Abstract
Sheepdogs smartly herd a flock of sheep and guide them towards a goal. A single dog can herd a few hundred sheep in easy to navigate environments. Understanding the interaction space between the sheepdogs, sheep and the environment is important due to the possibility of transferring this knowledge to solve practical swarm robotics problems. This interaction space is a complex mesh of influencing factors. We scrutinize this interaction space to identify areas where the complexity of the herding problem changes from low (easy to solve) to high (harder to solve or becoming unsolvable) complexity. In particular, we study reactive models for shepherding, whereby agents respond directly to stimuli in the environments by fusing the set of force vectors influencing their behaviour. We present an enhanced shepherding model with higher success rate than its predecessor. We investigate four key factors that influence the complexity of the problem: the relative speed between the sheepdog and sheep, the spatial configuration of the sheep at the start of the task, the number of sheepdogs, and the density of obstacles in the environment. We discovered a phase transition in shepherding resulting from the interaction between the number of sheepdogs and obstacles. The phase transition occurs as the density of obstacles range from 0.2% for a single shepherding agent to 5% for 10 shepherding agents. During this phase transition, the problem changes from being an easy problem where the flock gets collected quickly, to a hard one where the overall herding task becomes utterly not achievable using reactive approaches.
Highlights
What makes a problem hard? Why are some problems that appear from the outset to possess similar characteristics, much harder than other similar problems? What is the true source of complexity in the problem space? These questions have been the subject of inquiry in artificial life [1] and complexity science [2] for decades
The aim of this paper is to focus on the interaction space between the sheepdog, the sheep, and the environment to understand a few sources of complexity for shepherding
WORK In this work, we identified influencing factors that impact the complexity of the swarm guidance problem using a shepherding approach
Summary
What makes a problem hard? Why are some problems that appear from the outset to possess similar characteristics, much harder than other similar problems? What is the true source of complexity in the problem space? These questions have been the subject of inquiry in artificial life [1] and complexity science [2] for decades. While shepherding is a fascinating problem on a fundamental level, understanding the complexity (and its causes) of the problem is paramount to identifying guidance and control solutions which are able to scale up in a practical setting. In their proposed solution the shepherding agents are heterogeneous with two distinct roles, “corner robot” and “sideline robot” This strategy was necessary due to their reliance on physical barriers rather than repulsive forces to contain the sheep, necessitating specialized hard-wired behaviors depending on position in the flock. We present a modified model for shepherding that avoids disturbing the flock when when the sheep dog approaches This is achieved by assigning a path to the sheepdog which maintains a distance to the flock greater than its influence range.
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