Multi-Agent Obstacle Avoidance using Velocity Obstacles and Control Barrier Functions

TL;DR

The paper addresses safe multi-agent collision avoidance where pure VO can be overly conservative and lacks formal safety guarantees. It introduces a VO-CBF framework that keeps VO guidance in the objective via a slack variable $\lambda$ while enforcing safety through a CBF constraint, ensuring forward invariance of the safe set. The optimization minimizes $J_i = k_u \|u_i - u_{\mathrm{ref},i}\|^2 + k_{vo} \sum_j w_{ij} \lambda_{ij}^2$ with $\dot{h}_{vo,ij} + \alpha_{vo}(h_{vo,ij}) \ge \lambda_{ij}$ and $\dot{h}_{c,ij} + \alpha_c(h_{c,ij}) \ge 0$, where $w_{ij}=1/T_{\mathrm{col},ij}$ and $T_{\mathrm{col},ij}$ is the time-to-collision. Empirical results on 2nd-order integrator and car-like dynamics show smoother, collision-free trajectories and competitive timing relative to VO/RVO/hVO/OVVO baselines, while providing formal safety guarantees suitable for real-time, decentralized deployment.

Abstract

Velocity Obstacles (VO) methods form a paradigm for collision avoidance strategies among moving obstacles and agents. While VO methods perform well in simple multi-agent environments, they don't guarantee safety and can show overly conservative behavior in common situations. In this paper, we propose to combine a VO-strategy for guidance with a CBF-approach for safety, which overcomes the overly conservative behavior of VOs and formally guarantees safety. We validate our method in a baseline comparison study, using 2nd order integrator and car-like dynamics. Results support that our method outperforms the baselines w.r.t. path smoothness, collision avoidance, and success rates.

Figures (4)

• Figure 1: An illustration showing that strict VO-based constraints can be overly conservative. Two red agents $A$ aim for a destination $A_\mathrm{des}$ while avoiding the obstacle $B$: the one with a relaxed constraint (left) follows a direct path, while the one with a strict constraint (right) cannot turn in front of the obstacle (whose initial VO is shown in light gray) as this would imply at some point selecting a velocity inside the VO. In more crowded scenarios, such strict constraints can severely limit available options.
• Figure 2: Illustration of the key idea and notation used in Velocity Obstacle methods. If agent $A$ chooses a velocity $\mathbf{v}_A$ outside the dark cone $VO_B^A(\mathbf{v}_B)$, it will not collide with agent $B$.
• Figure 3: Visualization of the resulting trajectories in the baseline comparison study. The arrows in each corresponding color describe the direction of motion of each agent. Our method (left-most column) remains stable and computes smooth trajectories for all evaluated scenarios. The hVO method encountered infeasibility (no available safe velocities) in the scenarios with $8$ and $12$ agents. The aspect ratio is equal for both dimensions and the scale is given by the bottom left reference.
• Figure 4: Trajectories when applying the proposed approach to cars.