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

arXiv: https://arxiv.org/abs/2507.09340 · HTML: https://mlsanity.com/paper/2507.09340/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 74 references that are in the map.
- First posted on arXiv 12 Jul 2025.

## Builds on (most cited first, 27 of 27)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Voxblox: Incremental 3D Euclidean Signed Distance Fields for On-Board MAV Planning](https://mlsanity.com/paper/1611.03631/) (2016)
- [EGO-Planner: An ESDF-free Gradient-based Local Planner for Quadrotors](https://mlsanity.com/paper/2008.08835/) (2020)
- [Robust and Efficient Quadrotor Trajectory Generation for Fast Autonomous Flight](https://mlsanity.com/paper/1907.01531/) (2019)
- [FIESTA: Fast Incremental Euclidean Distance Fields for Online Motion Planning of Aerial Robots](https://mlsanity.com/paper/1903.02144/) (2019)
- [RAPTOR: Robust and Perception-aware Trajectory Replanning for Quadrotor Fast Flight](https://mlsanity.com/paper/2007.03465/) (2020)
- [Learning Perception-Aware Agile Flight in Cluttered Environments](https://mlsanity.com/paper/2210.01841/) (2022)
- [Learning-based 3D Occupancy Prediction for Autonomous Navigation in Occluded Environments](https://mlsanity.com/paper/2011.03981/) (2020)
- [Autonomous Power Line Inspection with Drones via Perception-Aware MPC](https://mlsanity.com/paper/2304.00959/) (2023)
- [Restricted Isometry Property of Gaussian Random Projection for Finite Set of Subspaces](https://mlsanity.com/paper/1704.02109/) (2017)
- [FASTER: Fast and Safe Trajectory Planner for Navigation in Unknown Environments](https://mlsanity.com/paper/2001.04420/) (2020)
- [Autonomous UAV Exploration of Dynamic Environments via Incremental Sampling and Probabilistic Roadmap](https://mlsanity.com/paper/2010.07429/) (2020)
- [Lower bounds for oblivious subspace embeddings](https://mlsanity.com/paper/1308.3280/) (2013)
- [Search-based Motion Planning for Quadrotors using Linear Quadratic Minimum Time Control](https://mlsanity.com/paper/1709.05401/) (2017)
- [FASTER: Fast and Safe Trajectory Planner for Flights in Unknown Environments](https://mlsanity.com/paper/1903.03558/) (2019)
- [Optimal Embedding Dimension for Sparse Subspace Embeddings](https://mlsanity.com/paper/2311.10680/) (2023)
- [An Efficient Spatial-Temporal Trajectory Planner for Autonomous Vehicles in Unstructured Environments](https://mlsanity.com/paper/2208.13160/) (2022)
- [Kinodynamic Motion Planning: A Novel Type Of Nonlinear, Passive Damping Forces And Advantages](https://mlsanity.com/paper/1606.09270/) (2016)
- [PUTN: A Plane-fitting based Uneven Terrain Navigation Framework](https://mlsanity.com/paper/2203.04541/) (2022)
- [Sampling-free obstacle gradients and reactive planning in Neural Radiance Fields (NeRF)](https://mlsanity.com/paper/2205.01389/) (2022)
- [Informed Sampling for Asymptotically Optimal Path Planning (Consolidated Version)](https://mlsanity.com/paper/1706.06454/) (2017)
- [Intelligent bidirectional rapidly-exploring random trees for optimal motion planning in complex cluttered environments](https://mlsanity.com/paper/1703.08944/) (2017)
- [On Principal Components Regression, Random Projections, and Column Subsampling](https://mlsanity.com/paper/1709.08104/) (2017)
- [Deep, spatially coherent Occupancy Maps based on Radar Measurements](https://mlsanity.com/paper/1903.12467/) (2019)
- [APACE: Agile and Perception-Aware Trajectory Generation for Quadrotor Flights](https://mlsanity.com/paper/2403.08365/) (2024)
- [Machine Learning Friendly Set Version of Johnson-Lindenstrauss Lemma](https://mlsanity.com/paper/1703.01507/) (2017)
- [Accurate Analysis of Sparse Random Projections](https://mlsanity.com/paper/2407.14518/) (2024)

## Abstract (arXiv)

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.