## 4 Applying the CM Framework to a Case Study
### Results
For this purpose, Figure 12 shows the entire acquisition of the fourth joint torque signal under healthy and faulty conditions during the execution of the palletizing program. Meanwhile, Figures 13 and 14 show, respectively, the torque signal after using the proposed method for data unit extraction, during the execution of PTP(1) and PTP(2) moves. Every time the PTP(1) or PTP(2) commands are executed, data are extracted from the entire acquisition and collected together, as shown in Figures 13 and 14, where three subsequential data extractions are performed on an acquisition of 2750 samples at 40 Hz. There are plenty of methodologies that can be used to analyze these data sequences extracted from the entire acquisition: in this part, we define three well-known HIs to monitor the system health. In particular, we evaluate the dominant frequencies peaks, the wavelet entropy, and the signal kurtosis. These three HIs have been chosen according to [10] where the most effective HIs were derived from several review papers regarding the CM gearbox and bearing CM [28; 29]. However, the definition of the best methodology to analyze data is beyond the scope of this work, since in fact, the best methodology to choose depends on which kind of fault we want to identify. Our purpose is to suggest a general CM architecture that can be used in different situations with collaborative robots, and here we provide an example based on this case study. We show below Table 2 with HIs calculated on both data unit extractions and on Figures 15 and 16, respectively, the Fast Fourier Transform (FFT) applied on the torque data unit sequences in the case of healthy and faulty behavior. Applying this methodology we can define basic HIs, generally used for fault detection only under stationary conditions, which would be ineffective if directly applied to the entire raw torque acquisition. This is because, as previously discussed, the torque varies according to the system motions (i.e., speed, load, positions, etc. ), and it would thus be impossible select reference values to distinguish normal from abnormal behaviors. In contrast, using the proposed CM approach, it is possible to define HIs or rather more complex strategies to automatically detect malfunctions and monitor the health of the system. The analysis proposed is valid for any joint, giving equivalent results in terms of monitoring. The fourth joint was chosen since it is the most involved in all the movements of the palletizing program, but this does not preclude the choice of applying the same concepts to a different joint. Choosing another joint will lead to similar conclusions since all the joints are mechanically constructed with the same components. Potentially, the same analysis can be simultaneously performed on all the joints of the manipulator. Finally, since the torque signal is sensible to load variations, we must ensure that every data unit extraction has been performed under similar load conditions. For this purpose, as introduced above, we use the TCP \(z\) axis force estimation. The force is calculated using algorithms which, from joint torques, can estimate the force on the TCP [30], and is already available in the controller. Figure 17 shows the instantaneous estimated TCP force along the \(z\) axis related to data unit 1 extraction under the execution of PTP(1). In dark blue, the force estimation is performed when the robot is carrying a load of 1 kg, while in light blue, the force is performed when the robot executes the same motions but is unloaded. As it is now possible to notice in Figure 17, the estimated value is not really precise for control purposes (e.g., adaptive force control) but can be used to check whether the load conditions during a specific motion sequence are in the same range or not. To conclude, even if three basic HIs have been defined in this proof of concept (PoC), the data units extraction of the joint torque could be analyzed using other tools that provide good results, even under non-stationary conditions.