pipelines. to the varying sea conditions, similar to those facedDue by some South Korean ports, retrieval of the ASV has proven arduous for C&C conditions, similar to those those faced by South Korean conditions, similar to facedproven by some some Southfor Korean ports, retrieval of the ASV has arduous C&C Technologies. Previous attempts have been made to reduce ports, retrievalPrevious of the the ASV ASV has have proven arduous forreduce C&C ports, retrieval of has proven arduous for C&C Technologies. attempts been made to the difficulty of this task including the implementation of Technologies. Previous attempts have been made to reduce Technologies. Previous attempts have been made to reduce the difficulty of this task including the implementation of feedback control and input shaping. Despite this, several the difficulty of this task including the implementation of the difficulty of this including implementation of feedback control andtask input shaping.the Despite this, several factors make the and mobile harbors’ cranes easier to control feedback control input shaping. Despite this, several feedback control input shaping. Despite this, several factors make the and mobile harbors’ cranes easier to control [Park and Kwon (2010); Kim et al.cranes (2013)]. Theto main diffactors make the (2010); mobile Kim harbors’ easier control factors make the mobile harbors’ easier control [Park and Kwon et al.cranes (2013)]. Theto main differenceand is the size(2010); of the vessels used during operation. The [Park and Kwon (2010); Kim et al. (2013)]. The main dif[Park Kwon Kim et al. (2013)]. The main difference is the size of the vessels used during operation. The Fig. 2. An Autonomous Surface Vehicle container ships and crane-equipped mobile harbors The are ference is the the sizeand of the the vessels operation. 2. An Autonomous Surface Vehicle ference is size of vessels used used during during operation. container ships crane-equipped mobile harbors The are Fig. Fig. 2. An Autonomous Surface Vehicle much larger than both the ASV and host vessel. Because container ships and crane-equipped mobile harbors are container ships crane-equipped mobile harbors are Fig. 2. An Autonomous Surface Vehicle much larger thanand both the ASV and host vessel. Because of this,larger somethan oceanboth effects can beand neglected in theBecause mobile in the mobile harbors’ case, a docking mechanism locks much the can ASVbe and host vessel. vessel. much the ASV host of this,larger somethan oceanboth effects neglected in theBecause mobile in the mobile harbors’ case, a docking mechanism locks harbor control problem, such as drift force in and current, the container ship to thecase, mobile harbor, mechanism eliminating some in the the mobile ship harbors’ docking locks of this, some ocean effects can be neglected in the mobile of this, some ocean effects can be neglected the mobile mobile harbors’ aa docking locks harbor control problem, such as drift force and current, in the container to thecase, mobile harbor, mechanism eliminating some that cannot for the retrieval of the ASV. In addition, translation effects [Hong and Ngo (2012)]. In the case of the container ship to the mobile harbor, eliminating some harbor control problem, such as drift force and current, harbor control problem, such as drift force and current, the container ship to the mobile harbor, eliminating some that cannot for the retrieval of the ASV. In addition, translation effects [Hong and Ngo (2012)]. In the case of when the loading and offloading tasks are being completed the ASV, no special docking mechanism exists. translation effects [Hong and Ngo (2012)]. In the case of that cannot for the retrieval of the ASV. In addition, that for the retrieval oftasks the are ASV. Incompleted addition, translation andmechanism Ngo (2012)]. In the case of when cannot the loading and offloading being the ASV, noeffects special[Hong docking exists. the ASV, no special docking mechanism exists. when the loading and offloading tasks are being completed when the loading and offloading tasks are being completed the ASV, no special docking mechanism exists.
