# Dynamic Response Threshold Model for Self-Organized Task Allocation in a Swarm of Foraging Robots
## 1 Introduction
With a higher threshold, an individual robot is apt to stay in the nest; with a lower threshold, having many robots forage simultaneously increases the amount of physical interference [17]. Therefore, a swarm with a fixed threshold lacks adaptive capacity and cannot respond properly to an uncertain and dynamic environment. Using threshold-based methods, many robots forage simultaneously, which can lead to undesired physical interference. In the decentralized control approach, other TA mechanisms are based on probabilistic methods, wherein the decision of each robot to switch its activity is taken based on a probability. Some of these studies directly use fixed probabilities to achieve TA. [PERSON] et al. [18] and [PERSON] et al. [19] presented a self-organized method to partition a task into sequentially interdependent subtasks based on probabilistic methods. [PERSON] et al. [20] achieved self-organized TA based on a probabilistic method wherein, at each time step, an observer can become a scout with a fixed probability. A simple adaption rule is then used to adjust the probability of a robot leaving the nest, where the probability is raised or lowered as a fixed constant [21]. In the above study, various factors (e.g., information about food and the environment) that could affect the foraging efficiency are not accounted for. Therefore, TA based on fixed probabilities still has certain deficiencies. Other studies based on probabilistic methods use response threshold models, wherein the threshold values and other information are used to calculate probability. [PERSON] et al. introduced a fixed response threshold model (FRTM) to account for experimental observations of how social insects divide their labor [22; 23]. However, the FRTM uses a fixed threshold and so cannot cope with uncertain and dynamic environments. Therefore, [PERSON] et al. [24] and [PERSON] et al. [25] used a response threshold model with a variable threshold; when a robot engages in a task, the task-associated threshold is decreased. In order to improve the ability of rapid response to the environment, [PERSON] et al. proposed a sigmoid response threshold function to respond to changing task requirements by adapting the static response thresholds [26]. To make swarm robots more robust for foraging, [PERSON] et al. proposed an extended FRTM known as ARTM [27; 28]; when the stimulus decreases, the threshold tends to increase and fewer robots go foraging; when the stimulus increases, the threshold tends to decrease and far more robots go foraging. In ARTM, the changes regarding the threshold are only related to the number of food tokens in a nest. [PERSON] et al. not only provided a theoretical basis for response threshold functions of agents that share information being optimal strategies but also reinforced that using adaptive response thresholds is the correct strategy for the type of scenario investigated herein [29]. However, although the response threshold model improves foraging efficiency, it does not consider physical interference when seeking to improve TA performance. As has been noted elsewhere, the performance of swarm-robotics foraging is influenced by the physical interference among the active foraging robots [30; 31]: having too many robots foraging simultaneously leads to less efficient foraging [32; 33]. However, previous studies on TA did not take physical interference into account when adjusting the number of active foraging robots. To overcome the above drawbacks, this paper proposes the dynamic response threshold model (DRTM) with the aim of achieving self-organized TA and completing foraging tasks efficiently. Firstly, our approach uses a mutative threshold that varies with the external environment (e.g., the number of active foraging robots and the number of times robots avoid the obstacles), so DRTM makes the swarm system adaptive to the changing environment and robust to failures. Secondly, we also newly take into account the physical interference and traffic conditions to adjust the behavior of the robots dynamically.