Assessment and Future Directions of Nonlinear Model Predictive ...

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An Experimental Study of Stabilizing RecedingHorizon Control of Visual Feedback System withPlanar ManipulatorsMasayuki Fujita, Toshiyuki Murao, Yasunori Kawai, and Yujiro NakasoDepartment of Mechanical and Control Engineering, Tokyo Institute of Technology,2-12-1 S5-26 O-okayama Meguro-ku, Tokyo 152-8552, Japanfujita@ctrl.titech.ac.jpSummary. This paper investigates vision based robot control based on a recedinghorizon control strategy. The stability of the receding horizon control scheme is guaranteedby using the terminal cost derived from an energy function of the visual feedbacksystem. By applying the proposed control scheme to a two-link direct drive manipulatorwith a CCD camera, it is shown that the stabilizing receding horizon control nicelyworks for a planar visual feedback system. Furthermore, actual nonlinear experimentalresults are assessed with respect to the stability and the performance.1 IntroductionRobotics and intelligent machines need sensory information to behave autonomouslyin dynamical environments. Visual information is particularly suitedto recognize unknown surroundings. In this sense, vision is one of the highestsensing modalities that currently exist. Vision based control of robotic systemsinvolves the fusion of robot kinematics, dynamics, and computer vision to controlthe motion of the robot in an efficient manner. The combination of mechanicalcontrol with visual information, so-called visual feedback control or visual servoing,is important when we consider a mechanical system working in dynamicalenvironments [1].In previous works, Kelly [2] considered the set-point problem with a static targetfor a dynamic visual feedback system that includes the manipulator dynamicswhich is not be negligible for high speed tasks. The authors discussed passivitybased control of the eye-in-hand system [3, 4]. However, the control law proposedin [3] is not based on optimization, the desired control performance cannot beguaranteed explicitly.Receding horizon control, also recognized as model predictive control is awell-known control strategy in which the current control action is computed bysolving, a finite horizon optimal control problem on-line [5]. A large number ofindustrial applications using model predictive control can be found in chemicalindustries where the processes have relatively slow dynamics. On the contrary, fornonlinear and relatively fast systems such as in robotics, few implementationsof the receding horizon control have been reported. For the receding horizoncontrol, many researchers have tackled the problem of stability guarantees. AnR. Findeisen et al. (Eds.): Assessment and Future Directions, LNCIS 358, pp. 573–580, 2007.springerlink.com c○ Springer-Verlag Berlin Heidelberg 2007
574 M. Fujita et al. CameraCameraTargetObject Manipulator Image Plane 2 Manipulator 2 2 1 1 1 TargetObjectFig. 1. Planar visual feedback systemFig. 2. Schematic diagramapproach proposed by Parisini et al. [6] is based on using a quadratic endpointpenalty of the form ax T (t + T )Px(t + T )forsomea>0, some positive definitematrix P and a terminal state x(t + T ). Jadbabaie et al. [7] showed that closedloopstability is ensured through the use of a terminal cost consisting of a controlLyapunov function. Moreover, these results were applied to the Caltech DuctedFan to perform aggressive maneuvers [8, 9]. Visual feedback, however, is notconsidered here. Predictive control could be of significant benefit when used inconjunction with visual servoing. With the incorporation of visual information,the system could anticipate the target’s future position and be waiting there tointercept it [10].In this paper, stabilizing receding horizon control is applied to the planarvisual feedback system in [3], a highly nonlinear and relatively fast system. Thisrepresents a first step towards high performance visual servoing targeting moreaggressive maneuvers. The main idea is the use of the terminal cost derived froman energy function of the visual feedback system. By applying the proposedcontrol scheme to a two-link direct drive manipulator with a CCD camera, it isshown that the stabilizing receding horizon control nicely works for the planarvisual feedback system. Furthermore, the experimental results are assessed withrespect to performance.First, passivity-based control of a planar visual feedback system is reviewed.Next, a stabilizing receding horizon control for a planar visual feedback systemusing a control Lyapunov function is proposed. Then, the control performance ofthe stabilizing receding horizon control scheme is evaluated through experimentswith a two-link direct drive manipulator with a camera as shown in Fig. 1.2 Visual Feedback System with Planar ManipulatorThe dynamics of n-link rigid robot manipulators can be written asM(q)¨q + C(q, ˙q)˙q + g(q) =τ (1)
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Lecture Notesin Control and Informa
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Series Advisory BoardF. Allgöwer,
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ContentsFoundations and History of
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ContentsIXRobustness, Robust Design
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ContentsXIHybrid NMPC Control of a
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Nonlinear Model Predictive Control:
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Hybrid MPC: Open-Minded but Not Eas
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Hybrid MPC: Open-Minded but Not Eas
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22 S.E. Tuna et al.this says that i
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24 S.E. Tuna et al.In particular, f
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26 S.E. Tuna et al.W N (f(x, ¯κ N
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28 S.E. Tuna et al.where ᾱ := max
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30 S.E. Tuna et al.21.521.5µ=51
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32 S.E. Tuna et al.obstacle and gra
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34 S.E. Tuna et al.[19] C. Prieur.
