Cleaning high-altitude building windows is traditionally a high-risk task for human workers due to the danger of falls. To enhance safety in facade cleaning and similar tasks, the development of window-cleaning robots has become increasingly essential. However, current robots face challenges in navigating exoskeleton structures due to obstructive beams, limiting their application. This article proposes a novel biped window-cleaning robotic system (BWCRS) designed for exoskeleton structures. The system comprises two key components: a multifunctional biped climbing robot (BCR) and a specialized cleaning robot. The BCR is adept at overcoming obstacles inherent in exoskeleton structures and transitioning across various inclined window surfaces. The BCR adopts a symmetrical construction, and the ends of the feet are equipped with vacuum suction cups and electromagnets, which can switch between different actuators at the geometric base and end of the system. The system is further enhanced by air pressure sensors that monitor the suction cup adhesion in real time, ensuring stable operation. A crucial functionality of the BCR is its manipulation mode, guided by a visual camera. This mode enables precise location and manipulation of the cleaning robot, ensuring effective coverage of all window areas. The mechanical design and mathematical modeling of the BWCRS are thoroughly examined, demonstrating its robust window-cleaning capabilities. The experimental results reveal that the proposed BCR has a favorable window-climbing and manipulation ability and that the BWCRS has a favorable cleaning effect on the exoskeleton-structure windows. Note to Practitioners—This paper is motivated by the problem of window-cleaning for exoskeleton structures, but it also applies to solving window maintenance and inspection. Previous window-cleaning robots were mainly aimed at the facades or surfaces with low obstacles that cannot be applied directly to exoskeleton-structured windows. This paper proposes an exoskeleton-structure window-cleaning method based on a biped window-climbing robot and a cleaning robot. The biped robot can climb over obstacles on the exoskeleton structures and manipulate the cleaning robot to different cleaning areas. Here, we introduce the biped window-climbing robot from the perspective of mechanical design and mathematical kinematics. We then demonstrate multiple obstacle-crossing motion modes of the biped window-climbing robot. Combined with visual-based manipulation, the window-cleaning process for the exoskeleton structures by a biped window-climbing robot integrated with a cleaning robot is demonstrated. The results verify that the proposed design can complete window-cleaning tasks on exoskeleton structures.