Informed Hybrid Zonotope-based Motion Planning Algorithm

-- Optimal path planning in nonconvex free spaces is notoriously challenging, as formulating such problems as mixed-integer linear programs (MILPs) is NP -hard. We propose HZ-MP, an informed Hybrid Zonotope-based Motion Planner, as an alternative approach that decomposes the obstacle-free space and performs low-dimensional face sampling guided by an ellipsotope heuristic, enabling focused exploration along promising transit regions. This structured exploration eliminates the excessive, unreachable sampling that degrades existing informed planners such as AIT* and EIT* in narrow gaps or boxed-goal scenarios. We prove that HZ-MP is probabilistically complete and asymptotically optimal . It converges to near-optimal trajectories in finite time and scales to high-dimensional cluttered scenes.