Long-Horizon Geometry-Aware Navigation among Polytopes via MILP-MPC and Minkowski-Based CBFs

2026-03-31

AI Summary

This work addresses the challenge of long-horizon, safe navigation for polyhedral robots operating in complex non-convex environments under both dynamic and geometric constraints. The authors propose a hierarchical planning-and-control framework: at the high level, a global collision-free trajectory is generated by integrating mixed-integer linear programming (MILP) with model predictive control (MPC); at the low level, a safety filter based on higher-order control barrier functions (HOCBFs) is designed using the signed distance in Minkowski difference space to explicitly guarantee safety with respect to the robot’s exact geometric shape. By unifying global planning with geometry-aware safety enforcement, the approach effectively overcomes the susceptibility of purely reactive CBF methods to topological local minima, achieving real-time, safe, and geometrically precise navigation for both single- and double-integrator systems in U-shaped and maze-like environments.

Abstract

Autonomous navigation in complex, non-convex environments remains challenging when robot dynamics, control limits, and exact robot geometry must all be taken into account. In this paper, we propose a hierarchical planning and control framework that bridges long-horizon guidance and geometry-aware safety guarantees for a polytopic robot navigating among polytopic obstacles. At the high level, Mixed-Integer Linear Programming (MILP) is embedded within a Model Predictive Control (MPC) framework to generate a nominal trajectory around polytopic obstacles while modeling the robot as a point mass for computational tractability. At the low level, we employ a control barrier function (CBF) based on the exact signed distance in the Minkowski-difference space as a safety filter to explicitly enforce the geometric constraints of the robot shape, and further extend its formulation to a high-order CBF (HOCBF). We demonstrate the proposed framework in U-shaped and maze-like environments under single- and double-integrator dynamics. The results show that the proposed architecture mitigates the topology-induced local-minimum behavior of purely reactive CBF-based navigation while enabling safe, real-time, geometry-aware navigation.

Problem

• autonomous navigation
• non-convex environments
• robot geometry
• safety guarantees
• long-horizon planning

Innovation

• MILP-MPC
• Minkowski-based CBF
• geometry-aware navigation
• polytopic obstacles
• high-order CBF