Informed Hybrid Zonotope-based Motion Planning Algorithm

TL;DR

The paper introduces HZ-MP, a hybrid zonotope-based motion planner that efficiently explores nonconvex spaces, proving probabilistic completeness and asymptotic optimality, and demonstrating rapid convergence to high-quality paths.

Contribution

It presents a novel informed motion planning algorithm using hybrid zonotopes and face sampling, improving scalability and performance over traditional MILP-based methods.

Findings

HZ-MP converges quickly to high-quality trajectories.

HZ-MP is probabilistically complete and asymptotically optimal.

The method effectively handles narrow passages and enclosed goals.

Abstract

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.