STL-SVPIO: Signal Temporal Logic guided Stein Variational Path Integral Optimization

TL;DR

STL-SVPIO introduces a novel control optimization method that uses Signal Temporal Logic as a differentiable reward to efficiently synthesize complex, long-horizon robotic control trajectories, outperforming existing approaches.

Contribution

It presents STL-SVPIO, a new framework combining STL with Stein Variational Gradient Descent to improve control synthesis for complex, long-horizon tasks in robotics.

Findings

Outperforms existing methods in robustness and efficiency.

Successfully solves multi-agent coordination and synchronization tasks.

Demonstrates generalizability in robotic motion planning with nonlinear dynamics.

Abstract

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.