Fast and Robust Temporal Logic Planning via ADMM-based Trajectory Optimization

2026-09-19

AI Summary

本文提出一种基于ADMM的轨迹优化方法，快速稳健地解决满足时序逻辑要求的安全连续时间运动规划问题。

Abstract

We present a fast numerical method for safe continuous-time motion planning under Temporal Logic (TL) specifications. The method generates smooth continuous trajectories that remain collision-free while robustly satisfying temporal and logical task requirements. A central component of our method is the formulation of nonconvex safety and logic constraints as unions of convex sets where associated discrete decisions are encoded in a joint feasibility graph. This graph representation allows Euclidean projection onto the feasible set and proximal robustness maximization to be reformulated as shortest- and widest-path problems, respectively. Building on this structure, we develop a nonconvex splitting method based on the Alternating Direction Method of Multipliers (ADMM), which decouples smooth spatio-temporal trajectory optimization from nonsmooth discrete constraint handling within the optimization. The resulting algorithm exhibits reliable convergence across benchmarks and scales to large-scale motion-planning problems, providing a 4.7x average speedup over the state of the art on discrete and continuous-time logic problems.

Problem

• Temporal Logic
• Motion Planning
• Trajectory Optimization
• Collision-free

Innovation

• Alternating Direction Method of Multipliers (ADMM)
• Temporal Logic (TL) specifications
• nonconvex safety and logic constraints
• joint feasibility graph
• trajectory optimization