Optimisation of the geometrical design of a delta-type robot using the cross-entropy method

Abstract

The aim of this study was to optimise the geometric design of a delta robot using a heuristic-based approach, specifically aimed at maximizing its effective working volume. To achieve this, an inverse kinematics model was developed to determine whether a point in three-dimensional space could be reached, given specific geometric parameters of the robot. Based on this model, an evaluation function was implemented to estimate the working volume through a point-by-point validation process using a three-dimensional sampling of the workspace. The optimisation was performed using the cross-entropy method, an iterative technique that generates and updates probability distributions to efficiently guide the search toward optimal regions within the design space. The results demonstrated a rapid convergence of the algorithm toward configurations that significantly increased the attainable volume. Visualization of the workspace confirmed the continuity and density of the optimized volume. The proposed method proved to be both effective and flexible, offering new opportunities for the automated and efficient design of parallel manipulators in industrial settings.