Swarm Choreography Made Simple: Superposed Guiding Vector Fields for Rigid Formation Path Following

Abstract

This paper presents a decentralized guiding vector field framework for rigid formation path following in multi- UAV systems based on the superposition of simple rule-driven vector fields. Each control objective is encoded as a dedicated vector-field component: a normalized tangential term to ensure progression along a prescribed geometric path at a desired speed, a convergence term driving the formation toward the path, a local coordination term that preserves the desired formation shape through a pseudo-path parameter, and a local separation term for inter-agent collision avoidance. The coordination mechanism requires the exchange of only a single scalar per agent, resulting in low communication bandwidth. Partial theoretical results establish convergence of the swarm to the desired path and formation in the absence of the sepa- ration term, while collision avoidance is formally guaranteed. The approach is experimentally validated using a swarm of five quadrotors executing two 3D choreographies. The first experiment involves tracking a helical path while maintaining a rigid V-shaped formation. The second demonstrates a spiral- like motion obtained by a rotating circular formation tracking a vertical line. The experimental results support the effectiveness and practical applicability of the proposed framework.