Robust and flexible leader-following is a critical capability for robots to integrate into human society. While existing methods struggle to generalize to leaders of arbitrary form and often fail when the leader temporarily leaves the robot's field of view, this work introduces a unified framework addressing both challenges. First, traditional detection models are replaced with a segmentation model, allowing the leader to be anything. To enhance recognition robustness, a distance frame buffer is implemented that stores leader embeddings at multiple distances, accounting for the unique characteristics of leader-following tasks. Second, a goal-aware adaptation mechanism is designed to govern robot planning states based on the leader's visibility and motion, complemented by a graph-based planner that generates candidate trajectories for each state, ensuring efficient following with obstacle avoidance. Simulations and real-world experiments with a legged robot follower and various leaders (human, ground robot, UAV, legged robot, stop sign) in both indoor and outdoor environments show competitive improvements in follow success rate, reduced visual loss duration, lower collision rate, and decreased leader-follower distance.

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