Game-theoretical strategies for decentralised multi-drone conflict resolution

Abstract

At the drone densities anticipated for urban and contested airspace over the coming decades, drone traffic must be managed by decentralised conflict-resolution schemes to ensure feasibility. This paper presents such a decentralised scheme using differential game theory. Each drone optimises its own trajectory over a receding prediction horizon while anticipating the behaviour of its neighbours. By choosing a parameterisation of the cost function, we represent cooperative, Nash and explicit adversarial assumptions about the opponent. The optimal conditions for the ego drone are solved by Pontryagin’s minimum principle using an iterative forward–backward sweep with Anderson-accelerated relaxation.We benchmark the framework against a calibrated reactive social-forces model, tuned so that any remaining differences can be attributed to anticipation. Pairwise experiments cover head-on, orthogonal crossing, overtaking and a one-on-one adversarial encounter; multi-drone experiments cover bi-directional head-on flow, orthogonal crossing flow, and a bottleneck with two cylindrical obstacles. We show that the anticipatory model resolves every cooperative encounter cleanly where the reactive benchmark fails in a distinct way — a “kissing stall” in the symmetric head-on, an off-axis force balance in the crossing, a trailing trap in the overtake — and these failures carry over at scale into reduced safety margins. In the adversarial case the framework absorbs pursuit-evasion under the same solver with a single sign change on one cost parameter, recovering the three qualitative regimes (escape, stalemate, capture) without modifying the iteration. Moreover, the framework reproduces similar efficient self-organising flow patterns (lanes, diagonal stripes) known from pedestrian flow theory in 3D space.