Legged robots equipped with manipulators have shown significant potential in the fields of daily life and industry in complex environments. However, existing methods mainly focus on global navigation or manipulation independently, while overlooking the last-mile navigation problem, where the robot must jointly determine the base placement, approach direction, and grasp execution to achieve reliable object grasping, and different manipulation stages require distinct control behaviors. To address these challenges, we propose Last-Mile Grasp-Navigation (LMGN), a unified policy learning model for Quadruped robot loco-manipulation. An Explicit Distance and Directional Reachability (ED-DR) representation is first introduced to explicitly represent the features of grasp-compatible base placement and approach direction. We then develop a semantically aligned Hierarchical Mixture-of-Experts (HMoE) policy that models stage-aware behaviors across the stages of base adjustment, pre-grasp alignment and grasp execution, and object lift. Finally, a new optimization method that jointly aligns navigation and manipulation, stage-dependent expert routing, and action-level consistency is proposed to optimize the HMoE policy. Extensive experiments on the Habitat and Isaac Gym simulators demonstrate that LMGN consistently outperforms state-of-the-art methods, denoting that integrating grasp-aware reachability with stage-aware policy learning significantly improves the success rates of last-mile navigation and target grasp for robots.

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