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.

翻译：控制屏障函数二次规划（CBF-QPs）因其适用于一般控制仿射系统并能通过优化强制执行约束，已成为实时安全关键控制的核心工具。然而，它们生成的轨迹常带有不良的局部极小值，阻碍了向目标点的收敛。另一方面，动态系统调制（Mod-DS）方法（包括法向、参考及流形上变体）通过几何方式重塑标称向量场，能以极少甚至无局部极小值实现避障。但Mod-DS缺乏直接处理输入约束的机制，且主要局限于全驱动系统。本文重新审视两种方法的理论基础，证明尽管二者构造看似不同，法向Mod-DS实为CBF-QP的特例，而参考Mod-DS则通过单一共享方程与CBF-QP关联。这些关联启发了我们提出调制CBF-QP（MCBF-QP）框架，该框架引入参考调制与流形上调制变体，可减少甚至完全消除CBF-QP在动态杂乱环境中运行时，针对一般控制仿射系统所固有的伪平衡点。我们在模拟医院场景中验证了所提控制器，并在全驱动Ridgeback机器人及欠驱动Fetch平台上进行了真实世界实验。所有评估结果表明，调制CBF-QP在各项性能指标上均持续优于标准CBF-QP。