Unified Linear Parametric Map Modeling and Perception-aware Trajectory Planning for Mobile Robotics

TL;DR

This paper introduces RMRP, a lightweight linear parametric mapping method with theoretical guarantees, and a perception-aware trajectory planner that improves autonomous navigation in complex environments for UAVs and UGVs.

Contribution

It presents RMRP, a novel mapping technique with theoretical guarantees, and RPATR, a unified perception-aware trajectory planning framework for mobile robots.

Findings

RMRP achieves faster mapping with less memory and higher accuracy.

RPATR enables safe, efficient navigation in complex environments.

The framework generalizes well to unobserved areas for proactive planning.

Abstract

Autonomous navigation in mobile robots, reliant on perception and planning, faces major hurdles in large-scale, complex environments. These include heavy computational burdens for mapping, sensor occlusion failures for UAVs, and traversal challenges on irregular terrain for UGVs, all compounded by a lack of perception-aware strategies. To address these challenges, we introduce Random Mapping and Random Projection (RMRP). This method constructs a lightweight linear parametric map by first mapping data to a high-dimensional space, followed by a sparse random projection for dimensionality reduction. Our novel Residual Energy Preservation Theorem provides theoretical guarantees for this process, ensuring critical geometric properties are preserved. Based on this map, we propose the RPATR (Robust Perception-Aware Trajectory Planner) framework. For UAVs, our method unifies grid and Euclidean Signed Distance Field (ESDF) maps. The front-end uses an analytical occupancy gradient to refine initial paths for safety and smoothness, while the back-end uses a closed-form ESDF for trajectory optimization. Leveraging the trained RMRP model's generalization, the planner predicts unobserved areas for proactive navigation. For UGVs, the model characterizes terrain and provides closed-form gradients, enabling online planning to circumvent large holes. Validated in diverse scenarios, our framework demonstrates superior mapping performance in time, memory, and accuracy, and enables computationally efficient, safe navigation for high-speed UAVs and UGVs. The code will be released to foster community collaboration.