In modern shipbuilding, the structural complexity of ship components and the constrained workspace make robotic grinding prone to collisions. To improve safety and stability, this paper proposes a collision-free posture optimization method for ship-component operations. First, forward and inverse kinematic models are established, and postures along the path are organized into a directed graph. Feasible postures are then identified under joint-limit and singularity constraints. Directed bounding boxes and the GJK collision detection algorithm are applied to construct a collision-free posture set. An improved A* algorithm is then introduced. It incorporates a multi-source heuristic based on joint-space geometric distance and a safety-distance penalty to compute an optimal posture sequence with minimal joint deviation. This design promotes smooth transitions between consecutive postures. Simulation results show that the proposed method avoids robot–workpiece interference in constrained environments and improves obstacle avoidance and motion smoothness. Compared with the standard A* algorithm, the proposed approach reduces search time by 15.8% and increases the minimum safety distance by nearly fivefold. Compared with a non-optimized posture sequence, cumulative joint variation is reduced by up to 92.5%. The joint amplitude range decreases by an average of 41.2%, and the standard deviation of joint fluctuations decreases by 37.8%. The proposed method provides a generalizable solution for robotic measurement, assembly, and machining in complex and confined environments.