Mobile manipulators always need to determine feasible base positions prior to carrying out navigation-manipulation tasks. Real-world environments are often cluttered with various furniture, obstacles, and dozens of other objects. Efficiently computing base positions poses a challenge. In this work, we introduce a framework named MoMa-Pos to address this issue. MoMa-Pos first learns to predict a small set of objects that, taken together, would be sufficient for finding base positions using a graph embedding architecture. MoMa-Pos then calculates standing positions by considering furniture structures, robot models, and obstacles comprehensively. We have extensively evaluated the proposed MoMa-Pos across different settings (e.g., environment and algorithm parameters) and with various mobile manipulators. Our empirical results show that MoMa-Pos demonstrates remarkable effectiveness and efficiency in its performance, surpassing the methods in the literature. %, but also is adaptable to cluttered environments and different robot models. Supplementary material can be found at \url{https://yding25.com/MoMa-Pos}.
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