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

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.