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

Evanns Morales-Cuadrado, Long Kiu Chung, Shreyas Kousik, Samuel Coogan

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.

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

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.
Paper Structure (16 sections, 22 equations, 4 figures, 1 table)

This paper contains 16 sections, 22 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Reachability-Based Trajectory Design
  4. Mixed Monotone Reachability
  5. Proposed Method: RTD-RAX
  6. RTD Candidate-Generation Layer
  7. Execution-Time Verification Layer
  8. Initial Interval Construction
  9. Embedding System Integration
  10. Workspace Projection and Collision Checking
  11. Repair After Runtime Rejection
  12. Experiments
  13. Case Study 1: Narrow Gap
  14. Case Study 2: Angled Obstacle with Runtime Repair
  15. Case Study 3: Planning Against Disturbances
  16. ...and 1 more sections

Figures (4)

  • Figure 1: Narrow-gap scenario; the robot is depicted as a circle in the starting position, goal as a star, obstacles as rectangles, the offline reachable set in green, and the online reachable set in blue. (a) Standard RTD: incorrectly classifies as infeasible. (b) RTD-RAX: feasible and certified safe by the mixed-monotone verifier.
  • Figure 2: RTD-RAX architecture.
  • Figure 3: Figures for the Narrow Gap scenario on the left and Angled Obstacle scenario on the right.
  • Figure 4: Disturbance-aware scenario. Left: standard RTD collides due to disturbances. Right: RTD-RAX with online certification accounts for disturbances and repairs unsafe candidates.