Clustering-based Recurrent Neural Network Controller synthesis under Signal Temporal Logic Specifications

TL;DR

This work tackles synthesizing recurrent neural network (RNN) controllers that satisfy Signal Temporal Logic (STL) specifications under varying initial states and obstacle configurations. It introduces a clustering-based framework that converts optimal trajectories into feature vectors, clusters them, trains cluster-specific RNN policies, and uses a permutation-invariant classifier to map new environmental conditions to the appropriate cluster. Experimental results on a dynamic vehicle path-planning task show that the clustering-based approach improves STL satisfaction accuracy and trajectory efficiency while reducing training effort compared to a single-controller baseline. The method enhances robustness and generalization by enabling specialized controllers that adapt to different trajectory regimes dictated by initial state and obstacle geometry.

Abstract

Autonomous robotic systems require advanced control frameworks to achieve complex temporal objectives that extend beyond conventional stability and trajectory tracking. Signal Temporal Logic (STL) provides a formal framework for specifying such objectives, with robustness metrics widely employed for control synthesis. Existing optimization-based approaches using neural network (NN)-based controllers often rely on a single NN for both learning and control. However, variations in initial states and obstacle configurations can lead to discontinuous changes in the optimization solution, thereby degrading generalization and control performance. To address this issue, this study proposes a method to enhance recurrent neural network (RNN)-based control by clustering solution trajectories that satisfy STL specifications under diverse initial conditions. The proposed approach utilizes trajectory similarity metrics to generate clustering labels, which are subsequently used to train a classification network. This network assigns new initial states and obstacle configurations to the appropriate cluster, enabling the selection of a specialized controller. By explicitly accounting for variations in solution trajectories, the proposed method improves both estimation accuracy and control performance. Numerical experiments on a dynamic vehicle path planning problem demonstrate the effectiveness of the approach.

Figures (8)

• Figure 1: Structure of the RNN.
• Figure 2: Examples of optimal trajectories from different initial angles.
• Figure 3: Overview of our approach for the case where the number of clusters is $2$.
• Figure 4: Illustration of transforming optimal trajectories into the feature vectors.
• Figure 5: Illustration of $\mathcal{N\!N}$ preserving permutation invariance with respect to $\Xi$.