Inference of Multi-Class STL Specifications for Multi-Label Human-Robot Encounters

Abstract

This paper is interested in formalizing human trajectories in human-robot encounters. Inspired by robot navigation tasks in human-crowded environments, we consider the case where a human and a robot walk towards each other, and where humans have to avoid colliding with the incoming robot. Further, humans may describe different behaviors, ranging from being in a hurry/minimizing completion time to maximizing safety. We propose a decision tree-based algorithm to extract STL formulae from multi-label data. Our inference algorithm learns STL specifications from data containing multiple classes, where instances can be labelled by one or many classes. We base our evaluation on a dataset of trajectories collected through an online study reproducing human-robot encounters.

Learning Signal Temporal Logic through Neural Network for Interpretable Classification

“…(2) The loss is small if the inferred formula can achieve a large margin. The loss function for the attribute-based classification problem for dataset S is defined as ReLU m yj − C(y i , j)r yj (s i ) − δm yj , (16) where δ > 0 is a tuning parameter used to control the compromise between maximizing the margin and classifying more data correctly. If δ is large, the learned STL formulae tend to maximize the margin, but it may cause more samples to be misclassified.…”

“…In this example, we implement experiments on a synthetic dataset and compare it with the state-of-the-art methods [21], [22]. The problem formulation in our paper is different from that in [21]; the "multi-label" of a signal in [21] is equivalent to attributes in our paper, so we generate a new dataset for better comparison. The trajectories in the synthetic dataset are 2-dimensional time-series data generated by four different STL specifications using a MILP approach.…”

“…The trajectories in the synthetic dataset are 2-dimensional time-series data generated by four different STL specifications using a MILP approach. Since the STLdifference method in [21] with the predicate in the form:…”

“…We conduct experiments on the datasets with sample sizes of 500, 2500 and 5000; these three datasets have 100, 500 and 1000 samples for each class, respectively. We also compare the performance with the decision-tree-based algorithm [21] and a recurrent neural network [22] on these datasets. The decision-tree-based method (dt∆) uses a decision tree with a Table VI shows the results of these three methods on a 5-fold cross-validation.…”

“…We are aware of two previous works for multi-class classification with DTs STL specifications [14], [16]. Both methods learn the parameters of Parametric Signal Temporal Logic (PSTL).…”