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

• URL: http://arxiv.org/abs/2603.04329v1
• Date: Wed, 04 Mar 2026 17:48:18 GMT
• Title: Gaussian Mixture-Based Inverse Perception Contract for Uncertainty-Aware Robot Navigation
• Abstract summary: An inverse perception contract (IPC) provides such a connection by mapping estimates to sets that contain the ground truth with high confidence.<n>We introduce Gaussian Mixture-based Inverse Perception Contract (GM-IPC), which extends IPC to represent uncertainty with unions of ellipsoidal confidence sets.<n>We show that the resulting uncertainty characterizations can be leveraged in downstream planning frameworks for real-time safe navigation.
• Score: 14.159772216001954
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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