Hybrid Control Barrier Functions for Nonholonomic Multi-Agent Systems

TL;DR

This paper proposes a hybrid formulation based on synergistic CBFs (SCBFs), which leverages a discrete switching mechanism to avoid configurations that would render the CBF invalid and ensures safety in the presence of moving obstacles and inter-agent interactions while respecting nonzero speed restrictions.

Abstract

This paper addresses the problem of guaranteeing safety of multiple coordinated agents moving in dynamic environments. It has recently been shown that this problem can be efficiently solved through the notion of Control Barrier Functions (CBFs). However, for nonholonomic vehicles that are required to keep positive speeds, existing CBFs lose their validity. To overcome this limitation, we propose a hybrid formulation based on synergistic CBFs (SCBFs), which leverages a discrete switching mechanism to avoid configurations that would render the CBF invalid. Unlike existing approaches, our method ensures safety in the presence of moving obstacles and inter-agent interactions while respecting nonzero speed restrictions. We formally analyze the feasibility of the constraints with respect to actuation limits, and the efficacy of the solution is demonstrated in simulation of a multi-agent coordination problem in the presence of moving obstacles.

Figures (3)

• Figure 1: Illustration of a synergistic CBF, comprising two candidate CBFs toggled by a discrete variable.
• Figure 2: Results from the first simulation. The planar trajectories are shown in Figure (a), where the vehicles are illustrated by triangular shapes and the obstacles by circular shapes. The desired path is the black, dashed line. Figure (b) shows the minimum $h^{\min}_0$ and the cross-track error $y_b$, and Figures (c)-(d) show the turning rates $r_i$ and speeds $u_i$ of all agents.
• Figure 3: Results from the second simulation. In Figure (a), the gray, solid line and circles indicate the trajectory of the barycenter $\boldsymbol{p}_b$ and the formation radii, respectively. The least transparent circle shows the position of the vehicles relative to the obstacle in red.

Theorems & Definitions (15)

• Definition 1: Forward Control Invariance harms2025safequadrotornavigationusing
• Definition 2: Control Barrier Function ames19
• Remark 1
• Remark 2
• Remark 3
• Proposition 1
• proof
• Proposition 2
• proof
• Proposition 3