Heterogeneous Predictor-based Risk-Aware Planning with Conformal Prediction in Dense, Uncertain Environments

TL;DR

H-PRAP addresses real-time planning under dense uncertainty by allocating prediction effort where it most improves safety. It blends heterogeneous predictors with a Probability-based Collision Risk Index (P-CRI) and conformal prediction radii into a chance-constrained MPC, all under a fixed compute budget. The framework enables dynamic routing of obstacles to predictors of differing fidelity while preserving distribution-free safety guarantees. Numerical results show H-PRAP achieves a superior balance between safety and trajectory efficiency compared with single-predictor baselines, particularly under tight compute budgets.

Abstract

Real-time planning among many uncertain, dynamic obstacles is challenging because predicting every agent with high fidelity is both unnecessary and computationally expensive. We present Heterogeneous Predictor-based Risk-Aware Planning (H-PRAP), a framework that allocates prediction effort to where it matters. H-PRAP introduces the Probability-based Collision Risk Index (P-CRI), a closed-form, horizon-level collision index obtained by calibrating a Gaussian surrogate with conformal prediction. P-CRI drives a router that assigns high-risk obstacles to accurate but expensive predictors and low-risk obstacles to lightweight predictors, while preserving distribution-free coverage across heterogeneous predictors through conformal prediction. The selected predictions and their conformal radii are embedded in a chance-constrained model predictive control (MPC) problem, yielding receding-horizon policies with explicit safety margins. We analyze the safety-efficiency trade-off under prediction compute budget: more portion of low-fidelity predictions reduce residual risk from dropped obstacles, but in the same time induces larger conformal radii and degrades trajectory efficiency and shrinks MPC feasibility. Extensive numerical simulations in dense, uncertain environments validate that H-PRAP attains best balance between trajectory success rate (i.e., no collisions) and the time to reach the goal (i.e., trajectory efficiency) compared to single prediction architectures.

Figures (3)

• Figure 1: Overall H-PRAP architecture. [Offline] An obstacle trajectory dataset $\mathcal{D}$ is split into a training set $\mathcal{D}_{\text{train}}$ and a calibration set $\mathcal{D}_{\text{cal}}$. $\mathcal{D}_{\text{train}}$ is used to train the predictor set $\mathcal{P}$, while $\mathcal{D}_{\text{cal}}$ is used to pre-compute predictor-wise conformal radii $\{\epsilon^{\ell}_{h}\}_{h\in\mathcal{H}}$. These radii calibrate the Gaussian surrogate variances $\{(\sigma^\ell_{h})^{2}\}_{h \in \mathcal{H}}$ used in the risk metric, P-CRI. [Online] At each step, sensed obstacles are scored by the P-CRI Calculator; the Router assigns a predictor $\phi_t(k)$ to the sensed obstacles. The Obstacle Prediction module outputs future trajectories $\hat{Y}^{\phi_t(k)}_{t+h}$, which together with the corresponding radii feed the MPC to compute a safe control input $u_t$.
• Figure 2: Sample visualization of $P^1$ versus $P^2$. Since $P^1$ is more accurate than $P^2$, the circular regions (shaded) around each prediction point (solid dot) are smaller compared to those of $P^2$.
• Figure 3: Example screenshot of the agent navigating with H-PRAP.

Theorems & Definitions (8)

• Lemma 1
• Lemma 2
• Proposition 1: Following conformal_prediction_planning
• proof
• Corollary 1
• proof
• Proposition 2: Impact of Conformal Radii on Steps-to-Goal
• proof