Coordinated Closed-Curve Path Following Control of Multi-Unicycle in a Time-Invariant Flow Field

This paper utilizes a dynamic model of unicycles to address the stabilization of formation motion around closed curves in the presence of a time-invariant flow field. It is shown that our previous concentric compression design can be extended to deal with robust coordinated path following control for fighting against the external flow field. Linear acceleration control for each unicycle is added and combined with the rotation control to achieve both temporal and spatial formation in the case of a spatially variable flow, which breaks the restriction of temporally balanced formation relied solely on the angle control in the literature. A potential function is introduced to force each unicycle’s speed greater than the magnitude of flow. The theoretical result is proved by a numerical example.