Informed Hybrid Zonotope-based Motion Planning Algorithm

2025-07-12

AI Summary

This paper addresses the NP-hard problem of optimal path planning in non-convex free spaces. The proposed framework employs a hybrid zonotope-based motion planning approach: first, the obstacle-free space is decomposed into zonotopes; second, an ellipsotope-informed heuristic guides low-dimensional face sampling, drastically reducing invalid samples; finally, high-quality trajectories are generated via nonlinear constrained optimization. The key contribution is the novel integration of ellipsotopes into the face-sampling guidance mechanism—uniquely balancing geometric expressiveness and computational efficiency. Theoretical analysis establishes probabilistic completeness and asymptotic optimality. Experiments demonstrate superior performance in high-dimensional, complex environments—particularly those with narrow passages and dense obstacles—achieving faster convergence, higher-quality paths, and greater robustness and scalability compared to state-of-the-art methods including AIT* and EIT*.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Security and Privacy: Large-scale security measurements

Abstract

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.

Problem

• Optimal path planning in nonconvex free spaces
• Reducing excessive sampling in narrow gaps
• Scaling to high-dimensional cluttered scenes

Innovation

• Hybrid Zonotope-based obstacle-free space decomposition
• Ellipsotope-guided low-dimensional face sampling
• Focused exploration in promising transit regions