# From Distances to Trajectories: Real-Time Signed Distance Function Mapping and Distance-Accelerated Motion Planning for UAVs

arXiv: https://arxiv.org/abs/2607.19306 · HTML: https://mlsanity.com/paper/2607.19306/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 66 references that are in the map.
- First posted on arXiv 21 Jul 2026.

## Builds on (most cited first, 30 of 37)

- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [The Replica Dataset: A Digital Replica of Indoor Spaces](https://mlsanity.com/paper/1906.05797/) (2019)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [Voxblox: Incremental 3D Euclidean Signed Distance Fields for On-Board MAV Planning](https://mlsanity.com/paper/1611.03631/) (2016)
- [iSDF: Real-Time Neural Signed Distance Fields for Robot Perception](https://mlsanity.com/paper/2204.02296/) (2022)
- [Autonomous Drone Racing with Deep Reinforcement Learning](https://mlsanity.com/paper/2103.08624/) (2021)
- [PIN-SLAM: LiDAR SLAM Using a Point-Based Implicit Neural Representation for Achieving Global Map Consistency](https://mlsanity.com/paper/2401.09101/) (2024)
- [Robust and Efficient Quadrotor Trajectory Generation for Fast Autonomous Flight](https://mlsanity.com/paper/1907.01531/) (2019)
- [Differential Flatness of Quadrotor Dynamics Subject to Rotor Drag for Accurate Tracking of High-Speed Trajectories](https://mlsanity.com/paper/1712.02402/) (2017)
- [FIESTA: Fast Incremental Euclidean Distance Fields for Online Motion Planning of Aerial Robots](https://mlsanity.com/paper/1903.02144/) (2019)
- [Funnel Libraries for Real-Time Robust Feedback Motion Planning](https://mlsanity.com/paper/1601.04037/) (2016)
- [Motion Planning around Obstacles with Convex Optimization](https://mlsanity.com/paper/2205.04422/) (2022)
- [nvblox: GPU-Accelerated Incremental Signed Distance Field Mapping](https://mlsanity.com/paper/2311.00626/) (2023)
- [H2-Mapping: Real-time Dense Mapping Using Hierarchical Hybrid Representation](https://mlsanity.com/paper/2306.03207/) (2023)
- [Geometrically Constrained Trajectory Optimization for Multicopters](https://mlsanity.com/paper/2103.00190/) (2021)
- [Fast, Autonomous Flight in GPS-Denied and Cluttered Environments](https://mlsanity.com/paper/1712.02052/) (2017)
- [Multi-Camera LiDAR Inertial Extension to the Newer College Dataset](https://mlsanity.com/paper/2112.08854/) (2021)
- [Regularized Deep Signed Distance Fields for Reactive Motion Generation](https://mlsanity.com/paper/2203.04739/) (2022)
- [Representing Robot Geometry as Distance Fields: Applications to Whole-body Manipulation](https://mlsanity.com/paper/2307.00533/) (2023)
- [Configuration Space Distance Fields for Manipulation Planning](https://mlsanity.com/paper/2406.01137/) (2024)
- [Search-based Motion Planning for Quadrotors using Linear Quadratic Minimum Time Control](https://mlsanity.com/paper/1709.05401/) (2017)
- [Bubble Planner: Planning High-speed Smooth Quadrotor Trajectories using Receding Corridors](https://mlsanity.com/paper/2202.12177/) (2022)
- [Multi-Resolution 3D Mapping with Explicit Free Space Representation for Fast and Accurate Mobile Robot Motion Planning](https://mlsanity.com/paper/2010.07929/) (2020)
- [HotSpot: Signed Distance Function Optimization with an Asymptotically Sufficient Condition](https://mlsanity.com/paper/2411.14628/) (2024)
- [Faithful Euclidean Distance Field from Log-Gaussian Process Implicit Surfaces](https://mlsanity.com/paper/2010.11487/) (2020)
- [Fast Path Planning Through Large Collections of Safe Boxes](https://mlsanity.com/paper/2305.01072/) (2023)
- [VDB-GPDF: Online Gaussian Process Distance Field with VDB Structure](https://mlsanity.com/paper/2407.09649/) (2024)
- [Safe Bubble Cover for Motion Planning on Distance Fields](https://mlsanity.com/paper/2408.13377/) (2024)

## Built on by (most cited first, 1 of 1)

- [E2DRL: End-to-End Differentiable Reinforcement Learning for 3D Obstacle Avoidance in Quadruped Robots](https://mlsanity.com/paper/2610.19627/) (2026)

## Abstract (arXiv)

Autonomous flight in cluttered environments requires a robot to build a geometric map of its surroundings and plan safe, dynamically feasible trajectories, all onboard and in real time. Conventional approaches treat mapping and planning as separate stages and often rely on binary occupancy for collision checking. We argue that these two stages should be co-designed around a single representation: a signed distance function (SDF). By encoding distance to the nearest obstacle, an SDF provides richer information for planning and trajectory optimization than occupancy alone. We develop an Octree REsidual Network (OREN) that pairs an explicit octree prior with an implicit neural residual to reconstruct SDFs online from point cloud observations with the efficiency of volumetric methods and the accuracy and differentiability of neural methods. In tandem, we develop Bubble^star, a search-based planner that exploits the distance information to grow maximal collision-free balls, which we call bubbles, with formal guarantees of termination, completeness, and failure detection. Planning over a graph of bubbles significantly reduces collision checks compared to a grid-based A^star search and returns a bubble sequence that forms a safe corridor for trajectory optimization. We demonstrate the integrated OREN-Bubble^star approach onboard a quadrotor, navigating unseen indoor environments in real time under tight compute constraints. OREN improves SDF estimation by 22% compared to baselines, while Bubble^star finds trajectories spanning ≈ 90 m through a cluttered environment in 1-3 sec., whereas baselines take up to 10 sec. in the same environment.