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This paper aims to propose a dynamic trajectory-tracking control method for robotic transcranial magnetic stimulation (TMS), based on force sensors, which follows the dynamic movement of the patient’s head during treatment.

First, end-effector gravity compensation methods based on kinematics and back-propagation (BP) neural networks are presented and compared. Second, a dynamic trajectory-tracking method is tested using force/position hybrid control. Finally, an adaptive proportional-derivative (PD) controller is adopted to make pose corrections. All the methods are designed for robotic TMS systems.

The gravity compensation method, based on BP neural networks for end-effectors, is proposed due to the different zero drifts in different sensors’ postures, modeling errors in the kinematics and the effects of other uncertain factors on the accuracy of gravity compensation. Results indicate that accuracy is improved using this method and the computing load is significantly reduced. The pose correction of the robotic manipulator can be achieved using an adaptive PD hybrid force/position controller.

A BP neural network-based gravity compensation method is developed and compared with traditional kinematic methods. The adaptive PD control strategy is designed to make the necessary pose corrections more effectively. The proposed methods are verified on a robotic TMS system. Experimental results indicate that the system is effective and flexible for the dynamic trajectory-tracking control of manipulator applications.

Employing 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.

This 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.

Analysis 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.

This paper represents a SAT method based on CBF and elliptic curve cryptography techniques as an efficient mechanism that is resilient against tracing attacks.