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

Abstract: 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^*, 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^* search and returns a bubble sequence that forms a safe corridor for trajectory optimization. We demonstrate the integrated OREN–Bubble^* 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^* finds trajectories spanning ≈90 m through a cluttered environment in 1–3 sec., whereas baselines take up to 10 sec. in the same environment.

Overview

Mapping and planning are co-designed around one representation: a signed distance function. OREN reconstructs the SDF online from depth observations, and Bubble^* consumes the distance values directly to accelerate planning; the resulting bubble corridor is handed to a trajectory optimizer for smooth, dynamically feasible flight.

22%

better SDF estimation than baseline mappers

1–3 s

to plan ≈90 m trajectories where baselines take up to 10 s

Onboard

real-time mapping and planning under tight compute constraints

Reconstructed mesh with SDF slice and bubble corridor — Everything in one view: the mesh reconstructed by OREN, a horizontal slice of the SDF colored by distance to the nearest obstacle, and the Bubble^* bubble corridor with the planned trajectory threading through the clutter.

Simulation

Forest

Industrial

Exploring the forest while OREN maps it online.

Exploring the industrial environment while OREN maps it online.

Flying a Bubble^* trajectory through the forest.

Flying a Bubble^* trajectory through the industrial environment.

Mesh reconstruction comparison — Reconstruction quality comparison in the industrial environment.

Trajectory and bubbles through reconstructed environment — Planned trajectory and bubble corridor through the reconstructed environment.

Real-World Flight

Onboard mapping run: OREN builds the SDF online during flight.

Mesh from the mapping run with bubble corridor and trajectory — The map created from the mapping run, with a Bubble^* corridor and planned trajectory.

Planned routes across real-world runs — Planned routes over the online-built SDF across real-world runs.

OREN: Octree Residual Network

OREN pairs an explicit octree prior with an implicit neural residual. The octree gives the efficiency and incremental updates of volumetric mapping; the neural residual restores the accuracy and differentiability of implicit neural SDFs. Together they reconstruct Euclidean signed distance fields online from point clouds.

System overview diagram — Depth and pose stream into OREN, which maintains an online SDF; Bubble^* plans over the SDF and trajectory optimization runs inside the bubble corridor.

Bubble^*: Distance-Accelerated Planning

Bubble^* grows maximal collision-free balls (bubbles) directly from the SDF and searches over a graph of bubbles instead of a dense grid, with formal guarantees of termination, completeness, and failure detection. This drastically reduces collision checks compared to grid-based A^*, and the resulting bubble sequence doubles as a safe corridor for trajectory optimization.

Bubble* successor generation — Successor generation: new bubbles are grown on the frontier of the current one.

Bubble* search in a 2D environment — Bubble^* search in a 2D environment: few bubbles cover the path.

Try It

Draw obstacles on the grid, drag the start and goal nodes, and press Start Search - or switch algorithms to compare Bubble^* against A^* and others. Open the demo full screen ↗

Gazebo Demo

This repository is a self-contained ROS 2 + Gazebo simulation of the full approach: a quadrotor orbits an obstacle field streaming depth images, OREN fuses depth and pose into an SDF online, and the quad then plans with Bubble^*, optimizes trajectories with erl_gcopter through the bubble corridors, and flies them. Everything (ROS 2, Gazebo, PyTorch/CUDA) is provisioned by pixi.

The demo in action: the quad orbits the obstacle field while OREN maps, then plans and flies trajectories over the learned SDF.

Mesh reconstructed online by OREN — Mesh extracted from the SDF that OREN reconstructs online from the demo's depth stream.

See the README for requirements and instructions on running the demo.

Code

OREN code
Online neural Euclidean SDF mapping. Bubble^* code
Distance-accelerated search-based planner. erl_gcopter code
Trajectory optimization through bubble corridors.

Acknowledgements

We gratefully acknowledge support from ARL DCIST CRA W911NF-17-2-0181 (N. Atanasov, Z. Dai), a research gift fund established by Shield AI (J. Stanley), and the Ministry of Trade, Industry and Energy (MOTIE), Korea, under the Strategic Technology Development Program, supervised by Korea Institute for Advancement of Technology (KIAT) [Grant No. P0026052] (K.M.B. Lee).

BibTeX

If you find this work useful, please cite our paper:

@article{stanley2026distances,
  title     = {From Distances to Trajectories: Real-Time Signed Distance Function Mapping and Distance-Accelerated Motion Planning for {UAVs}},
  author    = {Stanley, Jason and Dai, Zhirui and Qian, Qihao and Ho, Tzu-Chin and Fan, Tianxing and Saha, Siddharth and Barngrover, Christopher and Lee, Ki Myung Brian and Atanasov, Nikolay},
  journal   = {arXiv preprint arXiv:2607.19306},
  year      = {2026}
}

You can also cite the OREN component paper:

@inproceedings{dai2026oren,
  title     = {{OREN}: Octree Residual Network for Real-Time {Euclidean} Signed Distance Mapping},
  author    = {Dai, Zhirui and Qian, Qihao and Fan, Tianxing and Atanasov, Nikolay},
  booktitle = {IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)},
  year      = {2026}
}