Semi-Supervised Trajectory-Feedback Controller Synthesis for Signal Temporal Logic Specifications

There are spatio-temporal rules that dictate how robots should operate in complex environments, e.g., road rules govern how (self-driving) vehicles should behave on the road. However, seamlessly incorporating such rules into a robot control policy remains challenging especially for real-time applications. In this work, given a desired spatio-temporal specification expressed in the Signal Temporal Logic (STL) language, we propose a semi-supervised controller synthesis technique that is attuned to human-like behaviors while satisfying desired STL specifications. Offline, we synthesize a trajectory-feedback neural network controller via an adversarial training scheme that summarizes past spatio-temporal behaviors when computing current controls, and then online, we perform gradient steps to improve specification satisfaction. Central to the offline phase is an imitation-based regularization component that fosters better policy exploration and induces naturalistic human behaviors. Our experiments demonstrate that having imitationbased regularization leads to better qualitative and quantitative performance compared to optimizing for STL satisfaction only as done in prior work. We demonstrate the efficacy of our approach with an illustrative case study and show that our proposed controller outperforms a state-of-the-art shooting method in both performance and online computation time.