RRT$^η$: Sampling-based Motion Planning and Control from STL Specifications using Arithmetic-Geometric Mean Robustness

2026-02-18

AI Summary

This work addresses the limitations of traditional signal temporal logic (STL)-based sampling-based planning, which relies on min-max robustness metrics that consider only critical time points and subformulas, resulting in non-smooth optimization landscapes and inefficient search. To overcome this, the authors propose the RRT$^\eta$ framework, which introduces arithmetic-geometric mean (AGM) robustness semantics to evaluate satisfaction across all time points and subformulas, enabling continuous and globally aware trajectory reasoning. The approach integrates efficient incremental monitoring with a fulfillment-priority-logic-derived gradient-like vector that guides the search toward higher satisfaction. Experiments on a double integrator, unicycle, and a 7-DOF manipulator demonstrate that the method significantly improves planning performance and robustness under multi-constraint and weakly guided scenarios, while preserving probabilistic completeness and asymptotic optimality.

Technology Category

• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Multiagent Systems: Multiagent Planning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Agentic search
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Sampling-based motion planning has emerged as a powerful approach for robotics, enabling exploration of complex, high-dimensional configuration spaces. When combined with Signal Temporal Logic (STL), a temporal logic widely used for formalizing interpretable robotic tasks, these methods can address complex spatiotemporal constraints. However, traditional approaches rely on min-max robustness measures that focus only on critical time points and subformulae, creating non-smooth optimization landscapes with sharp decision boundaries that hinder efficient tree exploration. We propose RRT$^η$, a sampling-based planning framework that integrates the Arithmetic-Geometric Mean (AGM) robustness measure to evaluate satisfaction across all time points and subformulae. Our key contributions include: (1) AGM robustness interval semantics for reasoning about partial trajectories during tree construction, (2) an efficient incremental monitoring algorithm computing these intervals, and (3) enhanced Direction of Increasing Satisfaction vectors leveraging Fulfillment Priority Logic (FPL) for principled objective composition. Our framework synthesizes dynamically feasible control sequences satisfying STL specifications with high robustness while maintaining the probabilistic completeness and asymptotic optimality of RRT$^\ast$. We validate our approach on three robotic systems. A double integrator point robot, a unicycle mobile robot, and a 7-DOF robot arm, demonstrating superior performance over traditional STL robustness-based planners in multi-constraint scenarios with limited guidance signals.

Problem

• sampling-based motion planning
• Signal Temporal Logic
• robustness measure
• non-smooth optimization
• spatiotemporal constraints

Innovation

• Arithmetic-Geometric Mean Robustness
• Signal Temporal Logic
• Sampling-based Motion Planning
• Incremental Monitoring
• Fulfillment Priority Logic