We introduce a computationally efficient mapping and planning approach for autonomous flight that unifies signed distance function (SDF) reconstruction with SDF-accelerated motion planning. Our mapping method, OREN (Octree Residual Network), reconstructs a differentiable non-truncated SDF online by combining an explicit octree prior with an implicit neural residual. This hybrid approach achieves the accuracy of neural network methods at the memory and runtime efficiency of volumetric methods. For planning, we propose Bubble, a graph of collision-free bubbles that forms a safe corridor with guarantees of termination, completeness, and failure detection. This bubble corridor defines safety constraints for dynamically feasible trajectory optimization. Compared with baselines, Bubble is the only method that pairs a compact high-clearance corridor with a smooth underlying path, keeping both its search and trajectory optimization fast.
Related Work
This section reviews existing methods for SDF reconstruction and integrated mapping and planning for aerial robots.
OREN: Online Octree Residual Network
OREN reconstructs a differentiable non-truncated signed distance function online by combining an explicit octree prior with an implicit neural residual. The octree prior is computed by fusing depth measurements into a truncated signed distance field (TSDF) stored in an octree structure. The neural residual is a small multilayer perceptron (MLP) that learns to correct the errors in the octree prior, particularly in regions far from surfaces where the TSDF approximation degrades.
The key insight is that the octree prior captures the coarse structure of the environment efficiently, while the neural network models only the residual error. This decomposition allows OREN to achieve the accuracy of purely neural methods with significantly lower memory footprint and faster inference. The training data for the residual network is collected incrementally from the octree and ground truth depth images, enabling online adaptation to new environments.
Bubble*: Distance-Accelerated Motion Planning
Bubble constructs a graph of collision-free bubbles using the learned SDF. Each bubble is a sphere centered at a point in free space with radius equal to the distance to the nearest obstacle. These bubbles form a safe corridor through the environment. The algorithm searches over the bubble graph using a variant of A that considers both the cost to reach a bubble and the clearance it provides.
Bubble provides guarantees of termination, completeness, and failure detection. If a path exists through the bubble graph, Bubble will find it. If no path exists, Bubble* terminates and reports failure. The bubble corridor defines safety constraints for dynamically feasible trajectory optimization, ensuring the planned trajectory remains collision-free.
Trajectory Optimization
Given a bubble corridor from Bubble*, we formulate a trajectory optimization problem that generates smooth, dynamically feasible trajectories. The safety constraints are encoded as inequality constraints that require each point on the trajectory to stay within the union of bubbles. This formulation decouples the combinatorial planning problem from the continuous optimization, enabling efficient solutions.
The trajectory is parameterized as a piecewise polynomial, and we minimize jerk subject to constraints on dynamics and safety. The optimization is solved using sequential quadratic programming, with the bubble corridor providing a warm start that accelerates convergence.
Experimental Results
We evaluate OREN and Bubble* on both simulated and real-world quadrotor experiments. In simulation, we compare OREN against state-of-the-art SDF mapping methods, including purely volumetric approaches and purely neural approaches. OREN achieves lower reconstruction error than volumetric methods while matching the accuracy of neural methods, with memory usage comparable to volumetric methods and significantly lower than neural methods.
For planning, we compare Bubble against baseline planners including RRT, BIT, and standard corridor-based methods. Bubble produces trajectories with comparable smoothness and safety to the best baselines while requiring less computation time. The key advantage is that Bubble* consistently finds high-clearance corridors that lead to faster trajectory optimization, even in cluttered environments.
Conclusion
This paper developed an efficient unified approach for SDF reconstruction and SDF-accelerated motion planning for safe autonomous flight. Our mapping method, OREN, reconstructs differentiable non-truncated SDF online by combining an explicit octree prior with an implicit neural residual, attaining the accuracy of neural network methods at the memory and runtime efficiency of volumetric ones. Exploiting the SDF representation, Bubble constructs a graph of collision-free bubbles, which forms a safe corridor with guarantees of termination, completeness, and failure detection. Such a bubble corridor defines safety constraints for dynamically feasible trajectory optimization. Compared with baselines, Bubble is the only method that pairs a compact high-clearance corridor with a smooth underlying path, which keeps both its search and its trajectory optimization fast.
Frequently Asked Questions
How does OREN combine octree and neural methods for SDF mapping? OREN uses an octree to store a coarse TSDF prior from depth data, then a small neural network learns to correct the residual errors, achieving accuracy comparable to pure neural methods with memory efficiency similar to volumetric approaches.
*What guarantees does Bubble provide for motion planning?* Bubble guarantees termination, completeness (finding a path if one exists), and failure detection (reporting when no path exists through the bubble graph).
How does the bubble corridor accelerate trajectory optimization? The bubble corridor provides a high-clearance warm start for the trajectory optimizer, both reducing the search space for feasible trajectories and improving convergence speed compared to methods that use narrow corridors.
*Can OREN and Bubble run in real-time on quadrotors?** Yes, the mapping and planning approach was demonstrated on quadrotor hardware, with the octree providing fast updates from depth images and the neural residual requiring minimal computation per query.