Geometric Coherence via Weighted Matching for 3D Heterogeneous Multi-Agent Reach-Avoid Games

Reach-avoid (RA) games have significant applications in security and defense, particularly for unmanned aerial vehicles (UAVs). These problems are inherently challenging due to the need to consider obstacles, consider the adversarial nature of opponents, ensure optimality, and account for nonlinear dynamics. Hamilton-Jacobi (HJ) reachability analysis has emerged as a powerful tool for tackling these challenges; however, while it has been applied to games involving two spatial dimensions, directly extending this approach to three spatial dimensions is impossible due to high dimensionality. On the other hand, alternative approaches for solving RA games lack the generality to consider games with three spatial dimensions involving agents with non-trivial system dynamics. In this work, we propose a novel framework for dimensionality reduction by decomposing the problem into a horizontal RA sub-game and a vertical RA sub-game. We then solve each sub-game using HJ reachability analysis and consider second-order dynamics that account for the defender's acceleration. To reconstruct the solution to the original RA game from the sub-games, we introduce a HJ-based tracking control algorithm in each sub-game that not only guarantees capture of the attacker but also tracking of the attacker thereafter. We prove the conditions under which the capture guarantees are maintained. The effectiveness of our approach is demonstrated via numerical simulations, showing that the decomposition maintains optimality and guarantees in the original problem. Our methods are also validated in a Gazebo physics simulator, achieving successful capture of quadrotors in three spatial dimensions space for the first time to the best of our knowledge.

Combined Target Assignment and Path Finding (TAPF) requires assigning targets for agents while simultaneously planning collision-free paths. We present ITA-LaCAM, a complete and scalable TAPF solver inspired by LaCAM and ITA-CBS. In ITA-LaCAM, each joint-configuration node carries an agent-to-target matching. When a successor is generated, ITA-LaCAM incrementally repairs the matching for the agents that moved and uses the targets to guide PIBT successor generation. This design enables adaptive reassignment without explicitly enumerating the combinatorial assignment space, while preserving LaCAM's completeness and scalability. Across 9,760 benchmark instances on eight maps with 5--200 agents, ITA-LaCAM solved 100% of the instances, compared with 95.6% for IR-TAPF configured with DBS-Hungarian. ITA-LaCAM found an initial solution faster in 84.0% of the comparisons and achieved a lower sum of costs in 65.0% of the instances solved by both methods.

Asymmetric 3D pursuit-evasion in cluttered voxel environments is difficult under communication latency, partial observability, and nonholonomic maneuver limits. While many MARL methods rely on richer inter-agent coupling or centralized signals, these dependencies can become fragility sources when communication is delayed or noisy. Building on an inherited path-guided decentralized pursuit scaffold, we study a robustness-oriented question: can representational parsimony improve communication-free coordination? We instantiate this principle with (i) a parsimonious actor observation interface that removes team-coupled channels (83-D to 50-D), and (ii) Contribution-Gated Credit Assignment (CGCA), a locality-aware credit structure for communication-denied cooperation. In Stage-5 evaluation (4 pursuers vs. 1 evader), our configuration reaches 0.753 +/- 0.091 success and 0.223 +/- 0.066 collision, outperforming the 83-D FULL OBS counterpart (0.721 +/- 0.071, 0.253 +/- 0.089). It further shows graceful degradation under speed/yaw/noise/delay stress tests and resilient zero-shot transfer on urban-canyon maps (about 61% success at density 0.24). These results support a practical paradigm shift: explicitly severing redundant cross-agent channels can suppress compounding error cascades and improve robustness in latency-prone deployment.