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

• URL: http://arxiv.org/abs/2603.13333v1
• Date: Fri, 06 Mar 2026 00:53:38 GMT
• Title: STL-SVPIO: Signal Temporal Logic guided Stein Variational Path Integral Optimization
• Abstract summary: Signal Temporal Logic (STL) enables formal specification of complex constraints for robotic task planning.<n>We introduce Signal Vari Temporal Integral Optimization (STL-SVPIO), which reframes STL as a globally informative, differentiable reward-shaping mechanism.<n>We demonstrate that STL-SVPIO significantly outperforms existing methods in both robustness and efficiency for traditional STL tasks.
• Score: 8.345095354174623
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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