Robotics has experienced an increasing evolution and interest from the society in recent years. Robots are no longer produced exclusively to perform repetitive tasks in factories, they have been designed to collaborate with humans in several important application domains. Robotic systems that control these robots are, therefore, becoming larger, more complex and difficult to develop. In this scenario, Service-Oriented Architecture (SOA) has been investigated as a promising architectural style for the design of robotic systems in a flexible, reusable and productive way. Although a considerable amount of Service-Oriented Robotic Systems (SORS) has already been developed and used, most of them have been designed in an ad hoc manner. The little attention and limited support devoted to the design of SORS software architectures may not only hamper the benefits of SOA adoption but also reduce the overall quality of robotic systems, which are often used in safety-critical contexts. This paper presents Architectural Design of Service-Oriented Robotic System (ArchSORS), a process that supports a systematic design of SORS software architectures. Experimental results show that ArchSORS can lead to software architectures of higher quality, contributing to the robotics area and, as a consequence, to the areas that have benefited from the use of robots.