Copyright © 2015, IFAC 2015 141 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright © IFAC 2015 141 Copyright © IFAC 2015 141 Peer review under responsibility of International Federation of Automatic Copyright © IFAC 2015 141Control. 10.1016/j.ifacol.2015.09.367
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x
under the assumption that the target is only translating. The linearized equations of motion of the planar crane model are: x + mp lθ¨ = f (1) (mp + mt )¨ 2¨ x + mp l θ + mp glθ = 0 (2) mp l¨
mt
f
where mp and mt are the mass of the payload and trolley, respectively. The cable, which is assumed to be massless and inextensible, has length l. The position of the trolley is described by x, and the angular position of the payload is represented as θ. The variable f represents the input force on the trolley. In terms of this model, the control objective is to choose this force such that the position of the payload tracks the position of the target, xd .
g
m
The target’s position, xd , is generated using [Fossen (1994)]:
xd
2 Vwind g Hs Awave = 2 g ωwave = 0.4 Hs
Hs = 0.21
ASV Fig. 3. Planar Crane Model with Target Vessel Input shaping, a well-researched, open-loop control method, has proven itself to be a robust and easy-to-implement way of reducing the residual vibration of a system [Smith (1957); Singer and Seering (1990); Singhose (2009)]. Input shaping is implemented using the knowledge of a system’s natural frequencies and damping ratios. There are several different types of input shapers that offer robustness to changes in the system’s parameters [Vaughan et al. (2008)]. Unfortunately, due to its open-loop nature, input shaping cannot counteract disturbances. Because of this, a feedback mechanism is necessary. Some research has been conducted using a combination of feedback control and input shaping [Huey and Singhose (2012); Majid et al. (2013); Huey (2006)]. Research has also been conducted on an operator’s performance using PD control and input shaping [Vaughan et al. (2011)]. This paper furthers this prior work by implementing a blend of input shaping and feedback control for target tracking with minimal vibration. This is accomplished by intelligently transitioning between moving to the target and tracking. In the next section, an explanation of the crane model used and the assumptions made will be presented. Section 3 will discuss the theory and implementation of the controllers used. This will include a discussion of the blend of input shaping, feedback control, and the transition from one to the other when tracking is initialized. Finally, conclusions will be made in Section 4. 2. MODEL The model used during the phase of this research is a simple, planar crane model, shown in Fig. 3. External forces from the wind and waves that affect the vessel containing the crane are neglected. These forces’ affects on the ASV include heave, sway, yaw, pitch, and rotation. In this work, focus is given to improving tracking of the target 142
(3) (4) (5)
These equations, from the Pierson-Moskowitz Spectrum, use the assumption that the wind has been blowing over such a great distance that the time it has been blowing is neglected. This is referred to as fully developed seas. Significant wave height, Hs , is obtained through an assumed wind velocity, Vwind . This height is then used to determine the frequency, ωwave , and amplitude, Awave , of the waves. The assumption is made that the target vessel follows the path of the waves exactly. If tracking the wave exactly is achieved with this controller, it can be assumed that the slower dynamics of the ASV can be tracked with the same controller. 3. CONTROLLERS This section presents the different types of controllers used to track the ASV. First, a traditional feedback control is applied to the system to achieve tracking without any conditional logic is presented. Following this, an algorithm for transitioning between gross motion and tracking is presented. Finally, input shaping is used to assist the developed tracking controller by greatly reducing the residual vibration of the payload caused by the initial move of the trolley. 3.1 Gross Motion and Tracking Algorithm To establish some basic tracking capabilities, LQR feedback was applied to the system. Using this achieves the goal of tracking the target ASV to an extent. As can be seen in Fig. 4, an initial move is made towards the moving target, and tracking immediately begins once the trolley is in range. This method does provide some tracking, but the residual vibration from the gross motion move adds to the error produced by the LQR controller during the tracking phase. To determine the performance of this controller, RMS error was calculated and can be seen for a range
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Fig. 6. Flow Diagram of Logic for ASV Retrieval
