Kinematical Optimization of Closed-Loop Multibody Systems

Applying optimization techniques in the field of multibody systems (MBS) has become more and more attractive particularly thanks to the increasing development of computer resources. One of the main issues in the optimization of MBS concerns closed-loop systems which involve non-linear assembly constraints that must be solved before any analysis. The question that is addressed is: how to optimize such closed-loop topologies when the objective function evaluation relies on the assembly of the system? The authors have previously proposed to artificially penalize the objective function when those assembly constraints cannot be exactly satisfied. However, the method has some limitations. The algorithm is based on some tuning parameters that may affect the optimization results. Moreover, the penalization is not smooth, making the use of gradient-based optimization algorithms difficult. The key idea of this paper, to improve the penalty approach, is to solve the assembly constraints as well as possible and use the residue of these constraints as a penalty term instead of an artificial value. The method is easier to tune since the only parameter to choose is the weight of the penalty term. Besides, the objective function is continuous throughout the design space, which enables the use of efficient gradient-based optimization methods such as the sequential quadratic programming (SQP) method. To illustrate the reliability and generality of the method, two applications are presented. They are related to kinetostatic performance of parallel manipulators. The first optimization problem concerns a 3-dof Delta robot with 5 design parameters and the second one deals with a more complex 6-dof model of the Hunt platform with 10 design variables.

[1]  E. Haug,et al.  Generalized Coordinate Partitioning for Dimension Reduction in Analysis of Constrained Dynamic Systems , 1982 .

[2]  Jorge Angeles,et al.  Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms , 1995 .

[3]  E. Amezua,et al.  Nonlinear optimization of planar linkages for kinematic syntheses , 1995 .

[4]  Javier Cuadrado,et al.  A simple and general method for kinematic synthesis of spatial mechanisms , 1997 .

[5]  Septimiu E. Salcudean,et al.  Fast constrained global minimax optimization of robot parameters , 1998, Robotica.

[6]  Kaj Madsen,et al.  Optimization with constraints , 1999 .

[7]  Friedrich Pfeiffer,et al.  OPTIMIZATION OF AUTOMATIC GEARSHIFTING , 2001 .

[8]  Chunhong Zheng,et al.  Genetic design of kinematically optimal fine tuning Stewart platform for large spherical radio telescope , 2001 .

[9]  H. Zhou,et al.  Optimal synthesis of crank–rocker linkages for path generation using the orientation structural error of the fixed link , 2001 .

[10]  P. A. Simionescu,et al.  Optimum synthesis of the four-bar function generator in its symmetric embodiment: the Ackermann steering linkage , 2002 .

[11]  J. A. Cabrera,et al.  Optimal synthesis of mechanisms with genetic algorithms , 2002 .

[12]  A. Fattah,et al.  Isotropic Design of Spatial Parallel Manipulators , 2002, Int. J. Robotics Res..

[13]  Selim Datoussaid,et al.  Application of Evolutionary Strategies to Optimal Design of Multibody Systems , 2002 .

[14]  F. T. S. Marı́n,et al.  Global optimization in path synthesis based on design space reduction , 2003 .

[15]  Jeha Ryu,et al.  Volumetric error analysis and architecture optimization for accuracy of HexaSlide type parallel manipulators , 2003 .

[16]  Marco Ceccarelli,et al.  A multi-objective optimum design of general 3R manipulators for prescribed workspace limits , 2004 .

[17]  B. Shirinzadeh,et al.  Topology optimisation and singularity analysis of a 3-SPS parallel manipulator with a passive constraining spherical joint , 2004 .

[18]  Leila Notash,et al.  Configuration engine for architecture planning of modular parallel robots , 2004 .

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

[20]  P. Eberhard,et al.  Using augmented Lagrangian particle swarm optimization for constrained problems in engineering">Using augmented Lagrangian particle swarm optimization for constrained problems in engineering , 2006 .

[21]  P. Eberhard,et al.  Using Augmented Lagrangian Particle Swarm Optimization for Constrained Problems in Engineering , 2009 .