Scalable Multi-UAV Target Assignment via Permutation-Invariant Reinforcement Learning and Conditional Control-Barrier-Function Safety Filtering

Abstract

Coordinating multiple unmanned aerial vehicles (UAVs) to assign targets and generate collision-free trajectories in dynamic, obstacle-dense environments is a challenging problem with applications in search-and-rescue, surveillance, and precision agriculture. Existing deep reinforcement learning approaches for joint target assignment and path planning typically rely on fixed-size network architectures and soft reward penalties for collision avoidance, limiting their adaptability to changing team sizes and providing no explicit safety guarantee during deployment. This work addresses both limitations through a size-agnostic multi-UAV framework that integrates graph-based target assignment, permutation-invariant deep reinforcement learning, and formal safety filtering. The proposed approach replaces fixed-width assignment networks with a graph-attention encoder that produces a size-agnostic compatibility score for every (UAV, target) pair, decoded with the Hungarian algorithm (a differentiable Sinkhorn relaxation of the score matrix is implemented but is not used by the reported results), combined with a permutation-invariant twin-delayed deep deterministic policy gradient (TD3) actor–critic. A single model trained with five UAVs generalizes zero-shot to team sizes ranging from three to eight UAVs, achieving target completion rates of 87–93% without retraining. To provide a runtime, per-step collision-avoidance mechanism beyond reward shaping, the learned policy is further integrated with a Control Barrier Function (CBF) quadratic-program safety filter implemented using a dependency-free Dykstra alternating-projection solver; the filter’s forward-invariance property holds only conditionally—on accurate dynamics, a valid relative-degree model, a feasible constraint intersection, and (for peer UAVs) a bound on the peer’s unmodeled acceleration—and it is derived in continuous time but applied in discrete time with a finite-iteration solver, so it is not a formal guarantee of the implemented system. Hence, we report the filter’s constraint-residual behavior and an explicit priority-based policy for the rare cases in which the per-step constraints are jointly infeasible. In our single-seed, 30-episode evaluation, the original safety filter (with the unrobustified peer-acceleration assumption) reduced collisions without lowering target completion; the corrected robustified formulation was evaluated only in synthetic benchmarks and not in these trained-policy experiments. For the fixed-size baseline, the original filter reduces the collision rate from 0.60 to 0.30 collisions per episode while increasing the average number of targets reached from 4.43 to 4.70 out of 5. For the proposed graph-based architecture, collisions are completely eliminated, decreasing from 1.00 to 0.00 per episode, while target completion increases to 5.00 out of 5 (single seed, 30 episodes). Experiments further demonstrate that the proposed permutation-invariant architecture achieves comparable asymptotic performance to the fixed-size baseline despite requiring a longer warm-up period. In contrast to fixed-width architectures that require separate training for different team sizes, the proposed approach reuses a single trained model across varying team configurations while maintaining competitive or superior performance. These results demonstrate the potential of combining permutation-invariant learning with CBF-based safety filtering to achieve adaptable, high-performing, and safety-aware multi-UAV coordination.