Automated driving systems (ADS) are expected to be reliable and robust against a wide range of driving scenarios. Their decisions, first and foremost, must be well understood. Understanding a decision made by ADS is a great challenge, because it is not straightforward to tell whether the decision is correct or not, and how to verify it systematically. In this paper, a Sequential MetAmoRphic Testing Smart framework is proposed based on metamorphic testing, a mainstream software testing approach. In metamorphic testing, metamorphic groups are constructed by selecting multiple inputs according to the so-called metamorphic relations, which are basically the system's necessary properties; the violation of certain relations by some corresponding metamorphic groups implies the detection of erroneous system behaviors. The proposed framework makes use of sequences of metamorphic groups to understand ADS behaviors, and is applicable without the need of ground-truth datasets. To demonstrate its effectiveness, the framework is applied to test three ADS models that steer an autonomous car in different scenarios with another car either leading in front or approaching in the opposite direction. The conducted experiments reveal a large number of undesirable behaviors in these top-ranked deep learning models in the scenarios. These counter-intuitive behaviors are associated with how the core models of ADS respond to different positions, directions and properties of the other car in its proximity. Further analysis of the results helps identify critical factors affecting ADS decisions and thus demonstrates that the framework can be used to provide a comprehensive understanding of ADS before their deployment