Optimal Scaling Parameter Analysis for Optical Mirror Processing Robots via Adaptive Differential Evolution Algorithm

In large optical mirror processing (LOMP), the robot is required to carry a computer-controlled optical surfacing (CCOS) polishing tool capable of both fully covering the required material removal profile and maintaining sufficient redundancy for process adaptability. The designed LOMP robot is a five-degree-of-freedom (5-DOF) hybrid robot, where the workspace of its parallel mechanism is constrained by dimensional parameters, including the moving platform radius, the fixed/moving platform radius ratio, and link lengths. This paper presents an optimization study of dimensional parameters for robotic systems, aimed at meeting the workspace requirements of 1250 mm-diameter large optical mirrors. First, analytical models of the robot’s effective workspace and driving torque under different dimensional parameters are derived. Subsequently, workspace requirements and driving torque are established as optimization constraints, and a differential evolution algorithm is implemented to determine the optimal dimensional parameters for the LOMP system. To improve computational efficiency, the conventional differential evolution algorithm is enhanced through the integration of adaptive mutation and crossover operators, resulting in a modified adaptive differential evolution algorithm (ADEA) that demonstrates accelerated convergence characteristics while maintaining solution accuracy. Finally, MATLAB simulations demonstrate that the proposed ADEA successfully obtains optimal dimensional parameter combinations while satisfying all specified constraints. Based on the optimal dimensional parameters, an engineering prototype was manufactured. Experimental results verified the accuracy of the optimized design, providing a valuable reference for optimization of dimensional and structural parameters in similar engineering equipment.