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

2026-03-04

AI Summary

This work addresses the limitations of existing inverse perception contracts, which rely on a single ellipsoidal uncertainty set and a fixed confidence level, thereby failing to capture the multimodal and non-convex nature of perception errors and leading to overly conservative navigation policies. To overcome this, we propose Gaussian Mixture Inverse Perception Contracts (GM-IPC), which, for the first time, integrate Gaussian mixture models into the inverse perception contract framework. By representing complex uncertainties as the union of multiple ellipsoidal confidence sets and incorporating probabilistic containment constraints, distribution matching, and empty-space penalties, GM-IPC significantly reduces conservatism while guaranteeing probabilistic safety. The resulting approach enables efficient, adaptive, and real-time safe motion planning, substantially enhancing robotic navigation performance in complex environments.

Technology Category

• Intelligent Robots: Multimodal Perception & Sensor Fusion
• Planning, Routing, and Scheduling: Planning under Uncertainty
• Reasoning under Uncertainty: Uncertainty Representations

Application Category

• Security and Privacy: Large-scale security measurements
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI

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.

Problem

• uncertainty-aware navigation
• inverse perception contract
• multi-modal uncertainty
• Gaussian mixture models
• robot perception

Innovation

• Gaussian Mixture Model
• Inverse Perception Contract
• Uncertainty Quantification
• Safe Navigation
• Multi-modal Uncertainty