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In this work we propose algorithms to explicitly construct a conservativeestimate of the configuration spaces of rigid objects in 2D and 3D. Ourapproach is able to detect compact path components and narrow passages inconfiguration space which are important for applications in roboticmanipulation and path planning. Moreover, as we demonstrate, they are alsoapplicable to identification of molecular cages in chemistry. Our algorithmsare based on a decomposition of the resulting 3 and 6 dimensional configurationspaces into slices corresponding to a finite sample of fixed orientations inconfiguration space. We utilize dual diagrams of unions of balls and uniformgrids of orientations to approximate the configuration space. We carry outexperiments to evaluate the computational efficiency on a set of objects withdifferent geometric features thus demonstrating that our approach is applicableto different object shapes. We investigate the performance of our algorithm bycomputing increasingly fine-grained approximations of the object'sconfiguration space.

Free Space of Rigid Objects: Caging, Path Non-Existence, and Narrow Passage Detection