Space robots are vital for in-orbit maintenance of large satellites, but dense payloads and complex surface structures pose challenges for safe crawling operations. This study proposes an improved trajectory planning framework for three-dimensional satellite surfaces. In the path search stage, the traditional A* algorithm is enhanced with traction cost, reflecting surface adhesion, and proximity cost, ensuring collision avoidance. The resulting comprehensive cost function integrates path length, safety, and feasibility, producing paths more consistent with real mobility constraints. In the smoothing stage, cubic B-spline curves refine the discrete path, with real-time collision detection embedded in the optimization of control points to prevent trajectory penetration. Simulations show that the method achieves millisecond-level planning, with path length reduced by 6.82% and trajectory smoothness significantly improved, eliminating the phenomenon of sharp turns with folded corners. The approach ensures continuous, stable, and collision-free movement of space robots, highlighting its potential for reliable in-orbit operations.