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xd (t) 5
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Fig. 5. RMS Error of Tracking without Transition Control Scheme of wind speeds in Fig. 5. The error is always nonzero and increases with wind speed. This motivates the implementation of additional logic to decrease the error. By segmenting the two goals of the controller, moving to the target and tracking, and establishing when to transition between the two, error should be reduced. The primary mechanism for partitioning the control action is the natural partition between the two task objectives. For some part of each crane move, the crane must be moved to the nominal target location. Then, once near that location, a more-dedicated tracking algorithm can begin. Figure 6 shows a flow diagram depicting the decisions made during this natural partitioning of the task. Figure 7 further illustrates these decisions, where x ¯d (t) represents nominal location, xd represents the actual target location, and x(t) represents the current system state. The controller switches between the move-based controller, the top branch in Fig. 7, containing a command generation block, GCG , and the tracking controller, represented by the feedback block, GF B . Initially, the trolley and payload travel together towards the target. This move is shown in Fig. 8. Once both are within the buffer zone of the moving target, the trolley holds its position until the target is both near the payload and moving in the same direction. This time waiting falls between the “Move” section and the “Track” section of 143
x(t)
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Fig. 7. Block Diagram of Control Scheme 14
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Fig. 8. Simulation Illustrating Transition to Tracking the figure, which is exaggerated to better separate the two phases. Once this occurs, tracking of the target may begin. The response of the system to the application of this logic is shown in Fig. 9. Once the conditions defined by the algorithm are met, tracking may begin. Some improvements, resulting from the implemented algorithm, in RMS error can be seen at lower wind speeds, as seen in Fig. 10. At higher wind speeds, the accuracy of tracking is more dependent on the quality of the tracking controller than
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does not provide zero vibration at the model frequency. Instead, it is designed with a tolerable amount of vibration, Vtol , of 5% at the modeled frequency. As the system’s natural frequency moves away from the designed value, the percent residual vibration (PRV) decreases, providing extra robustness to the shaper.
Payload Error Trolley Error
0.5 0.4
In order to develop a command capable of decreasing the residual vibration of a system, knowledge of the system’s damping ratio, ζ, and natural frequency, ωn , is required. Due to the nature of cranes, the assumption can be made that the damping ratio is zero. This simplifies the calculations for the shaper command. The PRV produced by a shaper is [Singer and Seering (1990)]:
0.3 0.2 0.1 0.0 0
5
10
Fig. 11. Sensitivity Curves of ZV and EI Shapers
15
Wind Speed (knots)
20
25
Fig. 10. RMS Error of Unshaped Target Tracking
P RV = V (ζ, ω) = e−ζωtn
the transition between “Move” and “Track” segments. In an attempt to further improvements, the residual vibration caused by the initial move should be eliminated, allowing the tracking controller to begin without much error. This can be accomplished through the use of an input shaper. 3.2 Input Shaping
where C(ω, ζ) =
144
[C(ω, ζ)2 ] + [S(ω, ζ)2 ]
Ai eζωti cos(ωti
i=1
S(ω, ζ) =
Input shaping has proven a useful and easy-to-implement solution to vibration, including significant use on cranes [Yanyang et al. (2011); Vaughan et al. (2010)]. Although input shaping increases the rise time of a command, the percent overshoot and residual vibration can be drastically reduced. In this application, a slight increase in rise time is of no concern since the time it takes for the payload and trolley to reach the target is not the primary cost of the task. There exists multiple types of shapers. The differences become apparent when viewing the sensitivity curves of the shapers. Sensitivity curves are often used as a measurement of the performance shapers [Kozak et al. (2003)]. Figure 11 included the sensitivity curves for two shapers, the Zero-Vibration (ZV) shaper [Smith (1957)] and the Extra Insensitive (EI) shaper [Singhose (2009)]. As can be seen, each shaper behaves differently as one travels away from the model frequency, ωm , used to design the shaper. The ZV shaper provides zero vibration when the model is exact, but vibration rapidly increases as the modeled frequency deviates from the natural frequency. The EI shaper differs from the ZV shaper in that it
n
n i=1
Ai eζωti sin(ωti
(6)
1 − ζ 2)
(7)
1 − ζ 2 ).