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36 É. Gyurkovics and A.M. Elaiw[8]
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38 É. Gyurkovics and A.M. ElaiwWe
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Conditions for MPC Based Stabilizat
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A Computationally Efficient Schedul
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The Potential of Interpolation for
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The Potential of Interpolation 71Pr
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The Potential of Interpolation 73Th
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The Potential of Interpolation 75de
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Techniques for Uniting Lyapunov-Bas
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94 M. Lazar et al.Lipschitz continu
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96 M. Lazar et al.let X T ⊆ X den
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98 M. Lazar et al.S 0 {j ∈S|0
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100 M. Lazar et al.Fig. 1. State-sp
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102 M. Lazar et al.[11] Grimm, G.,
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Model Predictive Control for Nonlin
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ReferencesModel Predictive Control
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116 F.A.C.C. Fontes, L. Magni, and
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On the Computation of Robust Contro
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142 M. Srinivasarao, S.C. Patwardha
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Numerical Methods for Efficient and
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L i (s i ,u i ):=Numerical Methods
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182 A. Grancharova, T.A. Johansen,
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194 V. Sakizlis et al.presented her
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196 V. Sakizlis et al.linear PWA fu
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198 V. Sakizlis et al.non-linear sy
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200 V. Sakizlis et al.Remark 1. For
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202 V. Sakizlis et al.One should no
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204 V. Sakizlis et al.g0.050.10.15x
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Interior-Point Algorithms for Nonli
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n p,2 ≤Interior-Point Algorithms
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Hard Constraints for Prioritized Ob
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A Nonlinear Model Predictive Contro
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MPC for Stochastic SystemsMark Cann
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y i (k) =∑n um=1MPC for Stochasti
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MPC for Stochastic Systems 259we ha
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MPC for Stochastic Systems 261form
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MPC for Stochastic Systems 263( )κ
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MPC for Stochastic Systems 265Fig.
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MPC for Stochastic Systems 267⎡
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NMPC for Complex Stochastic Systems
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284 H. Chen et al.of the moving hor
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286 H. Chen et al.Hence, at each sa
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288 H. Chen et al.control inputs in
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290 H. Chen et al.Corollary 1. The
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292 H. Chen et al.c A[mol/l]10−10
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294 H. Chen et al.[CSA97] H.Chen,C.
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296 L. Xie, P. Li, and G. Woznyand
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298 L. Xie, P. Li, and G. WoznyDeta
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300 L. Xie, P. Li, and G. Wozny3.2
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304 L. Xie, P. Li, and G. Wozny[3]
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306 H. Arellano-Garcia et al.applic
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308 H. Arellano-Garcia et al.Fig. 1
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310 H. Arellano-Garcia et al.RECIPE
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312 H. Arellano-Garcia et al.optimi
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State Estimation Analysed as Invers
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384 K. Naidoo et al.polymer control
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386 K. Naidoo et al.are two key qua
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388 K. Naidoo et al.1. It greatly s
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390 K. Naidoo et al.However, with t
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392 K. Naidoo et al.Fig. 4. Bounded
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394 K. Naidoo et al.1. Maintain pro
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396 K. Naidoo et al.7 Commissioning
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398 K. Naidoo et al.[3] N.M.C. Oliv
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400 R. Franke and J. DoppelhamerImp
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406 R. Franke and J. Doppelhamer[3]
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408 B.A. Foss and T.S. Scheicritica
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410 B.A. Foss and T.S. ScheiFig. 2.
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412 B.A. Foss and T.S. Scheidiscuss
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414 B.A. Foss and T.S. ScheiOther a
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416 B.A. Foss and T.S. ScheiIn the
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NMPC of the Hashimoto Simulated Mov
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486 R. Lepore et al.In this study,
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488 R. Lepore et al.3 Control Strat
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490 R. Lepore et al.400.80.6|x−x
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492 R. Lepore et al.0.950.9w P;30.8
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Application of the NEPSAC Nonlinear
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Integrating Fault Diagnosis with No
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Page 521 and 522: 526 M. AlamirDefinition 4. The syst
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Page 573 and 574: 580 M. Fujita et al.Acknowledgement
Page 575 and 576: 582 A. Casavola, D. Famularo, and G
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Robust Model Predictive Control for
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630 J.J. Arrieta-Camacho, L.T. Bieg
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Author IndexAlamir, Mazen 523Alamo,
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Lecture Notes in Control and Inform
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