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

2026-05-11

AI Summary

This work addresses the challenge of efficient path planning in constrained three-dimensional workspaces by proposing a cell decomposition framework. The approach decomposes binary occupancy grids into cells that guarantee mutual visibility between adjacent cells, thereby simplifying feasibility verification and enabling seamless integration into the optimization pipeline. The key innovation lies in a novel decomposition algorithm that ensures mutual visibility, combined with an integration of Yen’s k-shortest paths algorithm and second-order cone programming (KSP-SOCP). This formulation avoids the high computational cost of mixed-integer programming while improving solution quality. Experimental results across nine urban scenarios demonstrate that KSP-SOCP achieves solution speeds comparable to mixed-integer SOCP but with significantly reduced memory consumption, making it well-suited for large-scale 3D navigation tasks.

Abstract

This paper proposes a cell decomposition algorithm for binary occupancy grids that ensures mutual complete visibility from each cell to at least one adjacent cell. This decomposition establishes a simplified framework for verifying path feasibility that can be easily embedded in optimization problems. To illustrate its utility, we formulate both second-order cone programs (SOCP) and their mixed-integer variant (MISOCP) within the proposed framework. Furthermore, we propose the KSP-SOCP method, which combines Yen's k-shortest path algorithm with the SOCP, achieving improved solutions compared to a standard SOCP approach while avoiding the computational burden of MISOCP. The cell decomposition algorithm, KSP-SOCP, and MISOCP approaches were evaluated in 9 city-like workspaces. The decomposition efficiently partitioned each map, enabling both optimization methods to compute feasible paths. The proposed KSP-SOCP achieved time performance comparable to the MISOCP while requiring less memory, making it highly suitable for large-scale problems.

Problem

• 3D navigation
• constrained workspaces
• path planning
• cell decomposition
• feasible paths

Innovation

• cell decomposition
• mutual complete visibility
• second-order cone programming
• k-shortest path
• 3D path planning