Feasibility Restoration under Conflicting STL Specifications with Pareto-Optimal Refinement

Temporal logic is a formal language for reasoning about system behaviors over time. Signal temporal logic (STL), in particular, has been used to encode spatio-temporal requirements for control synthesis in multi-agent systems, often under the assumption that agents are cooperative and their dynamics are known. However, real-world multi-agent applications, such as autonomous driving, typically involve stochastic and uncontrollable agents. Recent work explored robust control with worst-case or probabilistic formulations, but remains limited in that it either (1) certifies strict satisfaction of STL constraints without addressing feasibility recovery, or (2) relaxes infeasible constraints with ego-centric objectives. In this paper, we propose a model predictive control (MPC) framework that treats feasibility repair as a Pareto optimization problem to explicitly characterize tradeoffs among agent objectives. We further provide a probabilistic certificate on STL violation rate to formally quantify uncertainty under stochastic and uncontrollable agents. The proposed framework is evaluated on two autonomous driving scenarios. Results show that the framework recovers feasible control with demonstrated safe behaviors.

Signal Temporal Logic (STL) enables formal specification of complex spatiotemporal constraints for robotic task planning. However, synthesizing long-horizon continuous control trajectories from complex STL specifications is fundamentally challenging due to the nested structure of STL robustness objectives. Existing solver-based methods, such as Mixed-Integer Linear Programming (MILP), suffer from exponential scaling, whereas sampling methods, such as Model-Predictive Path Integral control (MPPI), struggle with sparse, long-horizon costs. We introduce Signal Temporal Logic guided Stein Variational Path Integral Optimization (STL-SVPIO), which reframes STL as a globally informative, differentiable reward-shaping mechanism. By leveraging Stein Variational Gradient Descent and differentiable physics engines, STL-SVPIO transports a mutually repulsive swarm of control particles toward high robustness regions. Our method transforms sparse logical satisfaction into tractable variational inference, mitigating the severe local minima traps of standard gradient-based methods. We demonstrate that STL-SVPIO significantly outperforms existing methods in both robustness and efficiency for traditional STL tasks. Moreover, it solves complex long-horizon tasks, including multi-agent coordination with synchronization and queuing while baselines either fail to discover feasible solutions, or become computationally intractable. Finally, we use STL-SVPIO in agile robotic motion planning tasks with nonlinear dynamics, such as 7-DoF manipulation and half cheetah back flips to show the generalizability of our algorithm.

Safety-aware motion planning remains a challenge in robotics, especially when missions are time-critical and are under complex specifications. In this paper, we propose safety-aware-stl-mppi, a computationally efficient sampling-based receding-horizon planning framework designed to promote satisfaction of constraints expressed in Signal Temporal Logic (STL). Our approach encodes discrete-time STL formulas into candidate time-varying control barrier functions (CBF), which are integrated into a model predictive path integral (MPPI) controller. Our method inherits the benefits of low computational cost from an efficiently parallelizable sampling based planner and utilizes CBF for constraints expressed in STL. We compare against several MPPI baselines using four artificial Mars Rover planning case studies with a diverse environment and cost setups, where we show our method consistently achieving high safety and efficiency. We show a quadcopter planning experiment with NVIDIA Isaac Lab.