A Temporal Barrier Framework for Collision Avoidance in Multi-Agent Autonomous Aerial Vehicles

Benedikt Barthel Sorensen; Mitchell Black; Erfaun Noorani; Themistoklis Sapsis

eess.SYAug 14, 2026

A Temporal Barrier Framework for Collision Avoidance in Multi-Agent Autonomous Aerial Vehicles

Authors: Benedikt Barthel Sorensen, Mitchell Black, Erfaun Noorani, Themistoklis Sapsis

Organizations: Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA · MIT Lincoln Laboratory, Lexington, MA, USA

Abstract

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.

Figures & tables

$a_{max}$ =	maximum acceleration, km/s 2
$b$ =	neural-network layer bias vector
$d_{ij}$ =	distance between agents $i$ and $j$ , km
$F,\,G$ =	joint (stacked) drift field and input matrix
$f_{i},\,g_{i}$ =	drift field and input matrix of agent $i$
$G_{\theta}$ =	neural-network surrogate model for the aTTC
$h$ =	control barrier function, s

Table 1

Panel of Figure 1 — Figure 1: Error metrics for NN surrogate model.

Figure 2: Schematic of the independent multi-agent (a) and formation-flight (b) pursuit–evasion scenarios and the pursuit control scheme (c). Evaders are shown in blue and pursuers in red; the leader is present only in the formation case.

Figure 3: Probability density function of evader distance from origin summed over all evaders. aTTC-CBF (blue), HOCBF (red). Zero, slow, and fast pursuer scenarios show in circles, triangles, squares respectively.

	No pursuers			Slow pursuers			Fast pursuers
	no CBF	HOCBF	aTTC-CBF	no CBF	HOCBF	aTTC-CBF	no CBF	HOCBF	aTTC-CBF
Collisions / 100 s	0.170	0.034	0.012	5.10	0.240	0.100	6.69	5.08	2.54
Waypoints / evader / 100 s	2.19	0.677	1.99	2.19	1.31	2.41	2.19	0.656	1.27
Median $\\|\mathbf{r}\\|$ [km]	4.66	4.49	4.68	4.66	5.58	5.04	4.66	8.64	6.40

Table 2: Statistics for the 3D independent multi-agent pursuit-evasion experiment, by adversary regime. Bold marks the better method within each (metric, regime) pair.

Panel of Figure 4 — Figure 4: Near-miss dynamics for the independent multi-agent pursuit-evasion experiment.

Panel of Figure 5 — Figure 5: Formation-flight pursuit-evasion under HOCBF vs. aTTC-CBF: formation coherence (a) and agent trajectories (b).

	Slow pursuers		Fast pursuers
	HOCBF	aTTC-CBF	HOCBF	aTTC-CBF
Collisions / 100 s	0.000	0.028	5.140	4.666
Waypoints / evader / 100 s	1.54	1.58	0.66	1.01
Mean slot deviation [km]	10.29	9.32	16.43	8.81
Core slot deviation [km]	6.80	5.66	10.14	5.08

Table 3: Statistics for the 3D formation multi-agent pursuit-evasion experiment, by adversary regime. Bold marks the better method within each (metric, regime) pair.

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Advanced Air Mobility (AAM) operations are expected to significantly increase aerial traffic in urban airspace, requiring autonomous traffic management systems to ensure collision-free operations in highly congested environments. In this paper, we propose a multi-agent coordination framework that uses minimum time-to-reach (TTR) as a unifying metric for priority assignment, temporal separation, and safety filtering. We focus on the problem of coordinating multiple aerial vehicles merging into an air corridor while maintaining safe separation between vehicles. Vehicles are assigned arrival-consistent priority based on TTR, and target TTR values are used to enforce temporal spacing that induces spatial separation. A priority-consistent safety filtering layer based on Hamilton-Jacobi reachability value functions ensures collision avoidance while minimally modifying the reference guidance. Simulation results in a highly congested corridor merging scenario show that the proposed method improves safety, fairness, and efficiency compared to time-optimal guidance and priority-agnostic safety filtering.

Abstract

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