Forward kinematics modelling of a parallel ankle rehabilitation robot using modified fuzzy inference

This article deals with forward kinematics (FK) mapping of a parallel robot, especially designed for ankle joint rehabilitation treatments. Parallel robots exhibit highly coupled non-linear motions hence conventionally a unique closed form solution of their FK cannot be obtained. However, since FK is a key module in closed loop position and force control, its accurate and fast solution is indispensable. To solve the FK problem, a modified fuzzy inference system (FIS) is proposed in this paper for the first time which is time efficient and becomes very accurate when its parameters are optimized. In the proposed work, FIS has been optimized using three approaches namely: gradient descent (GD), genetic algorithm (GA) and modified genetic algorithm (MGA). The FIS, optimized by MGA has been found to be more accurate than the GD and GA optimized FIS. Performance of the MGA based fuzzy system has been found better both in terms of accuracy and computation time, when compared with Newton–Raphson iterative method and other fuzzy and neural approaches.

[1]  M. Husty.  An algorithm for solving the direct kinematics of general Stewart-Gough platforms , 1996 .

[2]  K. H. Hunt,et al.  Assembly configurations of some in-parallel-actuated manipulators , 1993 .

[3]  Claudia-Adina Dragos,et al.  Stable and optimal fuzzy control of a laboratory Antilock Braking System , 2010, 2010 IEEE/ASME International Conference on Advanced Intelligent Mechatronics.

[4]  Kalyanmoy Deb,et al.  Optimization for Engineering Design: Algorithms and Examples , 2004 .

[5]  Dilip Kumar Pratihar,et al.  Evolution of Fuzzy Controllers and Applications , 2007, Advances in Evolutionary Computing for System Design.

[6]  J. Duffy,et al.  A forward displacement analysis of a class of stewart platforms , 1989, J. Field Robotics.

[7]  L. Haynes,et al.  Neural network solution for the forward kinematics problem of a Stewart platform , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[8]  Kah Bin Lim,et al.  Forward kinematics solution of Stewart platform using neural networks , 1997, Neurocomputing.

[9]  Charles W. Wampler.  FORWARD DISPLACEMENT ANALYSIS OF GENERAL SIX-IN-PARALLEL SPS (STEWART) PLATFORM MANIPULATORS USING SOMA COORDINATES , 1996 .

[10]  Jean-Pierre Merlet,et al.  Direct kinematics of parallel manipulators , 1993, IEEE Trans. Robotics Autom..

[11]  Fuan Wen,et al.  Displacement analysis of the 6-6 stewart platform mechanisms , 1994 .

[12]  S. Jack Hu,et al.  Forward Position Analysis of the 3-DOF Module of the TriVariant: A 5-DOF Reconfigurable Hybrid Robot , 2006 .

[13]  S.Q. Xie,et al.  Design and Control of a Parallel Robot for Ankle Rehabiltation , 2008, 2008 15th International Conference on Mechatronics and Machine Vision in Practice.

[14]  Karl Wohlhart,et al.  Displacement analysis of the general spherical Stewart platform , 1994 .

[15]  Ibrahim Ozkol,et al.  Forward kinematics analysis of the 6-3 SPM by using neural networks , 2007 .

[16]  Bhaskar Dasgupta,et al.  The Stewart platform manipulator: a review , 2000 .

[17]  P. C. Hughes,et al.  KINEMATIC ANALYSIS OF A GENERAL DOUBLE-TRIPOD PARALLEL MANIPULATOR , 1998 .

[18]  Hamid D. Taghirad,et al.  Dynamic Analysis of a Macro–Micro Redundantly Actuated Parallel Manipulator , 2008, Adv. Robotics.

[19]  Hamid D. Taghirad,et al.  Comparison of Different Methods for Computing the Forward Kinematics of a Redundant Parallel Manipulator , 2005, J. Intell. Robotic Syst..

[20]  Michael Pecht,et al.  A modified powell method for six-degrees-of-freedom platform kinematics , 1990 .

[21]  Charles C. Nguyen,et al.  Efficient computation of forward kinematics and Jacobian matrix of a Stewart platform-based manipulator , 1991, IEEE Proceedings of the SOUTHEASTCON '91.

