Tactile pose estimation and tactile servoing are fundamental capabilities of robot touch. Reliable and precise pose estimation can be provided by applying deep learning models to high-resolution optical tactile sensors.  Given the recent successes of Graph Neural Network (GNN) and the effectiveness of Voronoi features, we developed a Tactile Voronoi Graph Neural Network (Tac-VGNN)  to achieve reliable pose-based tactile servoing relying on a biomimetic optical tactile sensor (TacTip).  The GNN is well suited to modelling the distribution relationship between shear motions of the tactile markers, while the Voronoi diagram supplements this with area-based tactile features related to contact depth. The experiment results show that Tac-VGNN model can help enhance data interpretability during graph generation and model training efficiency significantly than CNN-based methods. The proposed Tac-VGNN improved pose estimation accuracy along vertical depth by 28.57% over vanilla GNN without Voronoi features and also achieved better performance on the real surface following tasks with smoother robot control trajectories.

Five experiments were conducted using five types of objects for the surface following task. To quantify the tactile servoing performance, we defined an evaluation metric called smoothness whose value is smaller, the trajectory will be smoother.  From our experiments, the Tac-VGNN performed very well with less fluctuations and provides more accurate pose estimates as compared to the other models.