用预期自由能统一规划机器人探火星路径，兼顾找资源与省成本。

An autonomous robot efficiently exploring an unknown environment, such as looking for water sources on Mars, faces two simultaneous demands: building an accurate information map while quickly finding the regions of greatest value, and paying for every meter of travel and the cost of every measurement it takes. Classical information-seeking and reward-seeking criteria address only one of these objectives at a time. Here, we propose Expected Free Energy (EFE), the principled action-selection objective from active inference, as a unifying criterion for budgeted robotic informative path planning. Maintaining a Gaussian-process belief over the information field, our agent plans continuous trajectories that minimize expected free energy under hard path-length constraints. The results from multiple realizations show that EFE-based planning yields accurate posterior maps and locates the highest-value regions simultaneously, outperforming information-theoretic baselines under the same settings. In robotic exploration, these unified, easy-to-tune principled information-gathering strategies facilitate autonomous deployment while enforcing efficiency and resource constraints.