Bearing-based formation control for multiple underactuated autonomous surface vehicles with flexible size scaling

Most existing formation control approaches for Autonomous surface vehicles (ASVs) focused on achieving rigid patterns with invariant inter-vehicle distance in open ocean environment. However, these methods cannot be applied to the cooperative missions on irregular inland waterway with changing width (such as rivers, canals and fjords), wherein the inter-vehicle distance should be continuously adjustable to respond to the environment dynamically. This paper proposes a bearing-based formation scaling control scheme for underactuated ASVs to achieve the desired patterns but with a flexible size scaling. By assuming that the fleet satisfies a leader–first-follower structure, the formation scaling parameters are accessible only to leaders, while each follower needs to maintain the bearing constraints to its neighboring ASVs without any knowledge of scale information. We respectively design distributed control laws for leaders and follower, and adaptive neural networks (NNs) are incorporated to approximate the dynamic uncertainties induced by parameter perturbations, external disturbances and input saturations. To improve the tracking performance, an auxiliary adaptive law is resorted to compensate the non-zero estimation error of NNs. Theoretical analysis demonstrates that the closed-loop scaling maneuver tracking and formation tracking errors converge to zero asymptotically. The comparative simulation results are presented to substantiate the effectiveness of the designed control method.