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巨大的计算挑战。一种常见方法是将此类问题建模为混合整数线性规划（MILP），然而求解通用MILP在计算上难以处理且严重限制了可扩展性。为解决这些限制，我们提出HZ-MP——一种基于信息混合区域划分的运动规划器，它将无障碍空间进行分解，并执行由椭圆体启发式引导的低维面采样，从而将探索集中在有希望的过渡区域。这种结构化探索减轻了在窄通道或封闭目标场景中导致现有信息规划器性能下降的过度无效采样。我们证明了HZ-MP具有概率完备性和渐近最优性，并通过实验表明它能在少量迭代次数内收敛到高质量轨迹。