PurposeEmploying a fog computing (FC) network system in the robotic network system is an effective solution to support robotic application issues. The interconnection between robotic devices through an FC network can be referred as the Internet of Robotic Things (IoRT). Although the FC network system can provide number of services closer to IoRT devices, it still faces significant challenges including real-time tracing services and a secure tracing services. Therefore, this paper aims to provide a tracking mobile robot devices in a secure and private manner, with high efficiency performance, is considered essential to ensuring the success of IoRT network applications.Design/methodology/approachThis paper proposes a secure anonymous tracing (SAT) method to support the tracing of IoRT devices through a FC network system based on the Counting Bloom filter (CBF) and elliptic curve cryptography techniques. With the proposed SAT mechanism, a fog node can trace a particular robot device in a secure manner, which means that the fog node can provide a service to a particular robot device without revealing any private data such as the device's identity or location.FindingsAnalysis shows that the SAT mechanism is both efficient and resilient against tracing attacks. Simulation results are provided to show that the proposed mechanism is beneficial to support IoRT applications over an FC network system.Originality/valueThis paper represents a SAT method based on CBF and elliptic curve cryptography techniques as an efficient mechanism that is resilient against tracing attacks.