[22]  Dong-Soo Kwon,et al.  A tetrahedron approach for a unique closed-form solution of the forward kinematics of six-dof parallel mechanisms with multiconnected joints , 2002, J. Field Robotics.

[23]  Myung-Chul Han,et al.  The estimation for forward kinematic solution of Stewart platform using the neural network , 1999, Proceedings 1999 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human and Environment Friendly Robots with High Intelligence and Emotional Quotients (Cat. No.99CH36289).

[24]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[25]  Ilya V. Kolmanovsky,et al.  Predictive energy management of a power-split hybrid electric vehicle , 2009, 2009 American Control Conference.

[26]  M. Raghavan.  The Stewart platform of general geometry has 40 configurations , 1993 .

[27]  Jiang Hongzhou,et al.  Kinematics Analysis of a 3-dof Rotational Parallel Mechanism , 2008, 2008 International Workshop on Modelling, Simulation and Optimization.

[28]  Q. Liao,et al.  Forward Kinematics of the 6-6 Stewart Platform with Planar Base and Platform Using Algebraic Elimination , 2007, 2007 IEEE International Conference on Automation and Logistics.

[29]  Shangxian Peng,et al.  Direct displacement analysis of parallel manipulators , 2000, J. Field Robotics.

[30]  Myeong-Kwan Park,et al.  Forward Kinematics of Casing Oscillator , 2006, IEEE/ASME Transactions on Mechatronics.

[31]  Rohitash Chandra,et al.  Forward kinematics of the 6-6 general parallel manipulator using Real Coded Genetic Algorithms , 2009, 2009 IEEE/ASME International Conference on Advanced Intelligent Mechatronics.

[32]  Cai Hegao.  Geometric solution for direct kinematics of delta parallel robot , 2003 .

[33]  Qidan Zhu,et al.  Solution for Forward Kinematics of 6-DOF Parallel Robot Based on Particle Swarm Optimization , 2007, 2007 International Conference on Mechatronics and Automation.

[34]  Roger Boudreau,et al.  Solving the forward kinematics of parallel manipulators with a genetic algorithm , 1996, J. Field Robotics.

[35]  S. Q. Xie,et al.  Design and control of a parallel robot for ankle rehabilitation , 2010, Int. J. Intell. Syst. Technol. Appl..

[36]  J. Faugère,et al.  Combinatorial classes of parallel manipulators , 1995 .

[37]  Li-Chun T. Wang,et al.  Numerical direct kinematic analysis of fully parallel linearly actuated platform type manipulators , 2002, J. Field Robotics.

[38]  Kenneth J. Waldron,et al.  Direct kinematic solution of a Stewart platform , 1990, IEEE Trans. Robotics Autom..

[39]  Bin Zeng,et al.  Forward Displacement Analysis of the 4SPS-2CCS Generalized Stewart Platform Based on Hyper-Chaotic Neural Network Mathematical Programming Method , 2008, 2008 The 9th International Conference for Young Computer Scientists.

[40]  Carlo Innocenti,et al.  Direct position analysis of the Stewart platform mechanism , 1990 .

[41]  Kok-Meng Lee,et al.  Dynamic analysis of a three-degrees-of-freedom in-parallel actuated manipulator , 1988, IEEE J. Robotics Autom..

[42]  Huang Xiguang.  Forward Kinematics Analysis of the General 6-6 Platform Parallel Mechanism Based on Algebraic Elimination , 2009 .

[43]  Bhaskar Dasgupta,et al.  A constructive predictor-corrector algorithm for the direct position kinematics problem for a general 6-6 Stewart platform , 1996 .

[44]  Mohammad Eghtesad,et al.  Neural network solution for forward kinematics problem of HEXA parallel robot , 2008, ACC.

[45]  Bhaskar Dasgupta,et al.  A canonical formulation of the direct position kinematics problem for a general 6-6 stewart platform , 1994 .

[46]  Yun Ho Tsoi,et al.  Impedance control of ankle rehabilitation robot , 2009, 2008 IEEE International Conference on Robotics and Biomimetics.

[47]  C. Innocenti,et al.  Forward Kinematics of the General 6–6 Fully Parallel Mechanism: An Exhaustive Numerical Approach Via a Mono-Dimensional-Search Algorithm , 1993 .

[48]  C. Innocenti,et al.  A new kinematic model for the closure equations of the generalized Stewart platform mechanism , 1992 .