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Time-aware Motion Planning in Dynamic Environments with Conformal Prediction

Kaier Liang, Licheng Luo, Yixuan Wang, Mingyu Cai, Cristian Ioan Vasile

TL;DR

The paper tackles safe navigation for autonomous agents amid dynamic obstacles with unpredictable behaviors. It introduces two conformal-prediction-based planning frameworks: CP-SIPP for global, long-horizon planning with distribution-free safety guarantees, and ACP-RRT for local, online reactive planning that adaptively calibrates safety bounds in response to real-time data. A calibration-free adaptive quantile mechanism governs CP-based safety margins, allowing the planner to tighten regions around uncertain obstacles in high-uncertainty regions while preserving feasibility. Together, CP-SIPP and ACP-RRT provide a unified, provably safe approach to uncertainty-aware motion planning in both discrete and continuous domains, demonstrated through dynamic, cluttered environments and online adaptation to distribution shift.

Abstract

Safe navigation in dynamic environments remains challenging due to uncertain obstacle behaviors and the lack of formal prediction guarantees. We propose two motion planning frameworks that leverage conformal prediction (CP): a global planner that integrates Safe Interval Path Planning (SIPP) for uncertainty-aware trajectory generation, and a local planner that performs online reactive planning. The global planner offers distribution-free safety guarantees for long-horizon navigation, while the local planner mitigates inaccuracies in obstacle trajectory predictions through adaptive CP, enabling robust and responsive motion in dynamic environments. To further enhance trajectory feasibility, we introduce an adaptive quantile mechanism in the CP-based uncertainty quantification. Instead of using a fixed confidence level, the quantile is automatically tuned to the optimal value that preserves trajectory feasibility, allowing the planner to adaptively tighten safety margins in regions with higher uncertainty. We validate the proposed framework through numerical experiments conducted in dynamic and cluttered environments. The project page is available at https://time-aware-planning.github.io

Time-aware Motion Planning in Dynamic Environments with Conformal Prediction

TL;DR

The paper tackles safe navigation for autonomous agents amid dynamic obstacles with unpredictable behaviors. It introduces two conformal-prediction-based planning frameworks: CP-SIPP for global, long-horizon planning with distribution-free safety guarantees, and ACP-RRT for local, online reactive planning that adaptively calibrates safety bounds in response to real-time data. A calibration-free adaptive quantile mechanism governs CP-based safety margins, allowing the planner to tighten regions around uncertain obstacles in high-uncertainty regions while preserving feasibility. Together, CP-SIPP and ACP-RRT provide a unified, provably safe approach to uncertainty-aware motion planning in both discrete and continuous domains, demonstrated through dynamic, cluttered environments and online adaptation to distribution shift.

Abstract

Safe navigation in dynamic environments remains challenging due to uncertain obstacle behaviors and the lack of formal prediction guarantees. We propose two motion planning frameworks that leverage conformal prediction (CP): a global planner that integrates Safe Interval Path Planning (SIPP) for uncertainty-aware trajectory generation, and a local planner that performs online reactive planning. The global planner offers distribution-free safety guarantees for long-horizon navigation, while the local planner mitigates inaccuracies in obstacle trajectory predictions through adaptive CP, enabling robust and responsive motion in dynamic environments. To further enhance trajectory feasibility, we introduce an adaptive quantile mechanism in the CP-based uncertainty quantification. Instead of using a fixed confidence level, the quantile is automatically tuned to the optimal value that preserves trajectory feasibility, allowing the planner to adaptively tighten safety margins in regions with higher uncertainty. We validate the proposed framework through numerical experiments conducted in dynamic and cluttered environments. The project page is available at https://time-aware-planning.github.io

Paper Structure

This paper contains 13 sections, 2 theorems, 9 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Formulation
  3. Confidence Prediction for Dynamic Obstacles
  4. Problem Formulation
  5. Solution
  6. Global Time-Aware Planning
  7. Local Reactive Planning with Adaptive Conformal Prediction
  8. Calibration-free Adaptive Conformal Prediction
  9. time-aware conformal RRT
  10. Results
  11. CP-SIPP
  12. ACP-RRT
  13. Conclusion

Key Result

theorem 1

Let $\pi$ be any trajectory with collision-check grid $\mathcal{T}(\pi) = \{t_0, \ldots, t_k\}$ generated by a planner employing conformal prediction. For each $t \in \mathcal{T}(\pi)$, let $E_t$ denote the event that the robot’s configuration at time $t$ lies within the conformal safety set $\mathc

Figures (3)

  • Figure 1: CP-SIPP: four frames showing uncertainty-aware CP-SIPP navigating through complex environments with dynamic obstacles
  • Figure 2: Confidence Evolution Comparison: left: The ACP-RRT planner successfully maintains high confidence. right: The baseline RRT (without ACP) fails with a collision at $t=[9,12]$.
  • Figure 3: ACP-RRT: three frames showing online ACP-RRT adaptive generating trees to navigating through obstacles with uncertainty

Theorems & Definitions (2)

  • theorem 1: Trajectory-Level Safety under Marginal Conformal Guarantees
  • theorem 2: Time-average coverage control for calibration-free ACP