Homotopic information gain for sparse active target tracking

2026-02-20

AI Summary

This work addresses the ambiguity in conventional information gain formulations within multimodal motion scenarios, which hinders the performance of perception-aware trajectory planning for active target tracking. We propose “homotopic information gain”—a novel information-theoretic measure grounded in homotopy classes of target trajectories, which encode high-level motion patterns. This measure serves as a lower bound on information gain, is inherently sparse, and aligns naturally with environmental obstacle structures, making it well-suited for multimodal settings. By integrating probabilistic motion models, homotopy class analysis, and belief-space exploration, we optimize sensing trajectories to maximize this homotopic information gain. Experiments on both real-world and simulated pedestrian datasets demonstrate that our approach significantly improves future trajectory prediction accuracy with fewer observations, outperforming strategies based on traditional information gain.

Technology Category

• Machine Learning: Information Theory
• Intelligent Robots: Multimodal Perception & Sensor Fusion
• Planning, Routing, and Scheduling: Activity and Plan Recognition

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements

Abstract

The problem of planning sensing trajectories for a mobile robot to collect observations of a target and predict its future trajectory is known as active target tracking. Enabled by probabilistic motion models, one may solve this problem by exploring the belief space of all trajectory predictions given future sensing actions to maximise information gain. However, for multi-modal motion models the notion of information gain is often ill-defined. This paper proposes a planning approach designed around maximising information regarding the target's homotopy class, or high-level motion. We introduce homotopic information gain, a measure of the expected high-level trajectory information given by a measurement. We show that homotopic information gain is a lower bound for metric or low-level information gain, and is as sparsely distributed in the environment as obstacles are. Planning sensing trajectories to maximise homotopic information results in highly accurate trajectory estimates with fewer measurements than a metric information approach, as supported by our empirical evaluation on real and simulated pedestrian data.

Problem

• active target tracking
• information gain
• homotopy class
• sparse sensing
• multi-modal motion models

Innovation

• homotopic information gain
• active target tracking
• belief space planning
• multi-modal motion models
• sparse sensing