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.
Guiding or leading a group of individuals to a specific location is a task regularly performed by animals across taxa [1,2], ranging from primates leading troops to foraging sites [3] and sheepdogs herding flocks [4,5], to ants guiding or carrying conspecifics during nest relocation [6,7]. Understanding these phenomena is of interest not only in biology but also for engineering, as autonomous systems capable of transporting groups of inanimate objects or living agents have a wide range of potential applications [8], including wildlife conservation, environmental remediation, livestock management, crowd control, evacuation, and multi-robot coordination [9][10][11][12][13][14][15][16][17][18][19][20].
Biomimetic approaches to collective transport are therefore common, with most recent work focusing on shepherding inspired by sheepdog behavior [21]. Numerous shepherding algorithms have been studied in simulation [13,[22][23][24][25][26][27][28], and several have been implemented on robotic platforms transporting inanimate or living agents [29][30][31]. Transport via leadership has also been explored [32], and robotic leaders have been shown to elicit following behavior in a variety of animal systems [33,34]. While effective in specific settings, both approaches share a fundamental limitation: herding requires agents to evade the transporter, whereas leading requires agents to follow it.
In natural groups, however, individuals often exhibit heterogeneous and context-dependent behavioral responses [35], which may change over time due to habituation [30] and can undermine the effectiveness of purely herd-based or leader-based strategies. Beyond these two modes, nature also exhibits mixed transport strategies that can be described as “lead when possible and force, carry, or herd when necessary,” as observed in some ant species during nest relocation [7]. This biomimetic alternative has not yet been considered in the context of autonomous collective transport of living agents, despite its potential relevance for many proposed applications [8].
At the same time, a growing body of work has begun to address heterogeneity explicitly, considering differences in responsiveness, social affiliations, or behavioral rule sets [36][37][38][39][40]. These studies provide valuable insights into specific forms of heterogeneity but often rely on increasingly specialized control rules layered onto existing shepherding architectures. A complementary biomimetic perspective is that robust transport in nature frequently emerges from simple interaction mechanisms rather than progressively elaborate ones, a principle that has been explicitly exploited in earlier herding models [25]. Extending shepherding algorithms developed for different transport contexts [13,22,27,28] to incorporate alternative transport modes may therefore yield both more robust solutions and deeper theoretical insight into the autonomous transport of unwilling or variably responsive agents.
Here we introduce an algorithm for a transporter that adaptively switches between herding and leading depending on the response it receives from the agents. More specifically, we extend the shepherding model in [25] by adding a new mode of operation ’lead’ that the transporter will autonomously and adaptively switch to from ‘herding’ if it detects that agents are following it. Another modification made here is that the (sheep-like) agents now adopt one of two strategies: ‘follow’ or ’evade’ the transporter, and we introduce a parameter p that represents the proportion of followers in the group of agents. We note that when p = 0 (no followers) our new transporter algorithm is identical to the shepherding algorithm in [25], when p = 1 (all followers) the transporter will only lead, and for any p in (0, 1) the transporter will employ the ‘mixed’ strategy where it leads if at least one agent is following and herds if no agent is following. We also introduce a parameter π that represents the probability that an agent will switch strategy on each timestep.
To study how the performance of the mixed, herd-only, and lead-only algorithms depends on the proportion of followers in a group, we ran simulations for values of p from 0 to 1 and measured the time to completion and the proportion of agents delivered to the target. The mixed algorithm successfully delivers all agents for all proportions p ∈ [0, 1] within the allotted time (Fig. 1AB). In contrast, the herd-only algorithm succeeds only when all agents are evaders (p = 0), since the presence of any followers prevents the transporter from maintaining an effective driving position. Conversely, the lead-only algorithm succeeds only when all agents are followers (p = 1); if evaders are present, the transporter can guide the followers to the target but cannot induce the remaining agents to approach. The mixed algorithm avoids both failure modes by leading whenever at least one agent follows and reverting to herding otherwise, thereby
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