Abstract
This article presents a novel control strategy to herd groups of noncooperative evaders by means of a team of robotic herders. In herding problems, the motion of the evaders is typically determined by <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">strongly nonlinear</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">heterogeneous reactive</i> dynamics, which makes the development of flexible control solutions a challenging problem. In this context, we propose Implicit Control, an approach that leverages numerical analysis theory to find suitable herding inputs even when the nonlinearities in the evaders’ dynamics yield <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">implicit equations</i> . The intuition behind this methodology consists in driving the input, rather than computing it, toward the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unknown</i> value that achieves the desired dynamic behavior of the herd. The same idea is exploited to develop an adaptation law, with stability guarantees, that copes with uncertainties in the herd’s models. Moreover, our solution is completed with a novel caging technique based on uncertainty models and control barrier functions, together with a distributed estimator to overcome the need of complete perfect measurements. Different simulations and experiments validate the generality and flexibility of the proposal.
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