See abstract and datasets [10.5281/zenodo.5849300] There exist a large number of methods that can be used for anomaly detection/fault detection in collaborative robots. However, studies on these methods tend to only focus on a single or a couple of such methods, which can make it challenging to gauge their relative merits in specific robot scenarios. In this paper, we conduct a comprehensive comparison of 15 methods for anomaly detection, including methods based on principle component analysis, local outlier factor, and autoencoders. The methods are assessed in a typical pick-and-place application with respect to their capacity to detect a broad range of exogenous anomalies. The results of the study show that several methods perform well, but that their performance profiles differ across the studied anomalies. The results also give an indication of the application characteristics that have the potential to make anomaly detection challenging.