Robotics as a Service (RaaS) emerges as a new paradigm to motivate diversified potential of the "remote-controlled economy" for flexible and efficient service provision with the help of cloud computing. The multi-robot cooperation (MRC) technology has been widely used in various intelligent logistics scenarios, such as warehouses, factories, airports and subway stations, benefiting from the advantages of high operational efficiency and low labor cost. While promising, the corresponding challenge is that the service functions deployed on logistics robots (LRs) are more prone to failures such as resource exhaustion and error configuration in the multi-robot system (MRS). In this way, it becomes extremely important to discover and locate abnormal services as soon as possible so as to ensure the stable and secure operation of MRS, further reducing or even avoiding economic loss. Due to the flexibility, scalability and resilience of Network Function Virtualization (NFV), this paper aims at proposing a NFV based complete service chain tracking and positioning process with a more fine-grained level of LRs. Specifically, a micro-service-based system framework for high-accurate service tracking and fault function positioning is constructed, in which two main micro-service functions are designed for service chain tracking and positioning to maintain the stability and reliability of the MRS. On one hand, the tracking micro-service proposes an improved Hopcroft-Karp algorithm to determine the optimal probing and tracking path for MRC. On the other hand, the positioning micro-service proposes a delay-aware dichotomy probing algorithm to minimize the number of probe packets. Experimental results indicate that the proposed system framework and mechanisms outperform the state-of-the-art methods in terms of tracking and positioning accuracy in the MRS.