Automation and Robotics Automation and Robotics Edited by Juan Manuel Ramos Arreguin I-Tech Published by I-Tech Education and Publishing I-Tech Education and Publishing Vienna Austria Abstracting and non-profit use of the material is permitted with credit to the source. Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published articles. Publisher assumes no responsibility liability for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained inside. After this work has been published by the I-Tech Education and Publishing, authors have the right to repub- lish it, in whole or part, in any publication of which they are an author or editor, and the make other personal use of the work. © 2008 I-Tech Education and Publishing www.i-techonline.com Additional copies can be obtained from: publication@ars-journal.com First published May 2008 Printed in Croatia A catalogue record for this book is available from the Austrian Library. Automation and Robotics, Edited by Juan Manuel Ramos Arreguin p. cm. ISBN 978-3-902613-41-7 1. Automation. 2. Robotics. I. Ramos Arreguin V Preface In this book, a set of relevant, updated and selected papers in the field of automation and robotics are presented. These papers describe projects where topics of artificial intelligence, modeling and simulation process, target tracking algorithms, kinematic constraints of the closed loops, non-linear control, are used in advanced and recent research. Also, the lecturer can find some of the new methodologies applied to solve complex problems in the field of control and robotic research fields. Moreover, this book can serve as a good information source for scientific scholars, engineers and beginners who would like to start working with both automation and robotic areas. Combining the ideas of the diverse disciplines involved in such areas, this book give hints and help about how to implement them on products for industrial automation and robotics applications. I would like to thank all the researchers who send their works to share with the scientific community. The editors are extremely grateful to all of them for their support to complete this book. Editor Juan Manuel Ramos Arreguin Electronica y Automatizacion Universidad Tecnologica de San Juan del Rio jramos@mecamex.net VII Contents Preface V 1. Tracking Control for Multiple Trailer Systems by Adaptive Algorithmic Control 001 Tomoaki Kobayashi, Toru Yoshida, Junichi Maenishi, Joe Imae and Guisheng Zhai 2. Enhanced Motion Control Concepts on Parallel Robots 017 Frank Wobbe, Michael Kolbus and Walter Schumacher 3. Vision Guided Robot Gripping Systems 041 Zdzislaw Kowalczuk and Daniel Wesierski 4. Closed-Loop Feedback Systems in Automation and Robotics, Adaptive and Partial Stabilization 073 G. R. Rokni Lamooki 5. Nonlinear Control Law for Nonholonomic Balancing Robot 087 Alicja Mazur and Jan Kdzierski 6. Deghosting Methods for Track-Before-Detect Multitarget Multisensor Algorithms 097 Przemyslaw Mazurek 7. Identification of Dynamic Systems & Selection of Suitable Model 121 Mohsin Jamil, Dr. Suleiman M Sharkh and Babar Hussain 8. Towards an Automated and Optimal Design of Parallel Manipulators 143 Marwene Nefzi, Martin Riedel and Burkhard Corves 9. Identification of Continuous-Time Systems with Time Delays by Global Optimization Algorithms and Ant Colony Optimization 157 Janusz P. Paplinski 10. Linear Lyapunov Cone-Systems 169 Przemysaw Przyborowski and Tadeusz Kaczorek 11. Pneumatic Fuzzy Controller Simulation vs Practical Results for Flexible Manipulator 191 Juan Manuel Ramos-Arreguin, Jesus Carlos Pedraza-Ortega, Efren Gorrostieta-Hurtado, Rene de Jesus Romero-Troncoso, Jose Emilio Vargas-Soto and Francisco Hernandez-Hernandez1 VIII 12. Nonlinear Control Strategies for Bioprocesses: Sliding Mode Control versus Vibrational Control 201 Dan Seliteanu, Emil Petre, Dorin Popescu and Eugen Bobau 13. Sliding Mode Observers for Rotational Robotics Structures 223 Dorin Sendrescu, Dan Seliteanu, Emil Petre and Cosmin Ionete 14. A Declarative Framework for Constrained Search Problems in Manufacturing 243 Sitek Pawek and Wikarek Jaroslaw 15. Derivation and Calculation of the Dynamics of Elastic Parallel Manipulators 261 Krzysztof