In the realm of household robotics, the Zero-Shot Object Navigation (ZSON) task empowers agents to adeptly traverse unfamiliar environments and locate objects from novel categories without prior explicit training. This paper introduces VoroNav, a novel semantic exploration framework that proposes the Reduced Voronoi Graph to extract exploratory paths and planning nodes from a semantic map constructed in real time. By harnessing topological and semantic information, VoroNav designs text-based descriptions of paths and images that are readily interpretable by a large language model (LLM). In particular, our approach presents a synergy of path and farsight descriptions to represent the environmental context, enabling LLM to apply commonsense reasoning to ascertain waypoints for navigation. Extensive evaluation on HM3D and HSSD validates VoroNav surpasses existing benchmarks in both success rate and exploration efficiency (absolute improvement: +2.8% Success and +3.7% SPL on HM3D, +2.6% Success and +3.8% SPL on HSSD). Additionally introduced metrics that evaluate obstacle avoidance proficiency and perceptual efficiency further corroborate the enhancements achieved by our method in ZSON planning. Project page: https://voro-nav.github.io

This paper proposes an informative trajectory planning approach, namely, adaptive particle filter tree with sigma point-based mutual information reward approximation (ASPIRe), for mobile target search and tracking (SAT) in cluttered environments with limited sensing field of view. We develop a novel sigma point-based approximation to accurately estimate mutual information (MI) for general, non-Gaussian distributions utilizing particle representation of the belief state, while simultaneously maintaining high computational efficiency. Building upon the MI approximation, we develop the Adaptive Particle Filter Tree (APFT) approach with MI as the reward, which features belief state tree nodes for informative trajectory planning in continuous state and measurement spaces. An adaptive criterion is proposed in APFT to adjust the planning horizon based on the expected information gain. Simulations and physical experiments demonstrate that ASPIRe achieves real-time computation and outperforms benchmark methods in terms of both search efficiency and estimation accuracy.