Micro/nanopositioning coplanar stage with real-time compensation of volumetric error

•A micro/nanopositioning coplanar stage with real-time compensation of the volumetric error was designed.•A volumetric error measuring unit was designed to simultaneously real-time measure 13 geometric error components.•A novel volumetric error model was established using the Abbe and Bryan principles.•A control unit was improved to real-time compensate volumetric error and high-precision control position and velocity.•The actual positional error of the micro/nanopositioning coplanar stage has been reduced by approximately 97.6 %. A micro/nanopositioning coplanar stage is designed with real-time compensation of volumetric error. According to the topological structure of the stage, it has 13 geometric error components. Furthermore, there are positional shifts of a functional point from the displacement feedback point and the measurement point of geometric errors. To improve the positional accuracy, it is crucial to real-time measure, model, and compensate for the volumetric error at the functional point. Therefore, a volumetric error measuring unit (VEMU) is designed to simultaneously real-time measure 13 geometric error components. A volumetric error model is established using the Abbe and Bryan principles. A control unit with two backpropagation neural networks-based PID controllers combines with the VEMU and volumetric error model to realize the real-time compensation of the volumetric error. The positional error of the micro/nanopositioning coplanar stage is reduced approximately 97.6 %, from which the effectiveness and applicability of the proposed methods are verified.