(8)
This equation is used to form constraints on the residual vibration of the input shaper, along with additional constraints on impulse amplitudes is used in the formulation of the shaper. Applying this theory to the “Move” segment of the algorithm, a reduction in residual vibration can be achieved, allowing for more accurate tracking. Figure 12 shows the 5m move to tracking using a ZVshaper for the gross-motion portion of the move. Comparing this to Fig. 10, the residual vibration from that portion of the task is greatly reduced. In addition, the tracking portion of the command is able to begin almost immediately, as the payload has nearly settled upon arrival at the target location. The RMS error of tracking for 0 to 25 knot wind conditions following a ZV-shaped move is shown in Fig. 13. The error is much lower than the unshaped case at low wind speeds. At higher wind speeds, the performance of the tracking controller dominates the response, so less difference is seen between the unshaped and ZV-shaped cases.
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5
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Fig. 14. EI-Shaped Response with Wind Velocity of 20 knots
Error (m)
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Fig. 13. RMS Error of Tracking Target Following a ZVshaped Move
Fig. 15. RMS Error of Tracking Target Following a EIshaped Move
Table 1. Percent Difference of the RMS Error of Travel
Table 2. Percent Difference of the RMS Error of Tracking
Wind Speed (knots) Payload ZV (%) Trolley ZV (%) Payload EI (%) Trolley EI (%)
5
10
15
20
25
4.38 3.47 7.46 6.42
4.28 4.15 7.33 7.08
4.16 2.95 7.19 6.34
2.97 2.15 5.62 4.49
2.80 1.98 5.90 4.93
Wind Speed (knots) Payload ZV (%) Trolley ZV (%) Payload EI (%) Trolley EI (%)
A similar trial, with similar results, for an EI shaper is shown in Fig. 14. The robustness of the EI shaper slightly reduces the residual vibration resulting from the move portion of the command from that of the ZV shaper. The RMS error over a range of wind speeds, shown in Fig. 15 nearly matches that of the ZV-shaped case. A comparison of several trials using both shapers can be seen in Table 1 and Table 2. The most significant improvements can be seen in the “Travel” partition. This can be attributed to the application of the input shapers. For the “Tracking” partition, the majority of improvements are seen at lower wind speeds. Even so, improved accuracy is still achieved through the implementation of the shapers. To improve upon the accuracy of the simulation, a time delay representing the processing time of the feedback mechanism, likely a machine vision system, could be introduced. Figures 16 and 17 show the response of the 145
5
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1.84 4.00 1.76 3.75
0.20 0.57 0.19 0.56
0.40 0.71 0.35 0.61
0.01 0.05 0.20 0.24
0.15 0.10 0.01 0.01
system with a 100ms time delay with a wind speed of 20 knots. This time delay forces the trolley to lag behind the target, degrading tracking performance. Although the accuracy was improved with the implementation of the transition logic and the shaper, the tracking controller still produces error at higher wind speeds. The addition of a more robust tracking controller is necessary to cope with the varying wind speeds the ASV will experience. 4. CONCLUSION This paper introduced a planar crane and wave motion model to represent the crane-based retrieval of an Autonomous Surface Vehicle by its host vessel. With feedback control alone, there was significant vibration during the tracking stage of the retrieval process. Input shaping was
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Fig. 17. EI-Shaped Response with 100ms Time Delay at 20 knots implemented to reduce vibration during the gross positioning phase of the ASV retrieval. Two input shapers, the Zero-Vibration (ZV) shaper and Extra Insensitive (EI) shaper, were used and example results shown. The combination of an input shaper for gross positioning and an intelligent transition to tracking achieve the goal of decreasing the error in tracking from that which would have occurred if only a traditional feedback controller were used. REFERENCES Fossen, T.I. (1994). Guidance and Control of Ocean Vehicles. John Wiley Sons Ltd. Hong, K.S. and Ngo, Q.H. (2012). Dynamics of the container crane on a mobile harbor. Ocean Engineering, 53, 16–24. Huey, J.R. (2006). The Intelligent Combination of Input Shaping and PID Feedback Control. Ph.D. thesis, Georgia Institute of Technology. Huey, J. and Singhose, W. (2012). Design of proportionalderivative feedback and input shaping for control of inertia plants. Control Theory Applications, IET, 6(3), 357–364. Kim, D., Park, Y., and sik Park, Y. (2013). Terminal tracking control of mobile harbor crane subject to actuator saturation. In Control, Automation and Systems 146
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