Re-Solving the Shepherding Problem: Lead When Possible, Herd When Necessary

TL;DR

This work tackles autonomous transport of groups with heterogeneous and time-varying agent behaviors, where pure shepherding or pure leadership can fail. It proposes a mixed strategy that switches to leading when followers are present and reverts to herding otherwise, parameterized by the follower proportion $p$ and strategy-switch probability $\pi$. The results show robust success for all $p\in[0,1]$, resilience to moderate strategy switching within a finite horizon, and even performance under high switching rates without time limits, with potential welfare benefits over purely coercive herding. Overall, the approach advances biomimetic, low-overhead, robust transport algorithms suitable for real-world multi-agent systems facing behavioral heterogeneity.

Abstract

Designing systems for autonomous transport of groups of living agents has received a lot of attention in recent years due to a wealth of important potential applications. Biomimetic approaches are often sought, and a range of herding algorithms, inspired by how dogs herd sheep, as well as leadership algorithms mimicking leader-follower systems, have been introduced. However, they suffer from a common problem: shepherding algorithms require that agents evade the shepherd, and leading algorithms require that agents follow. This can cause problems in real-world applications where the behavioral responses of the agents to a transporter are likely to be heterogeneous over both long and short timescales. Here, we introduce an algorithm that adaptively switches between leading and herding depending on the response it receives from the agents to mitigate this problem. We show via simulation that this mixed algorithm can transport groups with any follower and evader composition, and we compare its performance with lead-only and herd-only algorithms. We also show that the mixed algorithm can deal with groups where individual agents randomly switch their strategy over time, as long as sufficient time is provided to complete the task relative to the switching rate. Given that our algorithm overcomes issues associated with herd-only and lead-only algorithms and might also, as a side effect, mitigate the issue of habituation to robotic transporters, it takes us one step closer to realizing many of the proposed applications for these types of algorithms.

Figures (1)

• Figure 1: Performance of the algorithms. (A)-(B) Comparison of the original herd-only algorithm, a lead-only algorithm, and the mixed 'lead when possible, herd when necessary' algorithm with respect to time to completion (A), and proportion of agents delivered to target (B), as a function of proportion of followers ($p$). (C) Performance of the mixed algorithm when agents switch strategy with probability $\pi$ per timestep. We see that for $\pi$ up to 0.01 the algorithm delivers all agents to the target within the allotted time, but as the rate of strategy switches increases the mixed algorithm's capacity to deliver the agents to the target within the allotted time decreases. (D) Time to completion for the mixed algorithm for $\pi$ from 0 to 0.5. The red curve indicates mean completion time, the bars represent the standard deviation, and the dots represent the actual completion times from each simulation. We note that the mean completion time for all $\pi$ is around or below 20000 timesteps and that overall only a few individual simulations that take far longer than that to complete.