314
J. Eur. Opt. Society-Rapid Publ. 21, 30( 2025)
and does not incorporate feedback or closed-loop control, it contributes essential mathematical understanding relevant for deriving velocity fields as used in the current camerabased measurement approach.
From a control engineering perspective, the work of Chen et al. addresses the trajectory tracking challenge in hybrid machines composed of constant velocity and servo actuators [ 15 ]. Their iteration-based controller, rooted in sliding-mode control, compensates for actuation nonidealities at the end-effector level. Although not developed explicitly for polishing, their control strategy could inform future work aiming to stabilize or adapt relative velocity profiles in real time.
Recent advancements go beyond replication or modeling by introducing sensor-based and learning-based adaptations. Zhou et al. propose an adaptive impedance control scheme for robotic grinding and polishing, allowing the robot to dynamically regulate contact forces [ 16 ]. Similarly, Li et al. integrate real-time compliance control in hybrid serial-parallel robots, effectively emulating manual polishing behavior for ultra-precise surfaces [ 17 ]. These methods align with the outlook in this work, particularly regarding the potential for future pressure monitoring and control within lever-arm machines.
Additionally, Mohsin et al. present a method for polishing freeform surfaces by combining force-controlled path planning with trajectory optimization on industrial robots [ 18 ]. Although focused on sub-aperture systems, their approach underscores the importance of synchronizing motion and load – analogous to the considerations of coverage and relative speed discussed in this paper.
Finally, the reinforcement learning-based approach of Cramer et al. introduces CHEQ, a hybrid controller that autonomously adjusts motion and impedance parameters [ 19 ]. While still in the experimental phase, their architecture illustrates a promising direction for future intelligent control of polishing tasks – potentially enabling self-correction based on velocity fields and removal correlations like the one quantified in this work( Pearson correlation of 31.5 %).
In summary, the current study complements and extends these efforts by offering a production-ready system for mapping velocity fields on lever-arm polishing machines with minimal hardware intrusion. By demonstrating a measurable correlation between calculated velocity and actual material removal, it provides a physically grounded basis for future developments such as adaptive pressure control or machine learning-based removal models. Unlike previous studies, which often isolate mechanical or control parameters, this work brings them together under real production conditions – bridging the gap between theory, laboratory validation, and industrial application.
2 Set up
The set up presented here is optimized for the maximum number of image acquisitions per second and should at thesametimebeusabledirectlyinshopfloor. The machine used was a Stock DH 400 P lever arm polishing machine with two eccentric spindles and a rotary spindle. Thanks to its individual design, the system( see Fig. 4) can be
Fig. 4. Knowledge based polishing set up.
attached to any machine, e. g. even to machines with one eccentric spindle, gantry polishing machines or robots. An infrared light source( IR) and an Imaging Source camera DBK 33GX462 are installed above the machine. Special optics and filters can support image capture and quality. The camera has no IR cut filter and GigE interface. IR trackers are mounted on the back of the work piece. The reflector holders reflect particularly little IR light [ 20 ]. Six trackers are used: four for position and two for orientation of the work piece.
For the evaluation, all images are saved and all features are marked( see Fig. 5). These images are no longer saved later for the ongoing process in order to be able to evaluate more images per second.
Large blue circle: calibrated rotational tool; small orange circles: position trackers; small green circles: orientation trackers; red circle: work piece size; horizontal red line: 0 °-orientation line.
This means that the position of the workpiece, its orientation and the position of the polishing dish are known for each image taken.
3 Materials and methods
3.1 Used material
For the polishing trials, specific glass types and polishing abrasives are used. A lithium aluminum silicate glass ceramic( LAS) is used for the experiments in this work. A glass ceramic is an original glass that has undergone a controlled partialorcompletetransformationintocrystals. Duetothe