The path planning and obstacle-crossing motion planning of cable trench inspection robots are essential for achieving automated inspection. To improve path planning efficiency and obstacle navigation in complex environments, an enhanced global path planning algorithm based on the A* algorithm has been developed, combined with an improved Dynamic Window Approach (DWA) for local path planning. For unavoidable obstacles, a specific obstacle-crossing motion planning strategy has been formulated. The enhanced A* algorithm improves efficiency and safety through adaptive neighborhood expansion and the elimination of redundant path points. The improved DWA algorithm enables real-time dynamic obstacle avoidance in local path planning. The simulation results on a $20 \times 20$ grid map indicate that the improved A* algorithm reduces the number of nodes by 58.4% and shortens the path length by 6.1% compared to the traditional A* algorithm, demonstrating significant advantages over other conventional path planning algorithms. In the simulation experiments integrating global and local path planning, the enhanced A* algorithm combined with the improved DWA algorithm reduces the path length by 3.2% on the $20 \times 20$ grid map compared to the integration with the traditional DWA algorithm. On the $30 \times 30$ grid maps with different obstacle configurations, the path lengths are reduced by 3.5% and 3.6%, respectively. In the obstacle-crossing experiments, the robot successfully overcame obstacles of 10 cm and 20 cm in height. The proposed path planning algorithm and obstacle-crossing motion planning strategy hold substantial application potential in complex environments, offering reliable technical support for cable trench inspection robots.