An efficient combined local and global search strategy for optimization of parallel kinematic mechanisms with joint limits and collision constraints

TL;DR

This paper introduces a combined local and global search optimization method for parallel kinematic mechanisms, effectively handling complex constraints like joint limits and collisions to improve design efficiency.

Contribution

A novel hybrid optimization approach integrating Nelder-Mead and low discrepancy sampling for efficient PKM design considering multiple constraints.

Findings

Enhanced optimization speed and accuracy for PKMs.

Effective handling of joint limits and collision constraints.

Successful application to different PKM configurations.

Abstract

The optimization of parallel kinematic manipulators (PKM) involve several constraints that are difficult to formalize, thus making optimal synthesis problem highly challenging. The presence of passive joint limits as well as the singularities and self-collisions lead to a complicated relation between the input and output parameters. In this article, a novel optimization methodology is proposed by combining a local search, Nelder-Mead algorithm, with global search methodologies such as low discrepancy distribution for faster and more efficient exploration of the optimization space. The effect of the dimension of the optimization problem and the different constraints are discussed to highlight the complexities of closed-loop kinematic chain optimization. The work also presents the approaches used to consider constraints for passive joint boundaries as well as singularities to avoid internal collisions in such mechanisms. The proposed algorithm can also optimize the length of the prismatic actuators and the constraints can be added in modular fashion, allowing to understand the impact of given criteria on the final result. The application of the presented approach is used to optimize two PKMs of different degrees of freedom.