A Feasibility-Enhanced Control Barrier Function Method for Multi-UAV Collision Avoidance

Operating teams of autonomous aircraft in dynamic, uncertain, and potentially adversarial environments requires safety protocols that are reliable yet selective, and allow agents to fly in close proximity while making progress toward mission objectives. We introduce adversarial time-to-collision (aTTC), a risk metric that quantifies, for a given agent, how quickly any surrounding agent could reach it assuming adversarial intent. We embed aTTC into the control barrier function (CBF) framework, defining the barrier directly in time rather than distance or velocity. The resulting aTTC-CBF is inherently anticipatory: agents modulate their own velocity based not on whether a peer is on a collision course, but on how quickly one could reach collision given its dynamical constraints. A differentiable neural-network surrogate makes the aTTC computable in real time within a standard CBF quadratic program. Across long time-horizon simulations of 3D independent-pursuit and formation-flight scenarios, the aTTC-CBF achieves up to twice the waypoint progress at half the collision rate of a higher-order distance-based CBF baseline.

Multi-robot Control Barrier Function (CBF) safety filters can become infeasible, but a failed quadratic program (QP) does not indicate why the conflict occurred or how to resolve it. To address this, we develop an exact feasibility certificate for multi-agent CBF filters with heterogeneous control-affine dynamics and convex input sets. The certificate quantifies a feasibility reserve by separating the demand imposed by safety constraints from the available actuator supply. This decomposition shows when CBF gain tuning or increased actuation can and cannot resolve infeasibility, and identifies the agents and interactions responsible for the conflict. We further propose an algorithm to optimally allocate shared safety constraints by maximizing the worst local feasibility margin, yielding a linear program for polyhedral input sets. In $320$ paired closed-loop simulations, the proposed allocation reduces infeasible control steps from roughly $50\%$ to $6.2\%$, and reduces safety-violating runs from $118/160$ to $24/160$. In addition, across $52$ infeasibility events, the certificate identifies an interaction whose relaxation restores feasibility in $94\%$ of cases.

This paper presents an approach to mutual collision avoidance based on Nonlinear Model Predictive Control (NMPC) with time-dependent Reciprocal Velocity Constraints (RVCs). Unlike most existing methods, the proposed approach relies solely on observable information about other robots, eliminating the need for excessive communication. The computationally efficient algorithm for computing RVCs, together with the direct integration of these constraints into the NMPC problem formulation at the controller level, allows the whole pipeline to run at 100 Hz. This high processing rate, combined with modeled nonlinear dynamics of the controlled Uncrewed Aerial Vehicles (UAVs), is a key feature that facilitates the use of the proposed approach for agile UAV flight. The proposed approach was evaluated through extensive simulations emulating real-world conditions in scenarios involving up to 10 UAVs and velocities of up to 25 m/s, and in real-world experiments with accelerations up to 30 m/s$^2$. Comparison with the state of the art shows 31% improvement in terms of flight time reduction in challenging scenarios, while maintaining a collision-free navigation in all trials.