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

• URL: http://arxiv.org/abs/2604.00162v1
• Date: Tue, 31 Mar 2026 19:10:34 GMT
• Title: Long-Horizon Geometry-Aware Navigation among Polytopes via MILP-MPC and Minkowski-Based CBFs
• Abstract summary: The proposed framework bridges long-horizon and geometry-aware safety guarantees for a robot navigating among polytopic obstacles.<n>The results show that the proposed architecture mitigates the topology-induced behavior of purely reactive CBF-based navigation.
• Score: 6.0390093427687725
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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