A Stackelberg Game Approach for Signal Temporal Logic Control Synthesis with Uncontrollable Agents
Bohan Cui, Xinyi Yu, Alessandro Giua, Xiang Yin
TL;DR
This work introduces a Stackelberg game framework for signal temporal logic (STL) control synthesis with uncontrollable agents. The leader commits to a plan first, and a rational follower computes a best response with its own STL objective, enabling non-adversarial interaction and reduced conservatism compared to zero-sum robustness. The authors formulate the Stackelberg STL synthesis problem (SSP-STL), propose two synthesis approaches for cooperative and antagonistic solutions, and develop a counterexample-guided, single-stage optimization scheme to compute leader plans while accounting for follower responses. They validate the framework through two case studies (a double integrator with joint inputs and a multi-robot planning problem), showing feasible coordination and trade-offs between plan cost and task robustness. The work lays groundwork for STL control under Stackelberg dynamics and points to future extensions in reactive control and quantitative robustness optimization.
Abstract
In this paper, we investigate the control synthesis problem for Signal Temporal Logic (STL) specifications in the presence of uncontrollable agents. Existing works mainly address this problem in a robust control setting by assuming the uncontrollable agents are adversarial and accounting for the worst-case scenario. While this approach ensures safety, it can be overly conservative in scenarios where uncontrollable agents have their own objectives that are not entirely opposed to the system's goals. Motivated by this limitation, we propose a new framework for STL control synthesis within the Stackelberg game setting. Specifically, we assume that the system controller, acting as the leader, first commits to a plan, after which the uncontrollable agents, acting as followers, take a best response based on the committed plan and their own objectives. Our goal is to synthesize a control sequence for the leader such that, for any rational followers producing a best response, the leader's STL task is guaranteed to be satisfied. We present an effective solution to this problem by transforming it into a single-stage optimization problem and leveraging counter-example guided synthesis techniques. We demonstrate that the proposed approach is sound and identify conditions under which it is optimal. Simulation results are also provided to illustrate the effectiveness of the proposed framework.