# Swarming Behavior Emerging from the Uptake-Kinetics Feedback Control in a Plant-Root-Inspired Robot
## 4 Discussion and Conclusions  
In this paper, plant roots are proposed as a source of inspiration for the design and architecture of robotic control. The behavior analysis from the literature led to the extraction of eight fundamental principles, which helped in the creation of a feedback control for a plant-inspired robotic platform (Plantoid). The proposed control, inspired by the uptake-kinetics of plant roots and by the internal communication system of plants, was implemented in simulation and on the Plantoid, showing the effective directionality of root growth towards attractive stimuli and a natural adjustment of the internal nutrient balance. The control runs independently on each individual root agent and is able to dynamically adjust nutrient priorities for that agent alone on the basis of local memory and to direct its growth on the basis only of local and instantaneous perception. Looking at the global architecture and internal state, roots are shown to organize themselves, leading to a collaborative behavior among the agents aimed at improving the equilibrium of nutrients and indeed plant wellness, thus autonomously satisfying _Property 1_, without the need of a centralized unit for the control of nutrient status and of tasks' distribution on the agents. The swarming behavior is an emergent result of the auto-regulation adopted by the uptake-kinetics control and the redistribution of nutrients among the agents. We have shown, in fact, that the internal imbalance never seems to converge to optimality with a stimulus-oriented control (alternative C, lacking an uptake mechanism and priority adjustment) compared to the proposed uptake-kinetics feedback control (imbalance with alternative A \(2.66\times 10^{-5}\ll 546\times 10^{-5}\) imbalance with alternative C after \(\sim\)3 h of simulated growth). Even though, there is not confirmation from biology on how uptake and stimuli priorities are related, here, we have proposed the use of a quadratic function to map uptake-kinetics parameters into nutrients' priorities, and by comparing this choice with the alternative that uses a linear function, we demonstrate that a priority function has an important role in defining root architecture and plant wellness. We show that the priority adjustment, independently actuated by each root, is a powerful instrument for the development of collaboration, without the need for a centralized unit to delegate task allocation. The developed control can be used in artificial root-like robots, which can move for instance in rescue scenarios for survival detection, in unstructured environments for mapping, or in space exploration. Wellness can be defined according to the application, for instance by adjusting ratios among several and different stimuli, not necessarily chemical. The work proposed here can be considered as a first milestone in plant-root inspired control, which can also contribute to understanding plant-root behavior. In fact, the implementation of hypothesis made on a biological model using a biomimetic platform, such as Plantoid, can help in hypothesis validation. For instance, the specific control can be incrementally adapted to include \begin{table}
\begin{tabular}{c c c c} \hline A & B & C & D \\ \hline
2.66\(\times 10^{-5}\) & 4.93\(\times 10^{-5}\) & 546\(\times 10^{-5}\) & 5.69\(\times 10^{-5}\) \\ \hline \end{tabular}
\end{table} 
Table 3: Nutrient imbalance. Nutrient imbalance obtained at the end of simulation (\(\sim\)3 h of simulated growth), for each of the control alternatives. Resulting imbalance is obtained as the averaged imbalance over three different runs, placing the centers of nutrients at different random locations: RUN 1 \(C_{N}=(3,2,-4)\), \(C_{K}=(-3,\ -2,\ -1)\), \(C_{P}=(3,\ 1,\ -5)\); RUN 2 \(C_{N}=(-3,\ 3,\ -4)\), \(C_{K}=(-3,\ -2,\ -3)\), \(C_{P}=(1,\ 1,\ -5)\); RUN 3 \(C_{N}=(1,\ 2,\ -2)\), \(C_{K}=(4,\ 1,\ -1)\), \(C_{P}=(2,\ 1,\ -2)\).