This work introduces Semantically-Guided Exploration (SGE), a modular exploration framework for ground vehicles that integrates pixel-level semantic segmentation into sampling-based waypoint selection and receding-horizon route optimization. Unlike conventional geometric exploration methods, SGE evaluates candidate exploration goals directly in the image space using a semantic-aware utility function that accounts for terrain traversability, obstacle proximity, objects of interest, and depth-based exploration reward. Sampled waypoints are projected into 3D and ordered through a real-time Traveling Salesman Problem (TSP) formulation, enabling receding-horizon goal selection. To address real-world navigation uncertainty, the framework introduces mechanisms, including temporary taboo regions to handle navigation failures and a graph-based relocation strategy for efficient backtracking across explored areas. We evaluate SGE in standardized simulation benchmarks against state-of-the-art exploration planners and demonstrate competitive performance in volumetric coverage, while enabling semantic task biasing that cannot be achieved by purely geometric methods. The framework is further validated through real-world experiments using multiple robotic platforms in indoor campus buildings and in limestone and coal mines. Results show consistent performance and adaptability across platforms and domains.
We formalize the Steiner Traveling Salesman Problem (Steiner-TSP) on Graphs of Convex Sets (GCS), which seeks a minimum-cost closed trajectory through required convex sets while allowing optional transit vertices and revisits. To explore the resulting infinite solution space, we propose a unified branch-and-bound search over rooted walk prefixes. Additive lower-bound-graph costs bound committed prefixes, while a cut-separated connected-flow relaxation lower-bounds the residual cost of visiting every remaining target and returning to the root. Under a uniform positive-cost assumption, best-first traversal terminates after finitely many expansions on every feasible instance without an initial incumbent, whereas depth-first traversal does so once a finite incumbent is available. For a user-specified factor $ε\geq1$, a global lower bound certifies that either strategy's incumbent cost is at most $ε$ times the global optimum. We further demonstrate joint sensing-mode, visitation-order, and continuous-trajectory selection for a mobile-manipulator inspection task, including action precedences expressed in linear temporal logic over finite traces (LTL$_f$). Both traversal strategies find feasible solutions on all benchmark instances within 30s with mean certified optimality gaps of 28.1% and 29.7%, respectively, whereas two recent baselines succeed on only about half of the instances