Kinematical Optimization of Closed-Loop Multibody Systems

Applying optimization techniques in the field of multibody systems (MBS) has become more and more attractive considering 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 of the system. The addressed question is: how to optimize such closed-loop topologies when the objective 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 fulfilled. However, the method suffers from some limitations especially due to the difficulty to get a differentiable objective function. Therefore, the key idea of this paper is to improve the penalty approach. Practically, instead of solving the assembly constraints, their norm is minimized and the residue is taken as a penalty term instead of an artificial value. Hence, the penalized objective function becomes differentiable 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 the isotropy of parallel manipulators. The first optimization problem concerns a three-dof Delta robot with five design parameters and the second one deals with a more complex six-dof model of the Hunt platform involving ten design variables.