Multi-robot Implicit Control of Herds

This paper presents a novel control strategy to herd a group of non-cooperative preys by means of a team of robotic hunters. In herding problems, the motion of the preys is typically determined by strong nonlinear reactive dynamics, escaping from the hunters. Besides, many applications demand the herding of numerous and/or heterogeneous entities, making the development of flexible control solutions challenging. In this context, our main contribution is a control approach that finds suitable herding actions, even when the nonlinearities in the preys' dynamics yield to implicit equations. We resort to numerical analysis theory to characterise the conditions that ensure the existence of such actions and propose a duple of design methods to compute them, one transforming the continuous time implicit system into an expanded explicit system, and the other applying a numerical method to find the action in discrete time. Additionally, the control strategy includes an adaptation law that makes it robust against uncertainty in the parameters of the preys. Simulations and real experiments validate the proposal in different scenarios.