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1. Variational problems for tree roots and branches

   https://doi.org/10.1007/s00526-019-1666-1  

   Bressan, Alberto; Palladino, Michele; Sun, Qing (November 2019, Calculus of variations and partial differential equations)

   This paper studies two classes of variational problems introduced in Bressan and Sun (On the optimal shape of tree roots and branches. arXiv:1803.01042), related to the optimal shapes of tree roots and branches. Given a measure μ describing the distribution of leaves, a sunlight functional S(μ) computes the total amount of light captured by the leaves. For a measure μ describing the distribution of root hair cells, a harvest functional H(μ) computes the total amount of water and nutrients gathered by the roots. In both cases, we seek a measure μ that maximizes these functionals subject to a ramified transportation cost, for transporting nutrients from the roots to the trunk or from the trunk to the leaves. Compared with Bressan and Sun, here we do not impose any a priori bound on the total mass of the optimal measure μ, and more careful a priori estimates are thus required. In the unconstrained optimization problem for branches, we prove that an optimal measure exists, with bounded support and bounded total mass. In the unconstrained problem for tree roots, we prove that an optimal measure exists, with bounded support but possibly unbounded total mass. The last section of the paper analyzes how the size of the optimal tree depends on the parameters defining the various functionals. 

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2. On the optimal shape of tree roots and branches

   https://doi.org/10.1142/S0218202518500604  

   Bressan, Alberto; Sun, Qing (December 2018, Mathematical Models and Methods in Applied Sciences)

   null (Ed.)

   This paper introduces two classes of variational problems, determining optimal shapes for tree roots and branches. Given a measure [Formula: see text], describing the distribution of leaves, we introduce a sunlight functional [Formula: see text] computing the total amount of light captured by the leaves. On the other hand, given a measure [Formula: see text] describing the distribution of root hair cells, we consider a harvest functional [Formula: see text] computing the total amount of water and nutrients gathered by the roots. In both cases, we seek to maximize these functionals subject to a ramified transportation cost, for transporting nutrients from the roots to the trunk and from the trunk to the leaves. The main results establish various properties of these functionals, and the existence of optimal distributions. In particular, we prove the upper semicontinuity of [Formula: see text] and [Formula: see text], together with a priori estimates on the support of optimal distributions. 

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3. A Tip Mount for Transporting Sensors and Tools using Soft Growing Robots

   https://doi.org/10.1109/IROS45743.2020.9340950  

   Jeong, Sang-Goo; Coad, Margaret M.; Blumenschein, Laura H.; Luo, Ming; Mehmood, Usman; Kim, Ji Hun; Okamura, Allison M.; Ryu, Jee-Hwan (October 2020, IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS))

   null (Ed.)

   Pneumatically operated soft growing robots that extend via tip eversion are well-suited for navigation in confined spaces. Adding the ability to interact with the environment using sensors and tools attached to the robot tip would greatly enhance the usefulness of these robots for exploration in the field. However, because the material at the tip of the robot body continually changes as the robot grows and retracts, it is challenging to keep sensors and tools attached to the robot tip during actuation and environment interaction. In this paper, we analyze previous designs for mounting to the tip of soft growing robots, and we present a novel device that successfully remains attached to the robot tip while providing a mounting point for sensors and tools. Our tip mount incorporates and builds on our previous work on a device to retract the robot without undesired buckling of its body. Using our tip mount, we demonstrate two new soft growing robot capabilities: (1) pulling on the environment while retracting, and (2) retrieving and delivering objects. Finally, we discuss the limitations of our design and opportunities for improvement in future soft growing robot tip mounts. 

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4. On a Possible Mechanism of Reactivation of Decayed Branches of Negative Stepped Leaders

   https://doi.org/10.1029/2020JD033305  

   Ding, Z.; Rakov, V. A.; Zhu, Y.; Tran, M. D. (December 2020, Journal of Geophysical Research: Atmospheres)

   Abstract Using visible‐range and infrared (3–5 μm) high‐speed video cameras, we observed luminosity transients that reilluminated decayed branches of two close (2 to 4 km) negative stepped leaders in Florida. Leader branches were energized via stepping at their tips and, as a result, were most heated near their lower ends, with the hotter sections being connected via cooler sections to the trunk. In the modeling of lightning leaders, usually a single tip is considered. In contrast, in the present study, many (up to 30 per major branch) tips were active at the same time, forming a network‐like structure with a descending multitip “ionization front” whose transverse dimensions were of the order of hundreds of meters. The front exhibited alternating stepping, with each step necessarily generating a positive charge wave traveling from the leader tip up along the channel, like a mini return stroke. We inferred that the step‐related waves can cause luminosity transients in the remnants of decayed negative branches at higher altitudes. Such reactivated branches, in turn, may facilitate further leader stepping at lower altitudes, as first reported by Stolzenburg et al. (2015,https://doi.org/10.1002/2014JD022933). The reactivation process is likely to involve multiple steps, as evidenced by a large number of active tips (some tens per 50‐μs frame) and corresponding electric field pulses occurring at time intervals of 2 μs or less. Additionally, our observations suggest that a transient in one decayed branch can trigger (or assist with triggering of) a transient in another branch. 

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5. Automatic Control of a Soft Trunk Robot Actuated by Strings

   Trivisonno, Jacob; Amaral, Cameron; Garofalo, Leonardo; Chen, Xiaotian; Jandaghi, Emadodin; Yuan, Chengzhi (September 2022, IEEE MIT Undergraduate Research Technology Conference)

   A soft robot is a robot made of soft materials and is capable of doing complex tasks. The soft robot that was created in this experiment is a soft trunk robot actuated by strings. The purpose of this robot is to be able to move around small spaces easily and be able to perform complex tasks. For example, positioning a tip mounted sensor to gather data. From the results in the experiment, the robot can move to a target position when given a set of coordinates by using a P-controller. 

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