Low-Latency Mapless ESDF Queries for MAV Reactive Collision Avoidance

Optimization-based local planning and control require high-rate evaluation of collision-avoidance constraints over a prediction horizon. Accurately accounting for robot and obstacle geometry in these evaluations can be computationally expensive. The resulting bottleneck motivates collision-avoidance constraints that combine computational efficiency with geometric fidelity. The proposed polygonal signed distance function (PSDF) returns the minimum of exact signed distances between a convex polygonal robot footprint and convex obstacle components represented by their boundary edges. It is implemented as a training-free, branch-free tensorized geometric pipeline enabling batched GPU execution and automatic differentiation. The PSDF is embedded in model predictive control by locally linearizing the PSDF-based safety constraint within a sequential quadratic programming--based real-time iteration scheme, yielding the PSDF-embedded model predictive controller (PSDF-MPC). The design separates CPU/GPU computation so that the GPU evaluates batched PSDF values and gradients while the CPU solves a sparse quadratic program whose size and sparsity are determined by system dimensions and horizon length rather than obstacle and edge counts. Microbenchmarks show that PSDF scales favorably relative to geometric and learned collision-field baselines. Closed-loop comparisons in simulation, together with real-world navigation experiments, demonstrate that PSDF-MPC operates in real time and achieves collision-free navigation in dense polygonal environments.

Real-time 3D mapping is fundamental for autonomous robotic navigation, with Euclidean Signed Distance Fields (ESDFs) serving as the standard representation for online motion planning. While recent advancements in non- projective distance fields yield highly accurate maps, their computational overhead remains a severe bottleneck. Conventional integrators redundantly re-fuse millions of depth pixels every frame, even long after the corresponding voxels have converged, wasting significant computational resources in environments dominated by large planar surfaces. In this paper, we present SHIFT (Surface-aware High-speed Integration For TSDFs), an efficient mapping framework designed to reduce this per-frame update cost. By exploiting structural redundancy directly from 3D depth geometry, SHIFT compresses flat local regions into weighted super-rays and freezes flat-voxel gradients. A compact ESDF voxel layout further reduces the memory footprint of the remaining wavefront. Extensive evaluations across various RGB-D and LiDAR sequences show that SHIFT cuts TSDF cost by 1.42 to 4.07 times, while holding mesh error within millimeters, and reduces ESDF-layer memory by up to 28%

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.