Asymptotic behavior and control of a “guidance by repulsion” model

Abstract

We model and analyze a herding problem, where the drivers try to steer the evaders' trajectories while the evaders always move away from the drivers. This problem is motivated by the guidance-by-repulsion model [10], where the authors answer how to control the evaders' positions and what is the optimal maneuver of the drivers. First, we obtain the well-posedness and the long-time behavior of the one-driver and one-evader model, assuming of the same friction coefficients. In this case, the exact controllability is proved in a long enough time horizon. We extend the model to the multi-driver and multi-evader case, and develop numerical simulations to systematically explore the nature of controlled dynamics in various scenarios. The optimal strategies turn out to share a common pattern to the one-driver and one-evader case: the drivers rapidly occupy the position behind the target, and want to pursuit evaders in a straight line for most of the time. Inspired by this, we build a feedback strategy which stabilizes the direction of evaders.Date: November 5, 2019.

Continuification Control of Large-Scale Multiagent Systems in a Ring

“…Remark 3 Notice that (10) is the periodic version of the more standard non-periodic repulsive kernel f (z) = sgn(z)e − |z| L , which is typically considered in the Literature [18], [56], [57], (see Appendix A). Also, note that our approach can easily be applied to the case of an attractive kernel by simply changing the sign in (10).…”

“…A key challenge is establishing analytical guarantees for achieving desired collective tasks. For instance, in the shepherding control problem, it is crucial to determine the optimal leader-to-follower ratios and sensing ranges to effectively manage group dynamics and corral and contain the followers towards desired regions in the state space [18]- [21]. In complex multi-agent scenarios, microscopic models using ordinary (stochastic) differential equations are often replaced by macroscopic models using partial integro-differential equations to simplify analysis and enhance control of spatial organization on a large scale, avoiding its inherent curse of dimensionality [22]- [34].…”

Controlling Swarms toward Flocks and Mills

“…Imposing consensus in velocity has also been analysed from the point of view of control [14,18,19,39]. These consensus models also have applications in swarm robotics [28,29], social and pedestrian dynamics [3,2,43,60] where control theory is applied with different regulation objectives expressed in both ad-hoc and optimal control designs [4,5,8,15].…”

Shepherding algorithm for heterogeneous flock with model-based discrimination

“…Hu et al [13] proposed a shepherding method in which the shepherd guides the flock by going behind the herd, and showed the effectiveness of the method by both simulations and robotic experiments. Ko and Zuazua [14] proposed a feedback-based shepherding method for a flock of agents trying to escape from a goal area.…”