RTD-RAX

Robotics
Safety
Python
JAX
Research
Safe trajectory planning with runtime reachability verification and repair.

View on GitHub Dedicated Website (it’s really nice)

RTD-RAX is a runtime-assurance extension of Reachability-based Trajectory Design (RTD) that replaces conservative offline reachable sets with fast online safety certification via mixed-monotone reachability (immrax).

RTD precomputes Forward Reachable Sets (FRS) offline and uses them at runtime to find collision-free trajectories. The problem: it inflates those sets with worst-case tracking-error bounds, making the planner overly cautious — it rejects safe trajectories, triggers unnecessary braking, and can’t handle disturbances like wind or ice that weren’t anticipated offline. RTD-RAX fixes this by splitting the problem: RTD handles fast candidate generation without the conservative inflation, while a separate online verifier certifies each candidate under the actual measured conditions. If a candidate can’t be certified safe, a repair procedure modifies it until a safe alternative is found.

  1. Plan — use the uninflated FRS to rapidly generate candidate trajectories.
  2. Verify — certify each candidate online via mixed-monotone reachability under current conditions.
  3. Repair — if unsafe, modify the candidate and re-verify before execution.

Gap Scenario

Standard RTD is too conservative to navigate a narrow corridor. RTD-RAX certifies a safe path through using the noerror FRS plus immrax verification.

Angled Obstacles with Repair

When immrax flags an unsafe candidate, the hybrid repair loop finds a safer alternative and re-verifies before execution.

Disturbance Course

A randomized multi-gap course with disturbance patches. Standard RTD collides; RTD-RAX detects the risk, repairs, and reaches the goal.

Planner Outcome Cycles Repairs Mean / p95 Compute
Standard RTD Collision (cycle 3) 3 – 10.5 ms / 21.9 ms
RTD-RAX Goal reached 19 3 10.5 ms / 37.4 ms

Key features:

  • First fully Python implementation of an RTD framework
  • Immrax interval-arithmetic reachability verification at runtime
  • Disturbance-aware verification with measured runtime disturbance bounds
  • Hybrid repair loop (speed-backoff + CEGIS buffer tightening) for unsafe candidates
  • Fully Dockerized with make command interface for reproducibility
  • Three case studies with manuscript-ready figure generation

Built with: Python · NumPy · SciPy · JAX · immrax · Docker