Some investigations into the optimal dimensional synthesis of parallel robots

In this paper, we will perform a comparison between two approaches of dimensional synthesis of parallel robots. The first one concerns the single-objective optimization approach; in this case, the dimensional synthesis is expressed by taking into account only one performance criterion but enables to get a final solution if it exists. The second one concerns the multi-objective optimization approach; it enables to simultaneously take into account several performance criteria. However, this approach appears to provide a set of solutions instead of a single expected final solution which should directly enable to carry out the structural synthesis. In fact, the search of a single final solution is postponed to a further step where the designers have to impose and/or restrict certain parameters. And we will establish if it is really necessary to make a multi-objective optimization approach or if a single-objective is sufficient to reach the objectives set in the specifications (user requirements). A discussion is proposed concerning the arising questions related to each approach and leading to the optimal dimensional synthesis. The PAR2 robot with two degree-of-freedom is used to exemplify the analysis and the comparison of the two approaches. The proposed comparison can be applied to any classes of parallel robots.

[1]  Sébastien Krut,et al.  Par2: a spatial mechanism for fast planar two-degree-of-freedom pick-and-place applications , 2011 .

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

[3]  H. Asada,et al.  A Geometrical Representation of Manipulator Dynamics and Its Application to Arm Design , 1983 .

[4]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[5]  Jun Wu,et al.  Dynamic dexterity of a planar 2-DOF parallel manipulator in a hybrid machine tool , 2008, Robotica.

[6]  Soumya Bhattacharya,et al.  On the optimum design of Stewart platform type parallel manipulators , 1995, Robotica.

[7]  Marc Gouttefarde,et al.  Above 40g acceleration for pick-and-place with a new 2-dof PKM , 2009, 2009 IEEE International Conference on Robotics and Automation.

[8]  M. J. D. Powell,et al.  THE CONVERGENCE OF VARIABLE METRIC METHODS FOR NONLINEARLY CONSTRAINED OPTIMIZATION CALCULATIONS , 1978 .

[9]  Tsuneo Yoshikawa,et al.  Dynamic manipulability of robot manipulators , 1985, Proceedings. 1985 IEEE International Conference on Robotics and Automation.

[10]  François Pierrot,et al.  Nonlinear dual mode adaptive control of PAR2: a 2-dof planar parallel manipulator, with real-time experiments , 2009, 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[11]  R. Saravanan,et al.  Evolutionary optimal trajectory planning for industrial robot with payload constraints , 2008 .

[12]  Mahmood Reza Azizi,et al.  Constrained grinding optimization for time, cost, and surface roughness using NSGA-II , 2014 .

[13]  Subir Kumar Saha,et al.  Dimensional design of hexaslides for optimal workspace and dexterity , 2005, IEEE Transactions on Robotics.

[14]  J. Merlet,et al.  Multi-criteria optimal design of parallel manipulators based on interval analysis , 2005 .

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

[16]  Jean-Pierre Merlet,et al.  Designing a Parallel Manipulator for a Specific Workspace , 1997, Int. J. Robotics Res..

[17]  Sébastien Krut,et al.  Par2: a Spatial Mechanism for Fast Planar, 2-dof, Pick-and-Place Applications , 2009 .

[18]  Ridha Kelaiaia,et al.  Multiobjective Optimization of 6-dof UPS Parallel Manipulators , 2012, Adv. Robotics.

[19]  Clément Gosselin,et al.  Conceptual Design and Dimensional Synthesis of a Novel 2-DOF Translational Parallel Robot for Pick-and-Place Operations , 2004 .

[20]  Med Amine Laribi,et al.  Analysis and dimensional synthesis of the DELTA robot for a prescribed workspace , 2007 .

[21]  Clément Gosselin,et al.  A Global Performance Index for the Kinematic Optimization of Robotic Manipulators , 1991 .

[22]  Sergiu-Dan Stan,et al.  Multi-objective Design Optimization of Mini Parallel Robots Using Genetic Algorithms , 2007, 2007 IEEE International Symposium on Industrial Electronics.

[23]  Ridha Kelaiaia,et al.  Multiobjective optimization of a linear Delta parallel robot , 2012 .

[24]  Andrzej Osyczka,et al.  7 – Multicriteria optimization for engineering design , 1985 .

[25]  Kai Zhou,et al.  Kinematic Analysis and Application Research on a High-Speed Travelling Double Four-Rod Spatial Parallel Mechanism , 2002 .

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

[27]  Belkacem Bounab,et al.  Multi-objective optimal design based kineto-elastostatic performance for the delta parallel mechanism , 2014, Robotica.

[28]  Michael L. Overton,et al.  A Sequential Quadratic Programming Algorithm for Nonconvex, Nonsmooth Constrained Optimization , 2012, SIAM J. Optim..