Velocity Obstacle-Based Control Barrier Function for Safety-Critical Predictive Control

This paper introduces the Velocity Obstacle-based Control Barrier Function (VO-CBF), a novel safety framework bridging geometric collision prediction with dynamic control. While classical Velocity Obstacles ignore system dynamics, the VO-CBF encodes collision cones directly into the dynamic state space. By natively coupling position and velocity, this formulation mathematically reduces the constraint's relative degree from two to one for force-controlled systems, fundamentally eliminating the solver conservatism and input saturation conflicts associated with standard high-order predictive barriers. We propose a hybrid Nonlinear Model Predictive Control (NMPC) architecture that enforces strict discrete-time invariance for the immediate step and affine approximations across the prediction horizon, balancing formal safety guarantees with computational tractability. Comparative simulations and hardware experiments demonstrate that the VO-CBF effectively throttles velocity to prevent collisions in high-inertia scenarios where standard kinematic baselines fail.