Adaptive control of distance-based spatial formations with planar and volume restrictions

Abstract

This paper explores a variation of distance-based formation control for the case of holonomic robots moving in 3D space modeled as double-integrators with any rigid undirected communication graph. Adaptive control techniques are used with a combined distance-based attractive-repulsive potential field to avoid possible inter-robot collisions. In order to prevent unwanted formation patterns verifying the same distance constraints, planar and volume restrictions are added which provide information about the unique desired relative position of each robot within the formation pattern. Under this control strategy the overall system is shown to converge to a set that includes the desired formation excluding its symmetric counterparts while the adaptive parameters remain bounded. The proposed algorithm is tested in numerical simulations showing good behavior. Finally, conclusions are drawn and current and future work are outlined.