Gaussian Mixture-Based Inverse Perception Contract for Uncertainty-Aware Robot Navigation

TL;DR

This paper introduces GM-IPC, a novel uncertainty representation for robot perception using Gaussian mixtures, improving navigation safety and efficiency by capturing complex error structures.

Contribution

The paper presents GM-IPC, extending inverse perception contracts with Gaussian mixture models to better represent multi-modal uncertainties in robot perception.

Findings

GM-IPC captures multi-modal and irregular perception errors.

The approach enables less conservative and more adaptive navigation.

Formal guarantees ensure the validity and compactness of uncertainty sets.

Abstract

Reliable navigation in cluttered environments requires perception outputs that are not only accurate but also equipped with uncertainty sets suitable for safe control. An inverse perception contract (IPC) provides such a connection by mapping perceptual estimates to sets that contain the ground truth with high confidence. Existing IPC formulations, however, instantiate uncertainty as a single ellipsoidal set and rely on deterministic trust scores to guide robot motion. Such a representation cannot capture the multi-modal and irregular structure of fine-grained perception errors, often resulting in over-conservative sets and degraded navigation performance. In this work, we introduce Gaussian Mixture-based Inverse Perception Contract (GM-IPC), which extends IPC to represent uncertainty with unions of ellipsoidal confidence sets derived from Gaussian mixture models. This design moves beyond deterministic single-set abstractions, enabling fine-grained, multi-modal, and non-convex error structures to be captured with formal guarantees. A learning framework is presented that trains GM-IPC to account for probabilistic inclusion, distribution matching, and empty-space penalties, ensuring both validity and compactness of the predicted sets. We further show that the resulting uncertainty characterizations can be leveraged in downstream planning frameworks for real-time safe navigation, enabling less conservative and more adaptive robot motion while preserving safety in a probabilistic manner.