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The plant root system shows remarkably complex behaviors driven by environmental cues and internal dynamics, whose interplay remains largely unknown. A notable example is circumnutation growth movements, which are growth oscillations from side to side of the root apex. Here we describe a model capable of replicating root growth behaviors, which we used to analyze the role of circumnuntations, revealing their emergence I) under gravitropic stress, as a combination of signal propagation and sensitivity to the signal carriers; II) as a result of the interplay between gravitropic and thigmotropic responses; and III) as a behavioral strategy to detect and react to resource gradients. The latter function requires the presence of a hypothetical internal oscillator whose parameters are regulated by the perception of environmental resources., Competing Interests: The authors have declared that no competing interests exist.

This paper aims to propose a novel approach to model the dynamics of objects that move within the soil, e.g. plants roots. One can assume that external forces are significant only at the tip of the roots, where the plant's growth is actuated. We formulate an optimal control problem that minimises the energy spent by a growing root subject to physical constraints imposed by the surrounding soil at the tip. We study the motion strategy adopted by plant roots to facilitate penetration into the soil, which we hypothesize to be a circumnutation movement. By solving the proposed optimal control problem numerically, we validate the hypothesis that plant roots adopt a circumnutation motion pattern to reduce soil penetration resistance during growth. The proposed formalisation could be applied to replicate such a biological behaviour in robotic systems, to adopt the most efficient strategy for autonomous devices in soil exploration.

Plants use many strategies to move efficiently in soil, such as growth from the tip, tropic movements, and morphological changes. In this paper, we propose a method to translate morphological features of Zea mays roots into a new design of soft robots that will be able to move in soil. The method relies on image processing and curve fitting techniques to extract the profile of Z. mays primary root. We implemented an analytic translation of the root profile in a 3D model (CAD) to fabricate root-like probes by means of 3D printing technology. Then, we carried out a comparative analysis among the artificial root-like probe and probes with different tip shapes (cylindrical, conical, elliptical, and parabolic) and diameters (11, 9, 7, 5, and 3 mm). The results showed that the energy consumption and the penetration force of the bioinspired probe are better with respect to the other shapes for all the diameters of the developed probes. For 100 mm of penetration depth and 7 mm of probe diameter, the energy consumption of the bioinspired probe is 89% lesser with respect to the cylindrical probe and 26% lesser with respect to the conical probe. The penetration performance of the considered tip shapes was evaluated also by means of numerical simulations, obtaining a good agreement with the experimental results. Additional investigations on plant root morphology, movement strategies, and material properties can allow the development of innovative bioinspired solutions exploitable in challenging environments. This research can bring to breakthrough scenarios in different fields, such as exploration tasks, environmental monitoring, geotechnical studies, and medical applications., Competing Interests: The authors have declared that no competing interests exist.

Objective: Within the field of biorobotics, an emerging branch is plant-inspired robotics. Some effort exists in particular towards the production of digging robots that mimic roots; for these, a deeper comprehension of the role of root tip geometry in excavation would be highly desirable. Here we demonstrate a photogrammetry-based pipeline for the production of computer and manufactured replicas of moth orchid root apexes., Results: Our methods yields faithful root reproductions. This can be used either for quantitative studies aimed at comparing different root morphologies, or directly to implement a particular root shape in a biorobot.

This paper presents a comparative analysis in terms of energy required by an artificial probe to penetrate soil implementing two different strategies: a straight penetration movement and a circumnutation, which is an oscillatory movement performed by plant roots. The role of circumnutations in plant roots is still debated. We hypothesized that circumnutation movements can help roots in penetrating soil, and validated our assumption by testing the probe at three distinct soil densities and using various combinations of circumnutation amplitudes and periods for each soil. The comparison was based on the total work done by the system while circumnutating at its tip level with respect to that shown by the same system in straight penetration. The total energy evaluation confirmed an improvement obtained by circumnutations up to 33%. We also proposed a fitting model for our experimental data that was used to estimate energy needed by the probe to penetrate soil at different dimensions and circumnutation amplitudes. Results showed the existence of a trade-off among penetration velocity, circumnutation period, and amplitude toward an energy consumption optimization, expressed by the lead angle of the helical path that should stay in the range between 46° and 65°. Moreover, circumnutations with appropriate amplitude (~10°) and period (~80 s) values were more efficient than straight penetration also at different probe tip dimensions, up to a threshold diameter (from 2 mm to 55 mm). Based on the obtained results, we speculated that circumnutations can represent a strategy used by plant roots to reduce the pressure and energy needed to penetrate soil. The translation of this biological feature in robotic systems will allow improving their energetic efficiency in digging tasks, and thus open new scenarios for use in search and rescue, environmental monitoring, and soil exploration.

An emerging challenge in soft robotics research is to reveal mechanical solicitations in a soft body. Nature provides amazing clues to develop unconventional components that are capable of compliant interactions with the environment and living beings, avoiding mechanical and algorithmic complexity of robotic design. We inspire from plant-root mechanoperception and develop a strategy able to reveal bending and applied force in a soft body with only two sensing elements of the same kind, and a null computational effort. The stretching processes that lead to opposite tissue deformations on the two sides of the root wall are emulated with two tactile sensing elements, made of soft and stretchable materials, which conform to reversible changes in the shape of the body they are built in and follow its deformations. Comparing the two sensory responses, we can discriminate the concave and the convex side of the bent body. Hence, we propose a new strategy to reveal in a soft body the maximum bending angle (or the maximum deflection) and the externally applied force according to the body's mechanical configuration.

Moving in an unstructured environment such as soil requires approaches that are constrained by the physics of this complex medium and can ensure energy efficiency and minimize friction while exploring and searching. Among living organisms, plants are the most efficient at soil exploration, and their roots show remarkable abilities that can be exploited in artificial systems. Energy efficiency and friction reduction are assured by a growth process wherein new cells are added at the root apex by mitosis while mature cells of the root remain stationary and in contact with the soil. We propose a new concept of root-like growing robots that is inspired by these plant root features. The device penetrates soil and develops its own structure using an additive layering technique: each layer of new material is deposited adjacent to the tip of the device. This deposition produces both a motive force at the tip and a hollow tubular structure that extends to the surface of the soil and is strongly anchored to the soil. The addition of material at the tip area facilitates soil penetration by omitting peripheral friction and thus decreasing the energy consumption down to 70% comparing with penetration by pushing into the soil from the base of the penetration system. The tubular structure provides a path for delivering materials and energy to the tip of the system and for collecting information for exploratory tasks.

Interactions between individuals that are guided by simple rules can generate swarming behavior. Swarming behavior has been observed in many groups of organisms, including humans, and recent research has revealed that plants also demonstrate social behavior based on mutual interaction with other individuals. However, this behavior has not previously been analyzed in the context of swarming. Here, we show that roots can be influenced by their neighbors to induce a tendency to align the directions of their growth. In the apparently noisy patterns formed by growing roots, episodic alignments are observed as the roots grow close to each other. These events are incompatible with the statistics of purely random growth. We present experimental results and a theoretical model that describes the growth of maize roots in terms of swarming.