5 Conclusions
We presented a method for obtaining time-consistent surface maps between deforming shapes, such maps consider all the object's geometry and allow defining shape control strategies in real scenarios. We applied the surface mapping method with our proposed control strategy to several deformation problems involving different objects, materials and 3D shapes. The method performed properly both in simulation and in real experiments. It is worth noting that even when used in simulations, with ground-truth tracked object points directly obtained from the simulation mesh, our proposed method still is relevant for maintaining time-consistent surface maps. Our time-consistent surface mapping method provides a versatile solution for the automation of deformable object manipulation, as it is capable of addressing a vast variety of shape mapping scenarios. It efficiently processes large numbers of point correspondences at industry-relevant frequencies. However, limitations such as unfavourable gripper positioning (Cuiral-Zueco et al., 2022), low robustness against poor lighting conditions and large occlusions, or requirements such as faster computation times still leave room for improvement.
Regarding future work, our proposed time-consistent mapping method has the potential to be applied to other existing control strategies (e.g., (McConachie and Berenson, 2018)). Additionally, the method could be used to complement and monitor other deformable object tasks, such as cloth folding (e.g., (Li et al., 2018)). Potential future research includes addressing the reliance on connected meshes: if occlusions separate the object's visible region into several regions, the resulting disconnected meshes can lead to incorrect basis computations. Other research lines could focus on making the gripper actuation concurrent rather than sequential, or using the time-consistent functional maps for analysing the feasibility of shape control tasks. Another avenue of research is the exploration of datasets based on synthetic surfaces (e.g., videos of simulated deformations). These datasets could serve as benchmark for other quantitative comparisons of emerging time-consistent surface mapping methods, not just in terms of computation cost as discussed in this paper, but also in accuracy, precision, and other quantitative measures.
