RTD-RAX: Fast, Safe Trajectory Planning for Systems under Unknown Disturbances

2026-03-23

AI Summary

This work proposes RTD-RAX, a novel framework that addresses the limitations of existing trajectory planning methods, which often become overly conservative or fail to guarantee real-time safety under unknown disturbances. RTD-RAX uniquely integrates non-conservative trajectory generation, disturbance-aware safety certification, and real-time repair mechanisms. By leveraging hybrid monotonic reachability analysis, the framework rapidly verifies trajectory safety and, upon detecting potential risks, synthesizes alternative trajectories that simultaneously advance task objectives and strictly satisfy safety constraints. This approach significantly enhances both safety assurance and operational efficiency in dynamic, disturbance-prone environments.

Technology Category

• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Intelligent Robots: Motion and Path Planning
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Reachability-based Trajectory Design (RTD) is a provably safe, real-time trajectory planning framework that combines offline reachable-set computation with online trajectory optimization. However, standard RTD implementations suffer from two key limitations: conservatism induced by worst-case reachable-set overapproximations, and an inability to account for real-time disturbances during execution. This paper presents RTD-RAX, a runtime-assurance extension of RTD that utilizes a non-conservative RTD formulation to rapidly generate goal-directed candidate trajectories, and utilizes mixed monotone reachability for fast, disturbance-aware online safety certification. When proposed trajectories fail safety certification under real-time uncertainty, a repair procedure finds nearby safe trajectories that preserve progress toward the goal while guaranteeing safety under real-time disturbances.

Problem

• trajectory planning
• unknown disturbances
• reachability analysis
• real-time safety
• conservatism

Innovation

• Reachability analysis
• Runtime assurance
• Mixed monotone systems
• Trajectory planning
• Disturbance-aware safety