In response to the problem of synchronization errors affecting machining accuracy caused by uneven load on the gantry synchronous dual drive(GSD)platform,current research has mostly ignored the cross-coupling effect between the dual drive shafts,or the impact of changes in the position of heavy loads on the gantry crossbeam on synchronization errors.To solve this problem,first,quantify the cross-coupling force between the dual drive motors by defining the virtual center of mass of the gantry crossbeam;Then,design a GSLQR optimal control and force feedforward decoupling control algorithm based on virtual centroid;Finally,conduct simulation experiments.The simulation experiment results show that the maximum synchronization error of the algorithm is reduced by about 70%and 60%compared to the GSLQR optimal control algorithm and thrust allocation algorithm,respectively,improving the synchronization and motion performance of the GSD platform.