To address the lack of traversable region awareness in conventional path planning algorithms for obstacle-crossing robots, an adaptive path planning method is proposed. First, a traversal-aware environment model is constructed by introducing graded traversable regions with associated physical traversal costs. To effectively navigate this complex model, a hybrid Ant Colony Optimization (ACO) framework integrating Jump Point Search (JPS) and the Genetic Algorithm (GA) is developed. Specifically, a JPS-inspired pruning strategy is incorporated into the state transition process to significantly reduce redundant node expansion. Crucially, genetic operators—namely crossover and mutation—are embedded within the main ACO iterative loop to dynamically sustain population diversity and effectively mitigate stagnation in local optima. Correspondingly, the pheromone initialization, state transition mechanisms, and update rules are redesigned to incorporate the robot’s obstacle traversal capabilities. The framework is further complemented by path optimization operations that reduce unnecessary turning points. Extensive simulation experiments demonstrate that the proposed method outperforms conventional ACO-based and classical path planning algorithms. In particular, it achieves an average reduction of 11.1% in path length and 65.5% in the number of waypoints, while ensuring effective coordination with the robot’s physical traversal capabilities. These results validate the superior search efficiency, robustness, and practical applicability of the proposed approach.