Optimization Algorithms for Kinematically Optimal Design of Parallel Manipulators

Optimal design is an inevitable step for parallel manipulators. The formulated optimal design problems are generally constrained, nonlinear, multimodal, and even without closed-form analytical expressions. Numerical optimization algorithms are thus applied to solve the problems. However, the optimization algorithms are usually chosen ad arbitrium. This paper aims to provide a guideline to choose algorithms for optimal design problems. Typical algorithms, the sequential quadratic programming (SQP) with multiple initial points, the controlled random search (CRS), the genetic algorithm (GA), the differential evolution (DE), and the particle swarm optimization (PSO), are investigated in detail for their convergence performances by using two canonical design examples, the Delta robot and the Gough-Stewart platform. It is shown that SQP with multiple initial points can be efficient for simple design problems, while DE and PSO perform effectively and steadily for all design problems. CRS can be used to generate good initial points since it exhibits excellent convergence evolution in the starting period.

[1]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[2]  R. Clavel,et al.  A Fast Robot with Parallel Geometry , 1988 .

[3]  P. Shiakolas,et al.  On the Optimum Synthesis of Six-Bar Linkages Using Differential Evolution and the Geometric Centroid of Precision Positions Technique , 2003 .

[4]  Yuxin Su,et al.  A real-coded genetic optimal kinematic design of a Stewart fine tuning platform for a large radio telescope , 2001, J. Field Robotics.

[5]  Xin-Jun Liu,et al.  Determination of the Link Lengths for a Spatial 3-DOF Parallel , 2006 .

[6]  F. Park,et al.  Singularity Analysis of Closed Kinematic Chains , 1999 .

[7]  K. Miller,et al.  Optimal kinematic design of spatial parallel manipulators: Application to Linear Delta robot , 2003 .

[8]  Charles A. Klein,et al.  Dexterity Measures for the Design and Control of Kinematically Redundant Manipulators , 1987 .

[9]  Zexiang Li,et al.  Optimal Design of a Parallel Machine Based on Multiple Criteria , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[10]  Chang Wook Ahn,et al.  On the practical genetic algorithms , 2005, GECCO '05.

[11]  R. Goulcher,et al.  The solution of steady-state chemical engineering optimisation problems using a random-search algorithm , 1978 .

[12]  Qingsong Xu,et al.  A Totally Decoupled Piezo-Driven XYZ Flexure Parallel Micropositioning Stage for Micro/Nanomanipulation , 2011, IEEE Transactions on Automation Science and Engineering.

[13]  Xin Chen,et al.  A Modified PSO Structure Resulting in High Exploration Ability With Convergence Guaranteed , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[14]  Jeha Ryu,et al.  Optimal design of 6 DOF parallel manipulators using three point coordinates , 2001, Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No.01CH37180).

[15]  Clément Gosselin,et al.  Stiffness mapping for parallel manipulators , 1990, IEEE Trans. Robotics Autom..

[16]  Qingsong Xu,et al.  Error analysis and optimal design of a class of translational parallel kinematic machine using particle swarm optimization , 2009, Robotica.

[17]  Dan Zhang,et al.  Optimum design of parallel kinematic toolheads with genetic algorithms , 2004, Robotica.

[18]  Clément Gosselin,et al.  Singularity analysis of closed-loop kinematic chains , 1990, IEEE Trans. Robotics Autom..

[19]  N. M. Rao,et al.  Dimensional synthesis of a spatial 3-RPS parallel manipulator for a prescribed range of motion of spherical joints , 2009 .

[20]  Zexiang Li,et al.  Randomized Optimal Design of Parallel Manipulators , 2008, IEEE Transactions on Automation Science and Engineering.

[21]  Darrell Whitley,et al.  A genetic algorithm tutorial , 1994, Statistics and Computing.

[22]  Tsuneo Yoshikawa,et al.  Manipulability of Robotic Mechanisms , 1985 .

[23]  Zexiang Li,et al.  Singularities of parallel manipulators: a geometric treatment , 2003, IEEE Trans. Robotics Autom..

[24]  Jeha Ryu,et al.  New dimensionally homogeneous Jacobian matrix formulation by three end-effector points for optimal design of parallel manipulators , 2003, IEEE Trans. Robotics Autom..

[25]  Keum Shik Hong,et al.  Manipulability analysis of a parallel machine tool: Application to optimal link length design , 2000, J. Field Robotics.

[26]  Damien Chablat,et al.  Architecture optimization of a 3-DOF translational parallel mechanism for machining applications, the orthoglide , 2003, IEEE Trans. Robotics Autom..

[27]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

[28]  Jean-Pierre Merlet,et al.  Jacobian, Manipulability, Condition Number and Accuracy of Parallel Robots , 2005, ISRR.

[29]  Radovan R. Bulatović,et al.  On the optimum synthesis of a four-bar linkage using differential evolution and method of variable controlled deviations , 2009 .

[30]  L. Tsai,et al.  Kinematics and Optimization of a Spatial 3-UPU Parallel Manipulator , 2000 .

[31]  Clément Gosselin,et al.  Kinematic Analysis and Optimization of a New Three Degree-of-Freedom Spatial Parallel Manipulator , 2000 .

[32]  Yuhui Shi,et al.  Particle swarm optimization: developments, applications and resources , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[33]  Jian Meng,et al.  Accuracy Analysis of Parallel Manipulators With Joint Clearance , 2009 .

[34]  Qingsong Xu,et al.  Design and Analysis of a Totally Decoupled Flexure-Based XY Parallel Micromanipulator , 2009, IEEE Transactions on Robotics.

[35]  Jorge Angeles,et al.  Kinematic Isotropy and the Optimum Design of Parallel Manipulators , 1997, Int. J. Robotics Res..

[36]  Christine M. Anderson-Cook.  Practical Genetic Algorithms (2nd ed.) , 2005 .

[37]  Alireza Fathi,et al.  Architecture optimization of 4PUS+1PS parallel manipulator , 2010, Robotica.

[38]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[39]  Julio R. Banga,et al.  Global Optimization of Chemical Processes using Stochastic Algorithms , 1996 .

[40]  Paul Fisette,et al.  Contribution to the Optimization of Closed-Loop Multibody Systems: Application to Parallel Manipulators , 2005 .

[41]  Panos S. Shiakolas,et al.  On the Optimum Synthesis of Six-Bar Linkages Using Differential Evolution and the Geometric Centroid of Precision Positions Technique , 2005 .