Trajectory Planning with Signal Temporal Logic Costs using Deterministic Path Integral Optimization

2025-03-03

AI Summary

This work addresses the low optimization efficiency and nonsmooth objective functions arising from Signal Temporal Logic (STL) specifications in trajectory planning for dynamical systems. We propose the first sampling-based STL optimal control framework grounded in deterministic path integral control. Unlike conventional gradient-based methods, our approach directly optimizes the original STL cost function without smoothing approximations, thereby overcoming nondifferentiability and convergence bottlenecks inherent to STL constraints. By tightly integrating Model Predictive Path Integral (MPPI) control with STL semantic modeling—and leveraging deterministic path integral approximation for efficient stochastic sampling—we achieve significant improvements in trajectory accuracy and real-time performance on standard motion planning benchmarks. To the best of our knowledge, this is the first method enabling high-fidelity, scalable, and online-feasible optimal control under hard STL constraints.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Planning, Routing, and Scheduling: Deterministic Planning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Formulating the intended behavior of a dynamic system can be challenging. Signal temporal logic (STL) is frequently used for this purpose due to its suitability in formalizing comprehensible, modular, and versatile spatiotemporal specifications. Due to scaling issues with respect to the complexity of the specifications and the potential occurrence of non-differentiable terms, classical optimization methods often solve STL-based problems inefficiently. Smoothing and approximation techniques can alleviate these issues but require changing the optimization problem. This paper proposes a novel sampling-based method based on model predictive path integral control to solve optimal control problems with STL cost functions. We demonstrate the effectiveness of our method on benchmark motion planning problems and compare its performance with state-of-the-art methods. The results show that our method efficiently solves optimal control problems with STL costs.

Problem

• Efficiently solve optimal control problems with STL costs.
• Address scaling issues in STL-based trajectory planning.
• Propose a novel sampling-based method for STL optimization.

Innovation

• Uses Signal Temporal Logic for behavior specification
• Applies Deterministic Path Integral Optimization
• Solves STL-based control problems efficiently