Stachera and Walter Schumacher 16. Orthonormal Basis and Radial Basis Functions in Modeling and Identification of Nonlinear Block-Oriented Systems 277 Rafa Stanisawski and Krzysztof J. Latawiec 17. Control System of Underwater Vehicle Based on Artificial Intelligence Methods 285 Piotr Szymak and Józef Maecki 18. Automatization of Decision Processes in Conflict Situations: Modelling, Simulation and Optimization 297 Zbigniew Tarapata 19. Fuzzy Knowledge Representation Using Probability Measures of Fuzzy Events 329 Anna Walaszek-Babiszewska 20. Multiple Multi-Objective Servo Design - Evolutionary Approach 343 Piotr Wozniak 21. Model-Based Control of a Nonlinear One Dimensional Magnetic Levitation with a Permanent-Magnet Object 359 Zhenyu Yang, Gerulf K.M. Pedersen and Jørgen H. Pedersen 22. Nonlinear Adaptive Tracking-Control Synthesis for General Linearly Parametrized Systems 375 Zenon Zwierzewicz Automation and Robotics 2 technique for nonlinear continuous time system. Our algorithmic design approach is a technique for ensuring robustness by adopting a numeric solution called Riccati Equation Based (REB) algorithm using quasi linearization that includes feedback solution. Moreover, though details are described later, the control technique by algorithmic design which we proposed is an effective method for nonholonomic systems because our method is switching and applying the control strategy on a short control interval and thus the controller is discontinuous time variant, which does not violate Brockett's theorem. We showed the effectiveness of proposed method applicable to nonholonomic systems through some simulations and an experiment with a differential-driven unicycle vehicle model (Kobayashi et al., 2005b). Then, we extend our design method by incorporating numerical robustness for disturbances and parameter uncertainties and, by focusing on the switching interval of control strategy on iterative process of algorithmic design (Kobayashi et al., 2006). We discussed about effectiveness of our approach for an unstable motion control of high order nonlinear system, in this paper. In the most of conventional research, the direct-hooked type model (Lee et al., 2001) is treated. The direct-hooked model can be transformed to a canonical form called chained form (Murray & Sastry, 1993). Then, control problem for the direct-hooked model can be reduced to a canonical problem. However, the direct-hooked model has a tracking error of follow-on trailers (Fig.1). Therefore, there are many suggestions for eliminating the tracking error by model constructions or mechanical linkage design. We pick up a off-hooked model (Lee et al., 2004) which has a most simple structure and cannot be converted to canonical form (Ishikawa, 1993). Therefore, proposed algorithmic design is considered as an effective strategy for the off-hooked trailer system, because our approach can treat the general nonlinear systems. The effectiveness is discussed through a numerical simulation result. The outline of this paper is as follows. In section 2, we describe the nonlinear optimal control problems and the Riccati Equation Based algorithm. In section 3, the algorithmic design method is described in detail. Also, we make an extension of our design method for robustness. The backward motion control problem of multiple trailer systems is formulated in section 4. In section 5, we show some simulation results in order to demonstrate the effectiveness of adaptive algorithmic design. Section 6 concludes the paper. ｖ v ω Tracking Error Fig. 1 Tracking error of the direct-hooked trailer system 2. Optimal control problem 2.1 Formulation We deal with the following general nonlinear system () (, (), ()) x tftxtut = (1) [...]... state) -1 (b) t = 1. 