No Minima, No Collisions: Combining Modulation and Control Barrier Function Strategies for Feasible Dynamic Collision Avoidance
Yifan Xue, Nadia Figueroa
TL;DR
This work investigates dynamic obstacle avoidance by juxtaposing Control Barrier Function Quadratic Programs (CBF-QPs) with Mod-DS methods, showing both offer complementary safety and trajectory properties. It reveals theoretical connections—normal Mod-DS is equivalent to CBF-QP in static fully actuated settings, and reference Mod-DS relates closely through a shared equation—leading to the Modulated CBF-QP (MCBF-QP) framework. MCBF-QP introduces two variants, Reference-MCBF-QP and On-Manifold-MCBF-QP, to reduce or eliminate undesirable local minima while preserving actuation constraints, validated through hospital-like simulations and real-robot experiments on Ridgeback and Fetch platforms. The results demonstrate improved target convergence, obstacle clearance, and robustness across fully actuated and underactuated systems, suggesting a practical, unified approach to safe navigation in dynamic, cluttered environments.
Abstract
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.