Direct-to-cell (D2C) satellite communications have emerged as a crucial alternative to terrestrial communications in the sixth generation (6G) mobile networks due to their wide-area coverage capability. Unlike human-oriented communications, future 6G robot-oriented D2C satellite communications in autonomous operations place greater emphasis on the ultimate task completion than on the intermediate stage of data transmissions. Such a difference renders it crucial to evaluate the performance of each stage in a systematic manner and consider a multistage integrated optimization. Motivated by this, we model the system with a sensing-communication-computing-control (SC3) closed loop and analyze it from an entropy-based perspective, from which a task-oriented system design method is developed. Furthermore, to manage the complexity of the closed-loop network, we decompose it into fine-grained functional structures and investigate the key challenges of collaborative sensing, collaborative computing, and collaborative control. A case study is presented to compare the proposed task-oriented scheme with conventional communication-oriented schemes, showing that the proposed method has better performance in system-level control cost. Finally, several open issues are outlined for future research and practical implementation.