0 [sec] 1 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 1 0 1 1 0.5 1 0.5 0.5 0 0.5 0 0 -0.5 0 -0.5 -0.5 -1 -0.5 -1 -1 (c) t = 2.0 [sec] -1 (d) t = 3.0 [sec] 1 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 1 0 1 disturbance V 1 0.8 0.5 1 0.5 0.5 0 1 0.5 0 0 -0.5 0 -0.5 -0.5 -1 -0.5 -1 -1 (e) t = 4.0 [sec] -1 (f) t = 5.0 [sec] (disturbed) 1 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 1 0 1 0.5 1 0.5 0.5 0 1 0.5 0 0 -0.5... inputs 10 0 10 -1 -2 10 0 5 10 15 20 25 30 0 5 10 15 Time [sec] 20 25 30 10 0 50 0 Fig 9 Simulation results: value of performance index (upper stand) Computation time of each ΔT and its bound (lower part) 13 Tracking Control for Multiple Trailer Systems by Adaptive Algorithmic Control 1 x [m] 0.5 0 -0.5 -1 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 5 10 15 20 25 30 5 10 15 20 25 30 1 y [m]... -0.5 -1 θ 1 [rad] 15 10 5 0 θ 2 [rad] 15 10 5 0 0 θ 3 [rad] 15 10 5 0 0 Time [sec] Fig 10 Simulation results: state trajectories (solid line: actual states, doted line: target states) 14 Automation and Robotics 1 1 0.8 0.8 Passive trailers Truck 0.6 0.4 ▼ } 0.2 0 1 0.5 0.4 0.2 ▼ 0 1 1 ▼ 0 0.6 0.5 0.5 1 0.5 0 0 -0.5 0 Target trajectory -0.5 -0.5 -1 -1 -0.5 -1 (a) t = 0.0 [sec] (initial state) -1 (b)... (1) i i i STEP A3 Select Ai ∈ ℜn×n , B 11 ∈ Ln×n , B12 ∈ Ln×r and B22 ∈ Lr ×r so that Kalman's sufficient ∞ ∞ ∞ conditions for the boundedness of Riccati solutions (Jacobson & Mayne, 19 70) hold, that is, for almost all t ∈ [t0, t1 ] , Ai (t ) ≥ 0 i B22 (t ) > 0 (5) i i i i B 11 (t ) − B12 (t ) B22 (t ) 1 B12 (t )T ≥0 i i where Ai , B 11 and B22 are symmetric and ( ⋅ )T means the transpose of vectors and. .. 0 1 0 1 0.5 1 0.5 0.5 0 1 0.5 0 0 -0.5 0 -0.5 -0.5 -1 -0.5 -1 -1 (g) t = 6.0 [sec] -1 (h) t = 7.0 [sec] 1 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 1 0 1 1 0.5 0.5 0 1 0.5 0.5 0 0 -0.5 -0.5 -1 -1 (i) t = 8.0 [sec] Fig 11 Simulation results 0 -0.5 -0.5 -1 -1 (jb) t = 9.0 [sec] Tracking Control for Multiple Trailer Systems by Adaptive Algorithmic Control 15 7 Conclusions We discussed the real time control... = Di 1 ≠ 0 ) which can eliminate the tracking error (Fig 5) However, the model of off- hooked trailer system cannot be transformed to canonical form Fig 4 shows a off-hooked model, and the following equation denotes the i th trailer's kinematics θ i = (sin(θ i 1 − θ i )vi 1 − cos(θ i 1 − θ i )θ i 1 Di 1 L i vi = cos(θ i 1 − θ i )vi 1 + sin(θ i 1 − θ i )θ i 1 Di 1 10 Automation and Robotics. .. Impulsive disturbances on 1 and θ2 have been added in this simulation at 5, 10 , 15 and 20[sec], whose magnitude is 0.5[rad] 12 Automation and Robotics 12 0 10 0 80 Computation Time τ [msec] θ i (5n) = θ i (5n − dt ) − 0.5, (i = 1, 2, n = 1, 2, 3, 4) 60 40 20 0 0 1 2 3 4 Number of Itaration N 5 6 Fig 7 Computational time o : average of the computation time, with the maximum and minimum computation time,... fu (t , x, u ) , Lx (t , x, u ) and Lu (t , x, u ) exist and are continuous in all their arguments ii For each compact set U ⊂ ℜr there exists some M1 ∈ (0, ∞) such that f (t , x, u ) ≤ M1 (| x | +1) for all t ∈ 1 , x ∈ ℜn and u ∈ U (4) 4 Automation and Robotics [Algorithm ] STEP A0 Let β ∈ (0 ,1) and M 2 ∈ (0 ,1) Select arbitrarily an initial input u 0 ∈ Lr ∞ STEP A1 i = 0 STEP A2 Calculate xi (t... 0.0 01 0.0 01 0.0 01] , R = diag[0.05 0. 01] ξ f (t ) is the target state, and it is the circle of radius 0.5[m] with constant velocity Furthermore, we treat the state constraints and input constraints by introducing the penalty term Tracking Control for Multiple Trailer Systems by Adaptive Algorithmic Control 2 t1 ri J = J + ∫ (∑ 2 2 i =1 θ i lim − (θ i 1 − θ i ) t0 +∫ rv t1 2 vlim − v 2 + rω 11 )dt (18 )... ) fu (t , xi , u i ) − B12 ) B22 1 ( B12T − fuT (t , xi , u i ) K (t )), (7) i K (t1 ) = − A , r (t ) = − f xT (t , xi , u i )r (t ) + LT (t , xi , u i ) x i i + {B12 − K (t ) fuT (t , xi , u i )}B22 1 (− LT (t , xi , u i ) + fuT (t , xi , u i ) r (t )), u (8) r (t1 ) = −G ( x(t1 )), and determine δ u i as follows i i δ u i (t ) = B22 1{ ( fuT (t , xi , u i ) K i (t ) − B12T )δ xi + fuT (t , xi , . trailer's kinematics. 11 111 11 111 )sin()cos( )cos()(sin( −−−−− −−−−− −+−= −−− = iiiiiiii i iiiiiii i Dvv L Dv θθθθθ θθθθθ θ Automation and Robotics 10 5. Problem formulation. 5 10 15 20 25 30 -1 -0.5 0 0.5 1 v [m/sec] 0 5 10 15 20 25 30 -2 0 2 ω [rad/sec] Fig. 8 Simulation results: control inputs. 10 -2 10 -1 10 0 5 10 15 20 25 30 Performance Index 0 5 10 15 . Mayne, 19 70) hold, that is, for almost all 0, 1 []ttt∈ , 22 1T 11 12 22 12 () 0 () 0 () () () () 0 i i iiii At Bt Bt BtBt Bt − ≥ > − ≥ (5) where 11 , ii A B and 22 i B are symmetric and