A cell-decomposition based path planner for 3D navigation in constrained workspaces

Autonomous robot navigation requires the rapid generation of obstacle-free regions for trajectory planning. However, existing corridor generators struggle to meet real-time, sensor-rate computational constraints. To resolve this bottleneck, we introduce PathCover, a framework driven by RISP; a novel randomized algorithm that constructs convex polytopes directly from raw point cloud data in expected linear time under a mild probabilistic elimination condition. PathCover generates sequences of overlapping, obstacle-free polytopes that safely constrain downstream MPC and trajectory optimization. We mathematically guarantee that the algorithm terminates in finite steps while ensuring continuous progress along any obstacle-free reference path. Extensive benchmarks on synthetic and real-world LiDAR datasets demonstrate an order-of-magnitude speedup over state-of-the-art methods while maintaining comparable corridor volumes. The complete pipeline is validated via high-fidelity quadrotor simulations and physical deployment on a quadrupedal robot navigating constrained environments using live LiDAR perception.

Motion planning through narrow passages remains a core challenge: sampling-based planners rarely place samples inside these narrow but critical regions, and even when samples land inside a passage, the straight-line connections between them run close to obstacle boundaries and are frequently rejected by collision checking. Decomposition-based planners resolve both issues by partitioning free space into convex cells -- every passage is captured exactly as a cell boundary, and any path within a cell is collision-free by construction. However, the number of candidate corridors through the cell graph grows combinatorially with environment complexity, creating a bottleneck in corridor selection. We present GNN-DIP, a framework that addresses this by integrating a Graph Neural Network (GNN) with a two-phase Decomposition-Informed Planner (DIP). The GNN predicts portal scores on the cell adjacency graph to bias corridor search toward near-optimal regions while preserving completeness. In 2D, Constrained Delaunay Triangulation (CDT) with the Funnel algorithm yields exact shortest paths within corridors; in 3D, Slab convex decomposition with portal-face sampling provides near-optimal path evaluation. Benchmarks on 2D narrow-passage scenarios, 3D bottleneck environments with up to 246 obstacles, and dynamic 2D settings show that GNN-DIP achieves 99--100% success rates with 2--280 times speedup over sampling-based baselines.

Existing exact methods for 4-connected grid pathfinding reduce online search, but often either retain fine-grained search states or require substantial preprocessing. This paper presents Key-Interval A* (KIA*), an optimal pathfinding algorithm that uses lightweight preprocessing to construct and search over a compact interval-level abstraction of free space. KIA* represents free space using intervals: maximal contiguous runs of traversable cells. It extracts key intervals that capture structural boundary changes and connects them through contiguous non-key regions. KIA* then performs A*-style search on the resulting key-interval graph and constructively reconstructs grid paths from interval chains, without cell-level local search. We prove the completeness and optimality of KIA* on 4-connected grids. Experiments on standard benchmarks show that KIA* preserves exact shortest-path lengths and achieves the fastest runtime on seven of eight benchmark groups, with the largest gains on structured and game maps.