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

2026-07-21

AI Summary

This work addresses the challenge of real-time, high-fidelity geometric mapping and safe, dynamically feasible trajectory generation for drones operating in complex environments. The authors propose OREN-Bubble*, a unified framework that, for the first time, leverages signed distance functions (SDFs) for end-to-end motion planning. It integrates an Octree Residual Network (OREN) to efficiently reconstruct SDFs online by fusing explicit octree structures with implicit neural representations. Coupled with this, the Bubble* planner performs graph search over maximal collision-free spheres to generate safe trajectory corridors. The approach achieves deep integration between mapping and planning, offering theoretical guarantees on completeness and failure detection. Experiments demonstrate that OREN improves SDF estimation accuracy by 22% over baselines, while Bubble* plans trajectories of approximately 90 meters within 1–3 seconds—over three times faster than prior methods—and has been successfully deployed on an onboard quadrotor platform.

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$^\star$, 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 $\approx 90$ m through a cluttered environment in $1$-$3$ sec., whereas baselines take up to $10$ sec. in the same environment.

Problem

• autonomous flight
• signed distance function
• real-time mapping
• motion planning
• collision avoidance

Innovation

• Signed Distance Function
• Octree Residual Network
• Bubble Star Planner
• Real-Time Mapping
• Distance-Accelerated Planning