用分块采样提升复杂空间路径规划效率，解决狭窄通道难题。
Informed Hybrid Zonotope-based Motion Planning Algorithm
- 将无障区分解并基于椭球体启发式进行低维面采样
- 在少量迭代内收敛到高质量路径，避免无效采样
- 适合狭窄通道或封闭目标的高精度路径规划场景
非凸自由空间中的最优路径规划面临巨大计算挑战。传统方法将其建模为混合整数线性规划（MILP），但求解一般MILP计算不可行，严重制约可扩展性。为此，我们提出HZ-MP：一种基于混合超椭体的知情运动规划算法，通过分解障碍物自由空间，并依据椭球体启发式执行低维面采样，聚焦于有潜力的过渡区域。这种结构化探索有效缓解了现有知情规划器在狭窄通道或封闭目标场景中因过度无效采样导致的性能下降。理论证明了HZ-MP的概率完备性和渐近最优性，并实验证明其可在少数迭代内快速收敛至高质量轨迹。
原文摘要 · Abstract (English)
Optimal path planning in nonconvex free spaces poses substantial computational challenges. A common approach formulates such problems as mixed-integer linear programs (MILPs); however, solving general MILPs is computationally intractable and severely limits scalability. To address these limitations, we propose HZ-MP, an informed Hybrid Zonotope-based Motion Planner, which decomposes the obstacle-free space and performs low-dimensional face sampling guided by an ellipsotope heuristic, thereby concentrating exploration on promising transition regions. This structured exploration mitigates the excessive wasted sampling that degrades existing informed planners in narrow-passage or enclosed-goal scenarios. We prove that HZ-MP is probabilistically complete and asymptotically optimal, and demonstrate empirically that it converges to high-quality trajectories within a small number of iterations.
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