Egocentric Conformal Prediction for Safe and Efficient Navigation in Dynamic Cluttered Environments

TL;DR

This paper tackles safety-aware navigation in dynamic clutter by shifting from obstacle-centric to egocentric conformal prediction (ECP). It introduces an egocentric score that evaluates prediction errors only in terms of their impact on the ego-vehicle’s safety, and integrates this with a tractable Egocentric CP-MPC (ECP-MPC) framework. The authors prove asymptotic safety guarantees and demonstrate cost efficiency improvements over prior ACP-based approaches, validated on dense pedestrian datasets with realistic motion models. The work advances practical safe autonomous navigation by reducing unnecessary conservatism while preserving formal safety, and it points to generalizations to broader safety constraints and imperfect sensing.

Abstract

Conformal prediction (CP) has emerged as a powerful tool in robotics and control, thanks to its ability to calibrate complex, data-driven models with formal guarantees. However, in robot navigation tasks, existing CP-based methods often decouple prediction from control, evaluating models without considering whether prediction errors actually compromise safety. Consequently, ego-vehicles may become overly conservative or even immobilized when all potential trajectories appear infeasible. To address this issue, we propose a novel CP-based navigation framework that responds exclusively to safety-critical prediction errors. Our approach introduces egocentric score functions that quantify how much closer obstacles are to a candidate vehicle position than anticipated. These score functions are then integrated into a model predictive control scheme, wherein each candidate state is individually evaluated for safety. Combined with an adaptive CP mechanism, our framework dynamically adjusts to changes in obstacle motion without resorting to unnecessary conservatism. Theoretical analyses indicate that our method outperforms existing CP-based approaches in terms of cost-efficiency while maintaining the desired safety levels, as further validated through experiments on real-world datasets featuring densely populated pedestrian environments.

Figures (4)

• Figure 1: Example of ACP-MPC applied to a mobile navigation scenario built from the UCY zara2 dataset lerner2007crowds, shown in temporal order. The predicted trajectories, denoted as $\mathbf{Y}_{t+i|t}$, are drawn as pink dashed lines, while the corresponding ground truth positions, $\mathbf{Y}_{t+i}$, are depicted as yellow solid lines. The shaded circles represent the confidence sets $\mathsf{C}^{\text{obs}}_{t+i|t}$ generated by ACP. Even though the observed prediction errors are not safety-critical, they cause the ACP parameters to decrease and the confidence sets to expand over time, leading to increasingly conservative vehicle motion plans (in cyan).
• Figure 2: Illustration of the egocentric score function in a scenario with three moving obstacles. In our formulation, errors for obstacles $v_1$ and $v_2$ are neglected since they are far from a given state $\mathbf{x}$, making these errors irrelevant for assessing its safety. Although a prediction error occurs for $v_3$, the obstacle closest to $\mathbf{x}$, it does not affect our score function because the true future position is farther from $\mathbf{x}$ than the predicted position. Consequently, $s^{\mathbf{x}}_1 = 0$ in this case.
• Figure 3: Comparison between the obstacle-centric safety constraint $\mathcal{S}^{\text{obs}}_{t+i|t}$ and its egocentric counterpart $\mathcal{S}^{\text{ego}}_{t+i|t}$. The gray area represents the obstacle-centric confidence set $\mathsf{C}^{\text{obs}}_{t+i|t}$ proposed by the original ACP (with its boundary shown in red). In this scenario, an obstacle undergoes abrupt velocity changes, causing $\mathsf{C}^{\text{obs}}_{t+3|t}$ to fail to cover the true future position $\mathbf{y}_{t+3}$ for $t \in [7, 9]$. Consequently, the ACP parameter $\alpha^3_t$ diminishes during $t \in [10, 12]$, and the size of $\mathcal{S}^{\text{obs}}_{t+3|t}$ rapidly shrinks from the region outlined by the red dotted boundary to that with the red solid boundary. In contrast, the egocentric score \ref{['eq:egocentric-score']} increases only for $\mathbf{x}$ on the right of the obstacle, since the prediction error is harmless for states on the left side. As a result, $\mathcal{S}^{\text{ego}}_{t+3|t}$ shrinks only from the right side.
• Figure 4: Trajectories of the vehicle produced by ECP-MPC, ACP-MPC, and the conformal controller in the univ scenario.

Theorems & Definitions (7)

• Proposition 1
• proof
• Proposition 2
• proof
• Theorem 1
• proof
• proof