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Having a representation of the capabilities of a robot is helpful when online queries, such as solving the inverse kinematics (IK) problem for grasping tasks, must be processed efficiently in the real world. When workspace representations, e.g. the reachability of an arm, are considered, additional quality information such as manipulability or self-distance can be employed to enrich the spatial data. In this work we present an approach of inverting such precomputed reachability representations in order to generate suitable robot base positions for grasping. Compared to existing works, our approach is able to generate a distribution in SE(2), the cross-space consisting of 2D position and 1D orientation, that describes potential robot base poses together with a quality index. We show how this distribution can be queried quickly in order to find oriented base poses from which a target grasping pose is reachable without …