In the upcoming sixth-generation (6G) era, supporting field robots for unmanned operations has emerged as an important application direction. To provide connectivity in remote areas, the space–air–ground integrated network (SAGIN) will play a crucial role in extending coverage. Through SAGIN connections, the sensors, edge platforms, and actuators form sensing–communication–computing–control (SC³) loops that can automatically execute complex tasks without human intervention. Similar to the reflex arc, the SC³ loop is an integrated structure that cannot be deconstructed. This necessitates a systematic approach that takes the SC³ loop rather than the communication link as the basic unit of SAGINs. Given the resource limitations in remote areas, we propose a radio-map-based task-oriented framework that uses environmental and task-related information to enable task-matched service provision. We detail how the network collects and uses this information and present task-oriented scheduling schemes. In the case study, we use a control task as an example and validate the superiority of the task-oriented closed-loop optimization scheme over traditional communication schemes. Finally, we discuss open challenges and possible solutions for developing nerve system-like SAGINs.