## 6 Conclusions  
This paper introduces a novel approach to anomaly detection in robotic manipulators. It adopts side-channel energy auditing and utilizes the time series of energy consumption profiles as the sole input data for analysis. This simple design and robust monitoring scheme mitigate the risks caused by operational anomalies, malicious attacks, and other threats targeting networked sensors, which can pose significant challenges to accurate online data processing and analysis. A novel reconstruction network named U-TFF is proposed to learn energy consumption patterns and detect anomalies during the operation of robotic manipulators. U-TFF consists of one encoder that extracts features as low-dimensional vectors in the latent space and one decoder that reconstructs the input using associated latent vectors. The encoder includes several delicately designed blocks to distill frequency domain features from temporal inputs while continuously reducing the feature dimension. Conversely, the decoder comprises the same number of blocks as the encoder but with an increasing output size to reconstruct the input. More specifically, the Fast Fourier Transform is first applied to the temporal input to convert it from the time domain to the frequency domain. Then, two fully connected layers are used to extract features from the real and imaginary parts, respectively. The inverse FFT is then used to transform the extracted frequency features back to the time domain. This process reveals temporal information predominant in the frequency domain; when combined with conventional data processing in the time domain, it is capable of producing a more comprehensive feature set for anomaly detection spanning both domains. A fully connected layer for the output is employed to reconstruct the input using feature vectors from the information of both the time and frequency domains. To further improve the reconstruction ability of the network, a U-shape architecture is implemented along with skip connections to link two encoder and decoder blocks at the same level of the feature hierarchy. The sliding window technique is applied to sequences of energy consumption in order to enrich the feature representations of the input. The network is trained in a semi-supervised manner using only samples from normal operations. During online testing, inputs with anomalous data are expected to yield a significantly large reconstruction error, which can then be used as an effective indicator of the presence of anomalies. For experimental evaluations of the proposed energy auditing system, we utilized a Lynxmotion robotic manipulator programmed to perform prescribed tasks as a test bed. Physical attacks were simulated by gripping objects of different weights that were injected \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Recall** & **Precision** & **Accuracy** \\ \hline DAE & 0.226 & 0.7346 & 0.8554 \\ GAN with one D & 0.787 & 0.8302 & **0.9368** \\ GAN with five D & 0.813 & 0.8044 & 0.935 \\ Anomaly & 0.342 & **0.9249** & 0.8881 \\ Transformer & 0.3373 & 0.6142 & 0.8522 \\ \hline Proposed & **0.8316** & 0.7603 & 0.933 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison results on the custom dataset. randomly during the operation of a series of tasks. A custom dataset consisting of normal and physical attack data was compiled for online testing of the proposal anomaly detection model, and experiments were conducted to compare the present U-TFF model with four other benchmarks. The proposed network was able to successfully detect 83% of abnormal data instants while maintaining a precision of 0.7603 and an accuracy of 0.933. For event-level detection, the proposed model achieved over 0.93 on all three evaluation metrics, demonstrating well-balanced performance. Future investigations will focus on real-time implementation of edge computing devices [32], deployment of the proposed system in relevant industrial settings, and performance assessment under varying operational conditions.