Assembling large, heavy space segments presents a significant challenge in aerospace engine production. Rigid collisions often occur during the docking process, impacting the precision and quality of engine assembly. Traditional manual docking depends on workers' experience to prevent collisions, but it is labor-intensive and low in productivity, making it impractical. Parallel robots, known for their high precision and heavy load capacity, are widely used in precision assembly under heavy load conditions. Therefore, automated docking methods using parallel robots capable of avoiding rigid collisions have emerged as an excellent solution to these issues. This paper presents a framework for easy implementation in practical production. The Stewart parallel robot facilitates automatic docking of heavy aerospace components without rigid collisions. Fractional-order variable damping admittance control is proposed, allowing the robot to dynamically adjust the assembly trajectory based on real-time interaction forces, thus preventing rigid collisions during docking. Additionally, adaptive robust sliding mode control is developed, enhancing the robot's tracking accuracy for desired poses and making it suitable for high-precision assembly.