2020/02/07 by Anastasiia Varava, Varava, Anastasiia, J. Frederico Carvalho +5 · 1 citation
Computer Science · Engineering · Materials Science · #Computational Geometry and Mesh Generation #Diatoms and Algae Research #FOS: Computer and information sciences #Modular Robots and Swarm Intelligence #Robotics (cs.RO)
paper · pdf · doi:10.48550/arxiv.2002.02715
openalex publication_date 2020/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work we propose algorithms to explicitly construct a conservative\nestimate of the configuration spaces of rigid objects in 2D and 3D. Our\napproach is able to detect compact path components and narrow passages in\nconfiguration space which are important for applications in robotic\nmanipulation and path planning. Moreover, as we demonstrate, they are also\napplicable to identification of molecular cages in chemistry. Our algorithms\nare based on a decomposition of the resulting 3 and 6 dimensional configuration\nspaces into slices corresponding to a finite sample of fixed orientations in\nconfiguration space. We utilize dual diagrams of unions of balls and uniform\ngrids of orientations to approximate the configuration space. We carry out\nexperiments to evaluate the computational efficiency on a set of objects with\ndifferent geometric features thus demonstrating that our approach is applicable\nto different object shapes. We investigate the performance of our algorithm by\ncomputing increasingly fine-grained approximations of the object's\nconfiguration space.\n