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.

翻译：非凸自由空间中的最优路径规划面临严峻的计算挑战。现有方法通常将此类问题建模为混合整数线性规划（MILP），然而求解通用MILP在计算上难以处理，严重限制了其可扩展性。为解决这些局限，我们提出HZ-MP，一种基于混合Zonotope的启发式运动规划器，该方法将障碍物自由空间进行分解，并利用椭球体启发式引导实现低维面采样，从而将探索聚焦于有前景的过渡区域。这种结构化探索机制有效减少了现有启发式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退化问题。我们证明了HZ-MP具有概率完备性和渐进最优性，并通过实验表明该方法可在少量迭代内收敛到高质量轨迹。