I. Introduction
Quadrupedal robots have demonstrated superior terrain traversability compared to traditional wheeled robots [1]–[3]. Significant progress has been made during the past few years to improve the robustness and agility of legged locomotion control [4]-[10], which enables the incorporation of exteroceptive sensors for autonomous navigation (e.g. Fig. 1). Taking into account legged robot morphology, prior navigation works have been mostly focused on rough terrain traversability [2], [11]–[15], multi-modal planning [2], [16]–[19], and multi-robot exploration [20], [21]. However, navigation safety and obstacle avoidance have not been formally analyzed, and the tested scenarios are limited to less dense environments. Safe navigation through unknown or partially unknown environments for quadrupeds is critical to the field deployment of legged robots yet remains under explored.