No Minima, No Collisions: Combining Modulation and Control Barrier Function Strategies for Feasible Dynamic Collision Avoidance

Control Barrier Function Quadratic Programs (CBF-QPs) have become a central tool for real-time safety-critical control due to their applicability to general control-affine systems and their ability to enforce constraints through optimization. Yet, they often generate trajectories with undesirable local minima that prevent convergence to goals. On the other hand, Modulation of Dynamical Systems (Mod-DS) methods (including normal, reference, and on-manifold variants) reshape nominal vector fields geometrically and achieve obstacle avoidance with few or even no local minima. However, Mod-DS provides no straightforward mechanism for handling input constraints and remains largely restricted to fully actuated systems. In this paper, we revisit the theoretical foundations of both approaches and show that, despite their seemingly different constructions, the normal Mod-DS is a special case of the CBF-QP, and the reference Mod-DS is linked to the CBF-QP through a single shared equation. These connections motivate our Modulated CBF-QP (MCBF-QP) framework, which introduces reference and on-manifold modulation variants that reduce or fully eliminate the spurious equilibria inherent to CBF-QPs for general control-affine systems operating in dynamic, cluttered environments. We validate the proposed controllers in simulated hospital settings and in real-world experiments on fully actuated Ridgeback robots and underactuated Fetch platforms. Across all evaluations, Modulated CBF-QPs consistently outperform standard CBF-QPs on every performance metric.