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This paper presents a hierarchical navigation framework for robots operating in complex, non-convex environments with polytopic obstacles. The approach combines a high-level MILP-MPC planner, which generates a coarse trajectory treating the robot as a point mass, with a low-level Minkowski-based Control Barrier Function (CBF) that enforces geometric constraints. Experiments in U-shaped and maze-like environments demonstrate the framework's ability to safely navigate while avoiding local minima, even with complex robot geometry and dynamics.
Achieve safe, real-time robot navigation in complex environments by combining global MILP planning with local, geometry-aware CBF control.
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.
