Leveraging Classification Metrics for Quantitative System-Level Analysis with Temporal Logic Specifications
This work addresses the need for quantitative safety analysis in autonomous systems by integrating perception performance metrics, though it is incremental in combining existing methods.
The paper tackles the problem of quantifying system-level safety in autonomy applications by computing the probability of satisfying temporal logic specifications using confusion matrices from perception algorithms, and demonstrates this on a car-pedestrian example with varying parameters.
In many autonomy applications, performance of perception algorithms is important for effective planning and control. In this paper, we introduce a framework for computing the probability of satisfaction of formal system specifications given a confusion matrix, a statistical average performance measure for multi-class classification. We define the probability of satisfaction of a linear temporal logic formula given a specific initial state of the agent and true state of the environment. Then, we present an algorithm to construct a Markov chain that represents the system behavior under the composition of the perception and control components such that the probability of the temporal logic formula computed over the Markov chain is consistent with the probability that the temporal logic formula is satisfied by our system. We illustrate this approach on a simple example of a car with pedestrian on the sidewalk environment, and compute the probability of satisfaction of safety requirements for varying parameters of the vehicle. We also illustrate how satisfaction probability changes with varied precision and recall derived from the confusion matrix. Based on our results, we identify several opportunities for future work in developing quantitative system-level analysis that incorporates perception models.